## Colloquium Series

**Spring 2024 Speakers**

**Speaker: **Cheng-Yao Lin, School of Education, SIUC**Title: **Ten Different Ways to Answer Why A Negative Times A Negative Is A Positive**Date: ** 2-22-24**Time: **3:00-4:00 pm **Place:** Neckers 156**Abstract: ** Why a negative times another negative is always equal to a positive answer? This is one of the most commonly asked questions in mathematics classes in middle and high school. In this session we will discuss ten different ways to answer why a negative times a negative is a positive. We will use some real–world examples to explain this concept.

Speaker's Website: https://academics.siu.edu/education/elementary-education/faculty/lin-cheng-yao.php

**Speaker: **Jurek "Jerzy" Kocik, SIUC**Title: **Metamorphic Life of Circles: Unexpected Connections**Date: ** 2-15-24**Time: **3:00-4:00 pm **Place:** Neckers 156**Abstract: ** In mathematical physics, spinors bring insight into the inner structure of matter. Quite similarly, the spinors of (2+1)-dimensional Minkowski space provide a fresh look at Apollonian disk packings and provide novel results including a parametrization of the integral packings, a fractal visualization of the Apollonian depth function, an alternative derivation of the Descartes' configuration, and more. On the other hand, Apollonian disk packing may be interpreted as a “space-time crystal”. These two seemingly different representations meet strikingly.

Speaker's Website: http://lagrange.math.siu.edu/Kocik/jkocik.htm

**Fall 2023 Speakers**

**Speaker: **Alejandra Alvarado, Eastern Illinois University**Title: **Arithmetic Progressions on Curves**Date: ** 11-16-23**Time: **3:00-4:00 pm **Place:** Neckers 156**Abstract: ** The study of arithmetic progressions has been around for centuries. But the study of arithmetic progressions on curves is more recent. In particular, what is the longest arithmetic progression on elliptic curves? We give a survey of some results.

Speaker's Website: https://www.eiu.edu/math/personnel.php?id=aalvarado2

**Speaker: **Karol Koziol, Baruch College, CUNY**Title: **An introduction to the mod p Langlands Program**Date: ** 10-26-23**Time: **3:00-4:00 pm **Place:** Neckers 156**Abstract: ** One of the crowning achievements of 20th century mathematics is Class Field Theory, which has its origins in Gauss' Law of Quadratic Reciprocity, and which (among other things) gives a description of all abelian field extensions of the rational numbers. This turns out to be the beginning of the Langlands Program, a wide-ranging web of conjectures that connects the areas of Number Theory, Representation Theory, and Algebraic Geometry. I'll give an introduction to this circle of ideas, and discuss a fairly recent development: the mod p, "local" version of these conjectures. I'll also indicate how this variant can be used to shed light on some questions arising from geometry.

Speaker's Website: https://karolkoziol.github.io

**Speaker: **Ali Mehrabani, SIUC School of Analytics, Finance and Economics**Title: **Estimation and Identification of Latent Group Structures in Panel Data with Interactive Fixed Effects**Date: ** 10-5-23**Time: **3:00-4:00 pm **Place:** Neckers 156**Abstract: ** This paper provides a framework for joint estimation and identification of latent group structures in panel data models with interactive fixed effects using a pairwise fusion penalized approach. The latent structure of the model allows individuals to be classified into different groups where the number of groups and the group membership are unknown. A penalized principal component (PPC) estimation procedure is introduced to detect the latent group structure. To implement the proposed approach, an alternating direction method of multipliers algorithm has been developed. The proposed method is further illustrated by simulation studies and an empirical application of economic growth which demonstrate the performance of the method.

Speaker's Website: https://academics.siu.edu/business/economics/faculty/mehrabani-ali.php

**Speaker: **Mohamad Kazem Shirani Faradonbeh, Southern Methodist University**Title: **Learning from Multiple Multivariate Time-Series**Date: ** 9-28-23**Time: **3:00-4:00 pm **Place:** Neckers 156**Abstract: **Autoregressive models are among the most popular ones for analyzing temporally dependent data. However, little is known about learning from multiple time-series trajectories, especially when it comes to multi-dimensional and non-stationary data. We study this problem and propose a joint estimation method for learning transition matrices of multiple vector autoregressive models that are unknown linear combinations of some unknown basis matrices. The setting is technically challenging due to high dimensionality of the parameter space as well as the compound nature of the uncertainty. Still, our theoretical analysis shows that the proposed joint estimator has an optimal sample-complexity and excels individual learning methods. Furthermore, applications to data-driven stabilization of dynamical systems through exogenously designed input experiments will be discussed.

Speaker's Website: https://www.smu.edu/Dedman/Academics/Departments/Math/People/Faculty/MohamadFaradonbeh

**Speaker: **Jun Liu, SIU Edwardsville**Title: **Direct Parallel-in-Time Solvers and Backward Heat Conduction Problem**Date: ** 9-7-23**Time: **3:00-4:00 pm **Place:** Neckers 156**Abstract: **In this talk, I will first briefly introduce some parallel in time (PinT) algorithms, including the widely used parareal algorithm and the diagonalization-based algorithms. I will then present our new well-conditioned direct PinT solvers, which show promising parallel efficiency for solving time-dependent differential equations (ODEs and PDEs). As an application, I will show how PinT algorithms can be applied to inverse PDE problems. Within the framework of quasi-boundary value method (QBVM), we designed a direct PinT solver for the ill-posed Backward Heat Conduction Problem. The novel idea is to maneuver the flexibility of regularization for better structured systems that enable fast diagonalization. The high efficiency of the proposed PinT algorithms is illustrated by numerical examples.

Speaker's Website: http://www.siue.edu/~juliu

**Spring 2023 Speakers**

**Speaker: **Ravindra Girivaru, University of Missouri-St. Louis**Title: **Matrix Factorizations of Polynomials**Date: ** 4-27-23**Time: **3:00-4:00 pm **Place:** Neckers 156**Abstract: **A matrix factorization of a polynomial F is a pair of (square) matrices (A, B) such that their product is F times the identity matrix. After spending some time on preliminaries, I will explain what is known about this question, and what its relevance is to the geometry of the set of zeroes of the polynomial F. I will also talk about its connection to the problem of determining the minimum number of polynomials required to define curves in three dimensional space and analogous questions. This talk should be accessible to undergraduates in the department.

Speaker's Website: https://www.umsl.edu/mpas/faculty/math/girivaru.html

**Speaker: **Natasha Dobrinen, University of Notre Dame**Title: **Ramsey theory on binary relational homogeneous structures**Date: ** 4-6-23**Time: **3:00-4:00 pm **Place:** Neckers 156**Abstract: **Generalizations of Ramsey's Theorem to colorings of infinite sets proceed via topological considerations. The Galvin-Prikry Theorem states that Borel subsets of the Baire space are Ramsey. Silver extended this to analytic sets, and Ellentuck gave a topological characterization of Ramsey sets in terms of the property of Baire in the Vietoris topology. We present work extending these theorems to several classes of countable homogeneous structures, answering a question of Kechris, Pestov, and Todorcevic. An obstruction to exact analogues of Galvin-Prikry or Ellentuck is the presence of big Ramsey degrees. We will discuss how different properties of the structures affect which analogues have been proved. Presented is work of the speaker for SDAP+ structures, and joint work with Zucker for binary finitely constrained FAP classes. A feature of the work with Zucker is showing that we can weaken one of Todorcevic's four axioms guaranteeing a Ramsey space, and still achieve the same conclusion. These axioms are built on prior work of Carlson and Simpson developing topological Ramsey space theory.

Speaker's Website: https://sites.google.com/site/kchoiy/colloquium/dobrinen

**Speaker: **Yu Jin, Southern Illinois University Carbondale

**Title:**Actuary Profession: A Career in Analyzing Risks and Managing Uncertainty

**Date:**3-2-23

**Time:**3:00-4:00 pm

**Place:**Neckers 156

**Abstract:**Actuaries are professionals who use mathematical models to analyze and quantify financial risks, particularly in the areas of insurance, pension plans, and investments. With the growing complexity of modern business, the demand for actuaries is steadily increasing, as they help organizations manage and mitigate financial risks, and make strategic decisions based on data-driven insights.

This presentation will provide an overview of the actuary profession, including the key skills required, the education and certification requirements, and the typical career path for aspiring actuaries. We will explore the various fields in which actuaries work, such as life and health insurance, property and casualty insurance, consulting, and government. We will also discuss the challenges and opportunities facing the actuarial profession in today's rapidly changing business environment, and the importance of staying current with emerging trends and technologies.

The presentation will conclude with a discussion of the rewards and benefits of pursuing a career as an actuary, including job security, high earning potential, and the opportunity to make a meaningful impact on society. Whether you are a student exploring career options or a professional looking to transition into a new field, this presentation will provide valuable insights into the actuary profession and its role in managing risks and uncertainties in today's economy.

Speaker's Website: https://math.siu.edu/faculty-staff/grad-stud/phd-stud/jin.php

**In Person Colloquium**

**Speaker: **Bhaskar Bhattacharya, Southern Illinois University Carbondale**Title: **Effect of misspecification of dependence in constrained statistical inference **Date: ** 2-23-23**Time: **3:00-4:00 pm **Place:** Neckers 156**Abstract: **The assumption of independent observations that underlies many statistical procedures is called into question when analyzing complex survey data. In clustered data, for example, two-stage samples exhibit positive intra-cluster correlation. Wu, et. al. (1988) showed that ignoring such correlations leads to serious consequences such as much larger variances of the estimates of regression coefficients and inflated type I error rates of the corresponding F-statistic. Misspecification of dependence in observations can happen in a more general setup beyond clustered data. We investigate how to adjust the conventional statistical inference in presence of inequalities when dependent samples are taken from the normal distribution. We extend the study to hypotheses testing in a constrained regression model. We analyze Covid data from 2020 to investigate the presence of trend using the procedure developed.

Speaker's Website: https://math.siu.edu/faculty-staff/faculty/bhattacharya.php

**In Person Colloquium**

**Speaker: **Lindsey-Kay Lauderdale, Southern Illinois University Carbondale**Title: **On a New variant: The Action-Genus of a Finite Group**Date: ** 2-9-23**Time: **3:00-4:00 pm **Place:** Neckers 156**Abstract: **In this talk, we will define a new invariant for finite groups, called the action-genus. Let G be a finite group. Among all graphs Γ whose automorphism group is isomorphic to G, define the *action-genus* of G to be the minimal genus of a closed connected orientable surface on which Γ can be cellularly embedded. Here, we will elucidate some basic properties for the action-genus of a finite group, establish the action-genus of a few infinite families of finite groups, and then conclude with some open questions about the action-genus of finite groups in general.

Speaker's Website: https://math.siu.edu/faculty-staff/faculty/lauderdale.php

**Fall 2022 Speakers**

**In Person Colloquium**

**Speaker: **Steven Senger, Missouri State University**Title: **Using graph theory, additive number theory, and geometric measure theory to study finite point configurations**Date: ** 11-10-22**Time: **3:00-4:00 pm **Place:** Neckers 156**Abstract: **In 1946 Paul Erdős asked for asymptotic estimates on how often a single distance could occur in a large finite point set in the plane. We discuss this and related problems, touching on methods from graph theory, additive number theory, and geometric measure theory. We will also look at a variety of settings, from discrete point sets and fractals in Euclidean space, to vector spaces over finite fields, and other algebraic settings.

Speaker's Website: math.missouristate.edu/profile-display.aspx?p=StevenSenger

**In Person Colloquium**

**Speaker: **Wesley Calvert, SIU**Title: **Almost-sure Computable Structure Theory**Date: ** 10-13-22**Time: **3:00-4:00 pm **Place:** Neckers 156**Abstract: **Novikov and Boone independently proved that there are finitely presented groups in which there is no algorithm to decide whether a word in the generators is equal to the identity. More recent work, though, has shown that in many of these cases, there is an algorithm that will decide this question for almost all words.

It is possible to generalize this analysis for other kinds of structures. The existence of structures where the basic properties are or are not computable, or where structures are classically isomorphic, but not isomorphic by a computable function, are well known. The present talk will describe recent joint work with Cenzer and Harizanov to explain what happens if we only ask the algorithm to be right almost always

Speaker's Website: http://lagrange.math.siu.edu/Calvert/

**In Person Colloquium**

**Speaker: **Benjamin Hutz, St. Louis University**Title: **Automorphism Groups for Arithmetic Dynamical Systems** ****Date: ** 9-29-22**Time: **3:00-4:00 pm **Place:** Neckers 156**Abstract: **Algebraic dynamics is the study of iteration of polynomial or rational functions. This talk focuses on endomorphisms of projective space with non-trivial automorphisms. Under the action of conjugation by the projective general linear group, we can form a moduli space of dynamical systems of a certain degree. Certain elements in these moduli spaces have non-trivial automorphisms. This is analogous to the elliptic curves with complex multiplication in the moduli space of elliptic curves. These special maps have connections to many problems in arithmetic dynamics. We focus on two problems: identifying the locus of maps with non-trivial automorphisms and the realizability of subgroups of the projective linear group as automorphism groups.

Speaker's Website: https://mathstat.slu.edu/people/hutz

**In Person Colloquium**

**Speaker: ** Mathew Gluck, Assistant Professor, Southern Illinois University**Title: **Infinitely Many Sign-Changing Solutions To A Conformally Invariant Integral Equation**Date: ** 9-22-22**Time: **3:00-4:00 pm **Place:** Neckers 156**Abstract: **The classical Sobolev inequality asserts the existence of a positive lower bound for the Sobolev quotient Q(u) as u varies through a suitable class of functions. The analysis of the Sobolev quotient has a variety of applications in both pure and applied mathematics. Of particular importance is the extremal problem for Q which seeks to determine both the minimal value of Q and the functions u for which the minimal value is attained. If one is interested in understanding the minimizers of Q, one is naturally led to analyze the Euler-Lagrange equation Q′(u) = 0. A simple computation shows that up multiplication by −1, the minimizers of Q must be strictly positive. Moreover, the classical results of Gidas, Ni, Nirenberg and Cafarelli, Gidas, Spruck specify the form of all positive solutions to the Euler-Lagrange equation (and hence also the minimizers of Q). This classification result inspired many attempts to show that any solution to the Euler-Lagrange equation that is positive somewhere must be of the same form as the minimizers of the Sobolev quotient. An influential result of Ding showed that these attempts were destined to fail.

In this talk I will discuss some recent work of mine that is inspired by Ding’s result. In short, my work establishes a result similar in spirit to that of Ding, but for the Hardy-Littlewood-Sobolev functional, a functional that can be viewed as a dual functional to the Sobolev quotient. To contextualize my work, I will overview the history and applications of the study of the critical points of Q. In addition, I will discuss both the underlying idea behind Ding’s argument and a variety of extensions of Ding’s result based on this idea.

Speaker's Website: https://math.siu.edu/faculty-staff/faculty/gluck.php

**Spring 2022 Speakers**

**Virtual Colloquium **

**Speaker: ** Bing Li, Verne M. Willaman Professor of Statistics, Pennsylvania State University**Title: Functional Directed Acyclic Graphs **by Kuang-Yao Lee, Lexin Li, and Bing Li**Date: ** 4-28-22**Time: **3:00-4:00 pm **Place:** Zoom**Abstract: **We introduce a new method to estimate directed acyclic graphs from multi-variate functional data, based on the notion of faithfulness that relates a directed acyclic graph with a set of conditional independence relations among the random functions. To characterize and evaluate these relations, we propose two linear op-erators, the conditional covariance operator and the partial correlation operator. Based on these operators, we adapt and extend the PC-algorithm to estimate the functional directed graph, so that the computation time depends on the sparsity rather than the full size of the graph. We study the asymptotic properties of the two operators, derive their uniform convergence rates, and establish the uniform consistency of the estimated graph, all of which are obtained while allowing the graph size to diverge to infinity with the sample size. We demonstrate the efficacy of our method through both simulations and an application to a time-course proteomic dataset.

Speaker's Website: https://science.psu.edu/stat/people/bxl9

**Virtual Colloquium **

**Speaker: ** Prof. George Michailidis, University of Florida **Title: A Bayesian Subset Specific Approach to Joint Selection of Multiple Graphical Models**

**Date:**4-21-22

**Time:**3:00-4:00 pm

**Place:**Zoom

**Abstract:**The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience and the social sciences. This work develops a Bayesian approach that decomposes the model parameters across the multiple graphical models into shared components across subsets of models and edges, and idiosyncratic ones. Further, it leverages a novel multivariate prior distribution, coupled with a jointly convex regression based pseudo-likelihood that enables fast computations through a robust and efficient Gibbs sampling scheme. We establish strong posterior consistency for model selection under high dimensional scaling where the number of variables growing exponentially with the sample size. The efficacy of the proposed approach in borrowing strength across models to identify jointly shared edges is illustrated on both synthetic and real data.

Speaker's Website: https://informatics.research.ufl.edu/homepage-2/about-us/michailidis.html

**Virtual Colloquium **

**Speaker: ** Dr. Xianyang Zhang, Texas A&M University **Title: Kernel Two-sample Metrics in High-dimension ****Date: ** 4-14-22**Time: **3:00-4:00 pm **Place:** Zoom**Abstract: **Motivated by the increasing use of kernel-based metrics for high-dimensional and large-scale data, we study the asymptotic behavior of kernel two-sample tests when the dimension and sample sizes both diverge to infinity. We focus on the maximum mean discrepancy (MMD), including MMD with the Gaussian kernel and the Laplace kernel, and the energy distance as special cases. We derive asymptotic expansions of the kernel two-sample statistics, based on which we establish the central limit theorem (CLT) under both the null hypothesis and the local and fixed alternatives. The new non-null CLT results allow us to perform asymptotic exact power analysis, which reveals a delicate interplay between the moment discrepancy that can be detected by the kernel two-sample tests and the dimension-and-sample orders. The asymptotic theory is further corroborated through numerical studies.

Speaker's Website: https://zhangxiany-tamu.github.io

**Virtual Colloquium **

**Speaker: ** Dr. Mehdi Maadooliat, Marquette University**Title: Functional Singular Spectrum Analysis****Date: ** 03-31-2022**Time: **3:00-4:00 pm **Place:** Zoom**Abstract: **In this talk, we introduce a new extension of the Singular Spectrum Analysis (SSA) called functional SSA to analyze functional time series. The new methodology is developed by integrating ideas from functional data analysis and univariate SSA. We explore the advantages of the functional SSA in terms of simulation results and two real data applications. We compare the proposed approach with Multivariate SSA (MSSA) and dynamic Functional Principal Component Analysis (dFPCA). The results suggest that further improvement to MSSA is possible, and the new method provides an attractive alternative to the dFPCA approach that is used for analyzing correlated functions. We implement the proposed technique to an application of remote sensing data and a call center dataset. We have also developed an efficient and user-friendly R package and a shiny web application to allow interactive exploration of the results.

Speaker's Website: https://www.mssc.mu.edu/~mehdi/

**Virtual Colloquium **

**Speaker: ** Dr. Sumanta Basu, Cornell University**Title: Learning Financial Networks with Graphical Models of Time Series Data****Date: ** 03-24-2022**Time: **3:00-4:00 pm **Place:** Zoom**Abstract: **After the 2007-09 financial crisis, there has been a growing interest in measuring systemic risk, broadly defined as the risk of widespread failure of the entire financial system. In a highly interlinked financial market, a large body of recent works have proposed to use network connectivity amongst financial institutions to assess their systemic importance. In this work, we will present some graphical modeling techniques for learning interactions among the components of a large dynamic system from multivariate time series data, where the core idea is to learn from lead-lag relationships (commonly known as Granger causality) between time series in addition to their co-movements. In the context of modeling networks of interactions amongst financial institutions and measuring systemic risk, we will demonstrate how linear and quantile-based Granger causality analyses using vector autoregressive (VAR) models can provide insight. We will present some non-asymptotic statistical theory for our proposed algorithms, estimate these graphical models using stock returns of large financial institutions in the U.S. and India, and demonstrate their usefulness in detecting systemically risky periods and institutions.

Speaker's Website: https://faculty.bscb.cornell.edu/~basu/

**Virtual Colloquium **

**Speaker: ** Youssef Raffoul, University of Dayton**Title: Introduction to Time Scales with Applications to Dynamic Equations****Date: ** 03-17-2022**Time: **3:00-4:00 pm **Place:** Zoom**Abstract: **The study of dynamic equations on time scales, which goes back to its founder Stefan Hilger (1988), is an area of mathematics that has recently received a lot of attention. It has been created in order to unify the study of differential and difference equations. In this talk, we give a brief introduction to the Calculus Time Scales and then use Lyapunov functions to qualitatively analyze the behavior of solutions of nonlinear **dynamic equations. **

Speaker's Website: https://udayton.edu/directory/artssciences/mathematics/raffoul_youssef.php

**Virtual Colloquium **

**Speaker: ** Dr. Anru Zhang, Duke University**Title: Statistical Learning for High-dimensional Tensor Data****Date: ** 03-03-2022**Time: **3:00-4:00 pm **Place:** Zoom**Abstract: **The analysis of tensor data has become an active research topic in statistics and data science recently. Many high order datasets arising from a wide range of modern applications, such as genomics, material science, and neuroimaging analysis, requires modeling with high-dimensional tensors. In addition, tensor methods provide unique perspectives and solutions to many high-dimensional problems where the observations are not necessarily tensors. High-dimensional tensor problems generally possess distinct characteristics that pose unprecedented challenges; there is a clear need to develop novel methods, algorithms, and theory for them.

In this talk, we discuss some recent advances in high-dimensional tensor data analysis through several fundamental topics and their applications in microscopy imaging and neuroimaging. We will also illustrate how we develop new methods and theories that exploit information from high-dimensional tensor data based on the modern theory of computation, non-convex optimization, applied linear algebra, and high-dimensional statistics.

Speaker's Website: https://anruzhang.github.io/

**Virtual Colloquium **

**Speaker: ** Dr. Liliana Forzani, Universidad Nacional del Litoral**Title: Saving dimensions: less data, same information****Date: ** 02-24-2022**Time: **3:00-4:00 pm **Place:** Zoom**Abstract:** Today, almost every action we take generates data: mobile communications, participation in social networks, web searches, business transactions, physical activity or sleep monitoring, clinical tests… the list is long and growing rapidly.What information can be extracted from this data? Can we use it to predict behaviors or other variables? The key to integrating so many sources of information is often to find smaller underlying structures to be analyzed, without losing relevant information.Mathematical statistics tries to give a rigorous answer by appealing to the concept of sufficiency. In this talk we will give an introduction to the topic, we will briefly review the recent contributions and we will discuss some of the problems that still remain to be solved.

Speaker's Website: https://sites.google.com/site/lilianaforzani/english

**Virtual Colloquium **

**Speaker: ** Professor R. Dennis Cook, School of Statistics, University of Minnesota**Title: ****Partial Least Squares Regression: What we learned in the past decade.****Date: ** 02-17-2022**Time: **3:00-4:00 pm **Place:** Zoom**Abstract:** Partial least squares (PLS) regression, which has been around for about four decades, is a dimension-reduction algorithm for fitting linear regression models without requiring that the sample size be larger than the number of predictors. It was developed primarily by the Chemometrics community where it is now ingrained as a core method, and it is apparently used throughout the applied sciences.

And yet it seems fair to conclude that PLS regression has not been embraced by the Statistics community, even as a serviceable method that might be useful occasionally. Nor does there seem to be a common understanding as to why this rather enigmatic method should not be used.

This talk is intended as an appraisal of PLS regression from a statistical perspective, with emphasis on what we have learned recently. This will include a little historical context, personal encounters, relationship to envelopes, a few asymptotic results for high-dimensional regressions and its (surprising) serviceability in nonlinear regressions.

Speaker's Website: http://users.stat.umn.edu/~rdcook/

**Virtual Colloquium **

**Speaker: ** Dr. Di Wang, Booth School of Business, University of Chicago**Title: **Robust estimation of high-dimensional vector autoregressive models**Date: ** 02-10-2022**Time: **3:00-4:00 pm **Place:** Zoom**Abstract:** High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series, but also the existence of aberrant observations, such as missing values, contaminated observations, and heavy-tailed distributions. For high-dimensional vector autoregressive (VAR) models, we introduce a unified estimation procedure that is robust to model misspecification, heavy-tailed noise contamination, and conditional heteroscedasticity. The proposed methodology enjoys both statistical optimality and computational efficiency, and can handle many popular high-dimensional models, such as sparse, reduced-rank, banded, and network-structured VAR models. With proper regularization and data truncation, the estimation convergence rates are shown to be nearly optimal under a bounded fourth moment condition. Consistency of the proposed estimators is also established under a relaxed bounded (2 + 2ε)-th moment condition, for some ε ∈ (0, 1), with slower convergence rates associated with ε. The efficacy of the proposed estimation methods is demonstrated by simulation and a real example. This talk is based on the joint work with Ruey S. Tsay.**Speaker's Website:** https://sites.google.com/site/statdiwang/

**Virtual Colloquium **

**Speaker: ** Dr. Zihau Su, University of Florida**Title: **Envelope model for function-on-function linear regression**Date: ** 01-27-2022**Time: **3:00-4:00 pm **Place:** Zoom**Abstract:** The envelope model is a recently developed methodology for multivariate analysis that enhances estimation accuracy by exploiting the relation between the mean and eigenstructure of the covariance matrix. We extend the envelope model to function-on-function linear regression, where the response and the predictor are assumed to be Gaussian random functions in Hilbert spaces. We use a double envelope structure to accommodate the eigenstructures of the covariance operators for both the predictor and the response. The central idea is to establish a one-to-one relation between the functional envelope model and the multivariate envelope model and estimate the latter by existing method. We also developed the asymptotic theories, confidence and prediction bands, an order determination method along with its consistency, and a characterization of the efficiency gain by the proposed model. Simulation comparisons with the standard function-on-function regression and data applications show significant improvement by our method in terms of cross-validated prediction error.**Speaker's Website:** http://archived.stat.ufl.edu/personnel/usrpages/su.html

**Fall 2021 Speakers**

**Virtual Colloquium **

**Speaker: **Dr. Kim Klinger-Logan, Rutgers University and Kansas State University**Title: **Two applications of solutions to differential equations in automorphic forms**Date: ** 11-18-2021**Time: **3:00-4:00 pm **Place:** Zoom**Abstract:** Automorphic forms were first studied in the context of number theory. Among their many interesting features, they give rise to $L$-functions (functions with similar properties to the Riemann zeta function). We will discuss the use of spectral theory of automorphic forms to solve differential equations and discuss two applications of such solutions. The first application may shed light on the location of zeros of $L$-functions. The equation in question arises from mistake that allowed for zeros of the Riemann zeta function to appear as eigenvalues for the $SL_2(\mathbb{R})$ - invariant Laplace-Beltrami operator on the Poincare upper half plane and has been studied by Bombieri and Garrett. The second application provides makes steps towards a quantum correction in the discrepancy between general relativity and empirical data. Specifically, Green, Russo and Vanhove discovered that the low energy expansion of scattering amplitude for gravitons (hypothetical particles of gravity represented by massless string states) has coefficients which satisfy differential equations in automorphic forms. We will discuss how spectral theory of automorphic forms can be used in both of these contexts.**Speaker's Website: **https://sites.google.com/view/kklingerlogan/home

**Virtual Colloquium **

**Speaker: **Roshini Gallage, SMSS, Southern Illinois University Carbondale**Title: **Numerical Approximation of Nonlinear Stochastic Differential Equations with Continuously Distributed Delay**Date: ** 11-4-2021**Time: **3:00-4:00 pm **Place:** Zoom**Abstract:** Stochastic delay differential equations (SDDEs) are systems of differential equations with a time lag in a noisy or random environment. Much research has been done using discrete delay where the dynamics of a process at time t depend on the state of the process in the past after a single fixed time lag \tau. We are researching processes with continuously distributed delay which depend on weighted averages of past states over the entire time lag interval [t-\tau, t]. We show the existence of a unique solution of certain nonlinear SDDEs with continuously distributed delay under local Lipschitz and generalized Khasminskii-type conditions. Further, we show that Euler-Maruyama numerical approximations of such nonlinear SDDEs converge in probability to their exact solutions. Joint work with Dr. Harry Randolph Hughes.

**Virtual Colloquium **

**Speaker: **Dr. Layla Sorkatti, University of Khartoum and Al-Neelain University**Title: **Nilpotent Symplectic Alternating Algebras**Date: ** 10-21-2021**Time: **3:00-4:00 pm **Place:** Zoom**Abstract:** Let F be a field. A Symplectic alternating algebra over F is a triple (V, ( , ), · ) where V is a symplectic vector space over F with respect to a non-degenerate alternating form ( , ) and · is an alternating bilinear and binary operation on V such that the law (u · v, w) = (v · w, u) holds. These algebraic structures have arisen from the study of 2-Engel groups but seem also to be of interest in their own right with many beautiful properties. We will give an overview with a focus on some recent work on the structure of nilpotent symplectic alternating algebras.

**Virtual Colloquium **

**Speaker: **Dr.** **Tian An Wong, University of Michigan-Dearborn**Title: **Prehomogeneous vector spaces and the Arthur-Selberg trace formula**Date: ** 10-14-2021**Time: **3:00-4:00 pm **Place:** Zoom**Speaker’s Website: **https://umdearborn.edu/users/tiananw**Abstract:** The Arthur-Selberg trace formula is a central tool in the theory of automorphic forms, and can be viewed as a nonabelian Poisson summation formula. Prehomogeneous vector spaces on the other hand, are arithmetic objects from which certain zeta functions can be defined. In this talk, I will give a gentle introduction to these ideas, then discuss an application of the theory of prehomogeneous vector spaces to the development of the trace formula, following earlier work of W. Hoffmann and P. Chaudouard.

**Virtual Colloquium**

**Speaker: **Dr. Henry Segerman, Oklahoma State University**Title: **Artistic Mathematics: Truth and Beauty

**10-07-2021**

Date:

Date:

**3:15-4:15 pm**

Time:

Time:

**Place:**Zoom

**https://math.okstate.edu/people/segerman/**

Speaker's Website:

Speaker's Website:

**Abstract:** I'll talk about my work in mathematical visualization: making accurate, effective, and beautiful pictures, models, and experiences of mathematical concepts. I'll discuss what it is that makes a visualization compelling, and show many examples in the medium of 3D printing, as well as some work in virtual reality and spherical video. I'll also discuss my experiences in teaching a project-based class on 3D printing for mathematics students.

**Virtual Colloquium**

**Speaker: **Dr.** **Aditya Potukuchi, University of Illinois Chicago**Title: **Faster algorithms for counting independent sets in regular bipartite graphs

**9-30-2021**

Date:

Date:

**3:00-4:00 pm**

Time:

Time:

**Place:**Zoom

**https://tripods.uic.edu/profiles/potukuchi-aditya/**

Speaker's Website:

Speaker's Website:

**Abstract:** I will present an algorithm that takes as input a d-regular bipartite graph G, runs in time exp(O(n/d log^3 d)), and outputs w.h.p., a (1 + o(1))-approximation to the number of independent sets in G. As a by-product of the intermediate steps to this algorithm, We also obtain, for fixed d, an FPTAS to approximate the number of independent sets in d-regular bipartite ``expanding'' graphs. More than the result itself, I wil focus more on the techniques used, which combines combinatorial methods (graph containers) with statistical physics methods (abstract polymer models and cluster expansion), and mention other recent applications. I will start from the basics, and no prior knowledge of any of the topics is assumed.

Joint work with Matthew Jenssen and Will Perkins.

**Virtual Colloquium**

**Speaker:** Dr. Kwangho Choiy, SMSS, Southern Illinois University Carbondale**Title: **The Principle of Functoriality and Invariants

**9-23-2021**

Date:

Date:

**3:00-4:00 pm**

Time:

Time:

**Place:**Zoom

**https://sites.google.com/site/kchoiy/**

Speaker's Website:

Speaker's Website:

**Abstract: **In the framework of the principle of functoriality programmed by R. Langlands, it is of interest to seek for invariants. We shall focus on an important class of representations, discrete series, and the setting of a connected reductive algebraic group over a $p$-adic field and its closed subgroup having the same derived subgroup. This talk shall uniformize previous relevant results and discuss how to formulate some invariants.

**Spring 2020 Speakers**

**Virtual Colloquium**

**Speaker: **Dr.** **Wesley Calvert, Southern Illinois University Carbondale**Title: **Uniformly Knowing Isomorphisms**Date: **4-30-2020**Time: **3:30-4:30 pm**Speaker's Website: http://lagrange.math.siu.edu/Calvert/**

**Abstract: **Rational vector spaces of a fixed dimension are unique up to isomorphism. Unfortunately, this isomorphism need not be simple. Indeed, there are explicit examples of two countable infinite-dimensional vector spaces over the rationals for which no explicit formula, algorithm, or description gives an isomorphism. Since they are isomorphic, however, there is an oracle relative to which an isomorphism is computable.

In this connection, we consider the following problem: Given any two isomorphic countable structures (e.g. vector spaces, fields, groups, graphs, etc.), compute an isomorphism between them. Mark Nadel proved in 1974 that there is an oracle that can solve this problem, but the classification up to Turing equivalence of all such oracles remains open. In this joint work with Johanna Franklin and Dan Turetsky, we give one characterization of these oracles, and prove something about their diversity.

**Speaker: **Chathurika Athapattu, Mathematics, SIUC**Title: **Parabolically induced Banach space representations of p-adic groups**Time: **3-4:00 pm**Place: **Neckers 156**Speaker's Website: ****https://math.siu.edu/faculty-staff/grad-stud/phd-stud/athapattu.php**

**Abstract: **The Langlands program, introduced by Prof. Robert Langlands (1967), is about the connection between number theory and geometry which is not highly obvious. Then he introduced local Langland conjectures as part of it. There are many different groups over many different fields for which these conjectures can be stated. The one version is p-adic Langlands correspondence. Our research project focuses on developing the theory of the p-adic Banach space representations of reductive algebraic group over non-archimedean local fields. Such representations play a fundamental role in the p-adic Langlands program. More specifically, we study parabolically induced representations. Parabolic induction is a basic tool in representation theory. Our goal is to describe parabolically induced representations in terms of tensor products over Iwasawa modules.

**Fall 2019 Speakers**

**Speaker**: Prof. Wesley Calvert, Mathematics, SIUC**Title**: Mathematical Logic and Probability**Date**: 11-21-19**Time**: 3-4:00 pm**Place**: Neckers 156**Speaker's website**:http://lagrange.math.siu.edu/Calvert/

**Abstract: **In the late 19th and early 20th centuries, logic and probability were frequently treated as closely related disciplines. Each has, in an important sense, gone its own way, so that neither, in its modern form, is in any proper sense a systematization of the ``Laws of Thought,'' as Boole called them.

However, the last four decades have seen a remarkable rapproachment. Algorithmic randomness has become central to computability, machine learning has become deeply entangled with model-theoretic notions of independence, and the study of random combinatorial objects and zero-one laws has arisen as a major area in neostability.

The present talk will survey some parts of the new nexus of probability and logic, along with some open questions.

**Speaker**: Prof. Greg Budzban, Dean, College of Arts and Sciences, SIUE**Title: **Convergence conditions for non-homogeneous Markov chains via random walks on groups and semigroups**Date**: 11-7-19**Time**: 3-4:00 pm**Place**: Neckers 156**Speaker's website**:https://www.siue.edu/arts-and-sciences/about/

**Abstract: **Probability on algebraic structures provides a set of techniques that can be used to analyze non-homogeneous Markov chains. This talk will discuss the correspondence between the two areas and provide examples of verifiable sufficient conditions, based only on the entries of the transition matrices, for the convergence of a class of non-homogeneous Markov chains. The talk will conclude with a discussion of some open problems in the field.

**Speaker**: Prof. Bogdan Petrenko Department of Mathematics and Computer Science, Eastern Illinois University**Title**: The smallest number of generators and densities of generating sets of an algebra finite over the integers**Date**: 10-10-19**Time**: 3-4:00 pm**Place**: Neckers 156**Speaker's website**:https://www.eiu.edu/math/personnel.php?id=bvpetrenko&subcat=

**Abstract: Let A be a ring whose additive group is free Abelian of finite rank. The topic of this talk is the following question: what is the probability that several random elements of A generate it as a ring? After making this question precise we will see that the answer which can be interpreted as a local-global principle. Some applications will be discussed, for example:1. What is the smallest number of generators of the direct product of 769 copies of the ring of integral 3-by-3 matrices?**

**2. What is the probability that 2 random 3-by-3 matrices generate the ring of integral 3-by-3 matrices?**

This talk will be based on my joint work with Rostyslav Kravchenko (University of Texas at Austin) and Marcin Mazur (Binghamton University).

This talk will be based on my joint work with Rostyslav Kravchenko (University of Texas at Austin) and Marcin Mazur (Binghamton University).

**Speaker**: Lakshika Gunawardana, Mathematics, SIUC**Title**: Locally Primitively Universal forms and the Primitive Counterpart to the Fifteen Theorem**Date**: 9-26-19**Time**: 3-4:00 pm**Place**: Neckers 156**Speaker's website**: https://math.siu.edu/faculty-staff/grad-stud/phd-stud/gunawardana.php

**Abstract**: The systematic study of positive definite integral quadratic forms that represent all positive integers (or all sufficiently large positive integers) was initiated by Ramanujan a little over a century ago. Such forms are now referred to as universal (or almost universal) forms. In a groundbreaking 1917 paper, Ramanujan determined all forms of the type ax^{2} + by^{2} +cz^{2} + du^{2} that are universal, and all those of the special type a(x^{2} + y^{2} + z^{2} ) + du^{2} that are almost universal.**In 1993, J.H. Conway and W.A. Schneeberger presented the Fifteen Theorem, which provides simple criteria to determine whether a positive definite classically integral quadratic form in any number of variables is universal. Later in 2000, M. Bhargava provided a refinement of the Fifteen Theorem and showed that there are exactly 204 positive definite classically integral quaternary quadratic forms, up to equivalence, which are universal. We try to determine which of the forms in the 204 list are primitively universal, and try to determine whether there exists a finite set S of integers such that every positive definite integral quadratic form that primitively represents the integers in S, primitively represents all positive integers. In the first half of this talk, we introduce quadratic forms in general with a brief history and present a conjecture which could be a primitive counterpart to the Fifteen Theorem. Then we review the p-adic numbers and p-adic norm and discuss their application of almost universal quadratic forms, concluding with some new results on almost primitively universal forms.**

** Speaker: Prof. Lingguo Bu, Curriculum and Instruction, SIUCTitle: 3D Design & Printing for Mathematics EducationDate: 9-12-19Time: 3-4:00 pmPlace: Neckers 156Speaker's website: **https://www.thingiverse.com/lgbu/designs

**Abstract**: The increasingly affordable technologies of 3D design and printing provide engaging opportunities for mathematics educators to play and model mathematical ideas and structures and serve the diverse needs of students at all levels. In the context of mathematics education, the speaker reflects on his experience with 3D design and printing using design examples and further discusses pedagogical possibilities.

** **

**Spring 2019 Speakers**https://www.physics.siu.edu/~pskumar/

**Speaker**: Prof. Poopalasingam Sivakumar, Physics, SIUC

**Title**: Challenges in analyzing spectroscopic data and the potentia of machine learning to accelerate bioanalysis with spectroscopy

**Date**: 4-25-19

**Time**: 3-4:00 pm

**Place**: Neckers 156

**Speaker's website**:

**Abstract**: Analyzing spectroscopic data can be tedious that can stretch weeks or months, depending on the sample. Especially, prompt identification of biochemical changes associated with cancer cells from spectra almost impossible using conventional spectral analysis techniques. Machine learning has the potential that could facilitate to detect minute changes in enormous spectroscopy information and to speed up the spectral analysis.

In this talk, I will discuss the application of high-resolution Raman spectroscopy to detect abnormal pancreatic cancer cells by exploiting the alteration of chemical signatures in the cells based on the vibrational signatures and address the challenges of reproducibility and replicability with Raman in bioanalysis. Raman spectroscopy provides molecular signatures and structural composition of the samples. Raman shows promising results in identifying and distinguishing biomolecules such as nucleic acids, lipids, and proteins and cells. The spectra of cancer cells are analyzed through combinations of data-preprocessing, various dimension reduction protocols, and machine learning classification algorithms Preliminary investigation of pancreatic Mia PaCa-2 cancer cells lines versus parental cell lines based on combing spectroscopic data with machine learning techniques shows a promising result.

** **

**Speaker**: Chathurangi Pathiravasan, Mathematics, SIUC

**Title**: Application of Kullback-Leibler Divergence in one-way ANOVA

**Date**: 4-18-19

**Time**: 3-4:00 pm

**Place**: Neckers 156

**Speaker's website**: https://math.siu.edu/faculty-staff/grad-stud/phd-stud/pathiravasan.php

**Abstract**: Kullback-Liebler (KL) divergence, known as relative entropy, is a measure of difference between two probability distributions. The concept was originated in probability theory and information theory, and now widely used in different literature such as data mining, time-series analysis and Bayesian analysis. In this study, we have shown the minimization problem with KL divergence plays a vital part in one-way Analysis of Variance (ANOVA) when comparing means of different groups. As immediate generalization, a new semi-parametric approach is introduced and it can be used for both means and variance comparisons of any type of distributions. The simulation studies show that the proposed method has favorable performance than the classical one-way ANOVA. The method is demonstrated on experimental radar reflectivity data and credit limit data. Asymptotic properties of the proposed estimators are derived with the purpose of developing a new test statistic for testing equality of distributions.

Keywords: Kullback-Leibler Divergence, Analysis of Variance, Asymptotic Properties

**Speaker**: Upul Rupassara, Mathematics, SIUC

**Title**: Joint exit time and place distribution for Brownian motion on Riemannian manifolds and the asymptotic independence condition**Date**: 4-11-19**Time**: 3-4:00 pm**Place**: Neckers 156**Speaker's website**: https://sites.google.com/view/upul-rupassara

**Abstract: **The joint distribution of first exit time and place of Brownian motion from normal balls of sufficiently small radius is considered. The asymptotic expansion of the joint Laplace transform of exit time and spherical harmonics of exit position is derived for a ball of small radius. A generalized Pizetti's formula is used to expand the solution of the related partial differential equations. These expansions are represented in terms of curvature in the manifold. The geometric properties of Riemannian manifolds are derived in the case where the first exit time and place are statistically independent. In particular, it is proven that an Asymptotic Uncorrelated Condition (AUC) involving orders of first exit time and position equivalent to the certain level of curvature conditions depending on the level of asymptotics. Further, a generalized formula is derived for arbitrary moments of first exit time at corresponding orders of asymptotics.

**Speaker**: Prof. Jerzy Kocik, Mathematics, SIUC

**Title**: Spinors, geometry, and numbers**Date**: 3-28-19**Time**: 3-4:00 pm**Place**: Neckers 156**Speaker's website**: http://lagrange.math.siu.edu/Kocik/geometry/geometry.htm

**Abstract: **Spinor spaces hold representations of the orthogonal groups and "explain" the curious behavior of certain object that need to be turned twice to return to the initial state. Quite intriguing, the same algebraic construct can be applied to configurations of circles. We shall define a "tangency spinor" and see how it connects various aspects of geometry, topology and algebra, not to mention visualization of otherwise mysterious properties of quantum objects.

Keywords: Split quaternions, Stern-Brocot tree, space-time, arithmetic functions, tessellations.

**Speaker**: Prof. Keith T. Gagnon, Biochemistry and Molecular Biology – SMC (Biochemistry & Molecular Biology, Chemistry & Biochemistry), SIUC

**Title**: Rational Design of Inhibitors to Safely Control CRISPR Gene-Editing Enzymes**Date**: 2-28-19**Time**: 3-4:00 pm**Place**: Neckers 156**Speaker's website**: http://www.labgagnon.com/index.html

Abstract: CRISPR is a new enzyme-based technology that can be used to precisely "edit" the genomes of living organisms. This technology is not only being developed for basic science, but also as a potential gene therapy. Although CRISPR is an exciting technology that could one day cure diseases like cancer or Alzheimer's, it is not perfect and can potentially produce unwanted side-effects. To improve the control and safety of therapeutic or technology development, inhibitors that can act as a "kill switch" to turn off the enzyme are needed. This seminar will describe CRISPR technology and the rational design of successful inhibitors based on biochemical principles.

**Speaker**: Prof. Banafsheh Rekabdar, Department of Computer Science, SIUC

**Title**: The current state of deep learning**Date**: 2-14-19**Time**: 3-4:00 pm**Place**: Neckers 156**Speaker's website**: http://www.cs.siu.edu/~brekabdar

Abstract: Deep Learning is a subset of Machine Learning which deals with deep neural networks. Deep learning allows computational models that are composed of multiple processing layers to learn representations of data with multiple levels of abstraction. These methods have dramatically improved the state-of-the-art in speech recognition, visual object recognition, object detection, time-seres data analytics, safety and security, natural language processing and many other domains such as biology and genomics.

**Fall 2018 Speakers**

**Speaker**: Kofi Placid Adragni, Senior Research Scientist, Eli Lilly and Company

**Title**: Sufficient Dimension Reduction of Features in the Presence of Dependent Observations**Date**: 11-15-18**Time**: 3-4:00 pm**Place**: Neckers 156**Speaker's website**:

Abstract: Sufficient dimension reduction methods are designed to help reduce the dimensionality of large datasets without loss of regression information for a better visualization, prediction, and modeling. We develop their use for dependent multi- dimensional features with respect to an outcome of interest in the presence of other covariates. Existing likelihood-based sufficient dimension reduction methods assumes independent and identically distributed samples. However, observations are often recorded on subjects or clusters. While the observations from cluster to cluster could be independent, the within-cluster observations are likely dependent. Treating the within-cluster observations as independent may adversely affect the estimation of the central subspace. We propose a method for estimation of the central subspace when the observations are dependent within cluster and discuss some structures of the dependence among the features.

**Speaker**: John P. McSorley, Professor, Southern Illinois University - Dept. of Mathematics

**Title**: Sequential Covering Designs**Date**: 10-25-18**Time**: 3-4:00 pm**Place**: Neckers 156**Speaker's website**: http://lagrange.math.siu.edu/McSorley/

**Speaker**: Min Li, Associate Professor, ShenZhen University

**Title**: Schatten Quasi-Norm Induced Models for Image Decomposition, Completion and Salient Object Detection**Date**: 9-27-18**Time**: 3-4:00 pm**Place**: Neckers 156

**Abstract**: Image decomposition, completion and salient object detection are not only ubiquitous but also challenging tasks in the study of computer vision. Image processing using mathematical methods has always been the trend of applied mathematics. In recent years, the latest research hotspot is the matrix rank minimization problem which arises in a wide range of applications. Inspired by this, we ﬁrstly propose a novel regularization model for image decomposition and data completion, which integrates relative total variation (RTV) with Schatten-1/2 or Schatten-2/3 norm, respectively. Secondly, we give salient object detection based on weighted group sparsity and Schatten-1 or Schatten-2/3 or Schatten-1/2 norm. The proposed model is in essence divided into ”regularization term+double nuclear norm” and ”regularization term+ Frobenius/nuclear hybrid norm”, which can be solved by splitting variables and then by using the alternating direction method of multiplier (ADMM). Meanwhile, Convergence of the algorithm is discussed in detail.

**Speaker**: Kwangho Choiy, Assistant Professor, Department of Mathematics, SIUC**Speaker's website**: https://sites.google.com/site/kchoiy/

**Title**: Some arithmetic objects in discrete series representations of p-adic groups**Date**: 9-13-18**Time**: 3-4:00 pm**Place**: Neckers 156

**Abstract**: Studying some classes of representations of a p-adic group, we encounter some interesting arithmetic objects in it. In this talk, we shall focus on discrete series representations that are simply related to L^{2}-space, introduce some arithmetic objects including their multiplicities in the restriction and formal degrees. We also discuss their connections to the local Langlands correspondence of p-adic groups.

**This talk will begin with basic concepts and backgrounds that are accessible to undergraduate and early-year graduate students.

**Spring 2018 Speakers**

**Speaker: **Dr. Arnab Dutta, Harris-Stowe State University

**Title**: Closed-Rangeness of Composition Operators

**Date**: 5-3-18

**Time**: 3-4:00 pm

**Place**: Neckers 156

**Abstract**: Let φ be an analytic self-map of the unit disk D := {z : |z| < 1}. We investigate inheritance of closed-rangeness property of Cφ from a larger Banach space of analytic functions on D to a subspace of it.

**Speaker: **Dr. Valentina Harizanov, George Washington University

**Speaker's Website: https://home.gwu.edu/~harizanv/ **

**Title**: Structure & Complexity of Orders on Structures

**Date**: 4-5-18

**Time**: 3-4:00 pm

**Place**: Neckers 156

**Abstract**: We study topological and computability-theoretic properties of orders on magmas. A magma is a structure with a binary operation. It is right-orderable if there is a linear ordering of its domain, which is right-invariant with respect to the operation. If the ordering is also left-invariant, then a magma is biorderable. Interesting rightorderable magmas the operation of which is self-distributive and not necessarily associative come from knot theory and are called quandles. There is a natural topology on the set of all right (left) orders or bi-orders of orderable magmas. These spaces are compact. A computable orderable group does not necessarily have a computable order. This can be used to show that the space of orders on such a group is homeomorphic to the Cantor set. For a large class of orderable residually nilpotent groups, including free groups and surface groups, we obtain orders in all Turing degrees.

**Speaker**: Dr. Jonny Stephenson, Valparaiso University

**Speaker's Website: https://blogs.valpo.edu/jstephenson/**

**Title**: Computable Structures and Isomorphisms

**Date**: 3-29-18

**Time**: 3-4:00 pm

**Place**: Neckers 156

**Abstract**: In computable structure theory, we focus on structures which have relations and functions that are each specified by a computable function. When considering such structures, we typically study them up the equivalence relation of computable isomorphism, which is a finer notion than isomorphism. If two copies of a structure are isomorphic, but not computably so, it is interesting to ask how complicated the

isomorphisms between the copies are. In this talk, we will take a fairly concrete example-based approach to explore these and related notions.

**Speaker**: Dr. Anush Tserunyan, University of Illinois at Urbana-Champaign

**Speaker's Website: https://faculty.math.illinois.edu/~anush/index.html**

**Title**: Orbit equivalence, cost and decompositions

**Date**: 3-22-18

**Time**: 3-4:00 pm

**Place**: Neckers 156

**Abstract**: Abstract: Let Fn[0, 1] and Fm[0, 1] be free actions of the free groups on n and m generators and assume that these actions preserve the Lebesgue measure and are ergodic (i.e. indecomposable). If these actions produce the same orbits (i.e. their orbit equivalence relations are equal), must n = m? This is an instance of the more general question: how much of the group is ”remembered” by the orbit equivalence relations of its free measure-preserving actions? The answer for free groups was given by Gaboriau in ’97 via cost: a numerical invariant for measure-preserving equivalence relations involving measured graphs and their combinatorics. I will introduce this invariant and discuss relevant results, obtained in joint work with Ben Miller, on decomposing ergodic graphs of cost n into at most n ergodic Z-actions.

**Salah Mohammad Memorial Colloquium Series**

**Speaker**: Zoi Rapti, Associate Professor, Department of Mathematics, UIUC

**Speaker's Website: https://faculty.math.illinois.edu/~zrapti/**

**Title**: Direct and Indirect Effects of Species Interactions in Disease Systems

**Date**: 11-16-17

**Time**: 3-4:00 pm

**Place**: Neckers 156

**Abstract**: Indirect effects, both density- and trait-mediated, have been known to act in tandem with direct effects in the interactions of numerous species. They have been shown to affect populations embedded in competitive and mutualistic networks alike. At the same time, in disease systems, pathogens can harm their hosts in a variety of ways. For this reason, we define virulence as an umbrella term that encompasses disease induced mortality, fecundity reduction and increased predation due to the disease. Moreover, competitors can alter the course of an epidemic through disease dilution or amplification. All these interactions greatly complicate the task of determining key factors and interactions in disease spread.

In this talk, we will introduce mathematical models based on coupled ordinary and partial differential equations to investigate the invasibility and prevalence of an obligately killing fungal parasite in a zooplankton host as they are embedded in a complex ecological network of predators, competitors and resources. Among our main findings is the demonstration that indirect effects cause qualitative and quantitative changes almost indistinguishable from direct effects and the theoretical verification of the fact that the effects of direct and indirect mechanisms cannot be disentangled. Our results underpin the conclusions of past studies calling for comprehensive models that incorporate both direct and indirect effects to better describe field data. We also demonstrate trade-offs among the various manifestations of virulence and how these together with life-history traits shape the disease dynamics.

This is joint work with C. Caceres, T. Stewart, J. Kavouras, and B.Mueller-Brennan.

**Salah Mohammad Memorial Colloquium Series**

**Speaker**: Anna Haensch, Assistant Professor, Department of Mathematics and Computer Science, DuQuesne University, Pittsburg, PA

**Speaker's Website: **https://www.mathcs.duq.edu/~haensch/

**Title**: Almost universal ternary sums of polygonal numbers

**Date**: 11-9-17

**Time**: 3-4:00 pm

**Place**: Neckers 156

**Abstract**: In 1796 Gauss showed that every natural number can be written as the sum of three triangular numbers. In 2009, Chan and Oh determined when a weighted sum of triangular numbers (i.e. triangular numbers with coefficients) represents all but finitely many natural numbers. We say such a sum is almost universal. In this talk we will determine when a sum of three generalized m-gonal numbers is almost universal. We will approach this question first from an algebraic, and then from analytic point of view, exploiting the capabilities of each method, and realizing new connections between the machinery.

**Salah Mohammad Memorial Colloquium Series**

**Speaker**: Yaser Samadi, Assistant Professor, Department of Mathematics, SIUC.

**Title**: Factor model for matrix and tensor time series data

**Date**: 10-26-17

**Time**: 3-4:00 pm

**Place**: Neckers 156

**Abstract**: Many data sets from across the sciences collect sequences of matrix- and tensor-structured data; we refer to such data as tensor time series. To explore and highlight the main dynamic structure of a set of multivariate time series, we extend the use of standard variance-covariance matrices for non-time series data in principal component analysis. This is also achieved by combining the principles of both canonical correlation analysis and principal component analysis for time series to obtain a new type of covariance/correlation matrix for a principal component analysis to produce a so-called “principal component time series”.

Another application, we are particularly motivated by electrophysiology studies in which electrical activity at multiple locations in the brain is measured over time. it is typical to pre-process such data to obtain tensors for each short time interval representing the level of coherence between each pair of brain regions at each spectral frequency. We propose a flexible class of nonparametric factor models for tensor time series data, which reduce dimensionality and maintain interpretability through the incorporation of sparsity constraints. The ability to accurately infer dynamically changing subnetworks is shown through simulations, and the methods are applied to mouse electrophysiology data.

**Salah Mohammad Memorial Colloquium Series**

**Speaker**: Wesley Calvert, Associate Professor, Department of Mathematics, SIUC. Speaker's website: http://lagrange.math.siu.edu/Calvert/

**Title**: Almost

**Date**: 10-19-17

**Time**: 3-4:00 pm

**Place**: Neckers 156

**Abstract**: For some problems in mathematics, we have algorithms. For others, we have none. Often, the proof of non-existence of an algorithm can feel severely contrived, so that the proof is unsatisfying --- we'd have to get fabulously unlucky where the algorithm fails. The worst-case complexity of the simplex method is horrible — if we encounter such an exotic example as to be in the worst case --- yet it runs without serious inconvenience every day.

What happens if, instead of asking for an algorithm that always works, we ask for one that works for everything except a very small set of pathological examples? Come and see.

**Salah Mohammad Memorial Colloquium Series**

**Speaker**: Eric Chitamber, Associate Professor, Department of Physics, SIUC. Speaker's website:https://www.physics.siu.edu/~echitamb/

**Title**: Transforming Resources within a Quantum Resource Theory

**Date**: 9-28-17

**Time**: 3-4:00 pm

**Place**: Neckers 156

**Abstract**: A quantum resource theory studies what physical processes are possible when constraints are placed on an experimenter’s operational capabilities. Under these restrictions, certain states become impossible to create, thereby rendering them as a “resource” for quantum information processing. The paradigm example of a quantum resource is entanglement, which cannot be generated by multiple experiments located in spatially separated laboratories.

In this talk I will discuss the mathematical structure of a general quantum resource theory and describe typical problems encountered. In particular, I will discuss the problem of resource transformation, which asks whether or not one state can be converted to another under the allowed operations of the theory. Recent work on the subject will be presented.

**Salah Mohammad Memorial Colloquium Series**

**Speaker**: Matthias Strauch, Professor, Department of Mathematics, Indiana University, Bloomington

Speaker’s website: https://pages.iu.edu/~mstrauch/

**Title**: Functions On a Covering for the P-adic Upper Half Plane

**Date**: 9-14-17

**Time**: 3-4:00 pm

**Place**: Neckers 156

**Abstract**: The Poincare upper half plane of complex numbers with positive imaginary part is an important source of representations of the group SL(2,R) which acts on it by Moebius transformations. In the world of p-adic numbers there is a space which plays an analogous role, the so-called p-adic upper half plane. Interestingly, whereas the Poincare upper half plane is simply connected, the p-adic upper half plane carries a whole tower of equivariant covering spaces. In this talk I will first explain the geometry of one particular of these covering spaces, following work by J. Teitelbaum. Secondly, I will discuss a method for analyzing the space of functions on this covering as a representation. This is joint work with Deepam Patel and Tobias Schmidt.

**Colloquium**: Math SIUC

Title: Bootstrapping Analogs of the One Way Manova Test

Speaker: Hasthika Rupasinghe, Graduate Student, Department of Mathematics, SIUC

(speaker’s website: https://sites.google.com/site/hasthisri/)

Date: 4-27-17

Time: 3:00-4:00pm

Place: Neckers 156

Abstract: The classical one way MANOVA model is used to test whether the mean measurements are the same or differ across p groups, and assumes that the covariance matrix of each group is the same. This work suggests using the Olive (2017abc) bootstrap technique to develop analogs of one way MANOVA test. A large sample theory test has also been developed. The bootstrap tests can have considerable outlier resistance, and the tests do not need the population covariance matrices to be equal. The two sample Hotelling's T^2 test is the special case of the one way MANOVA model when p =2.

**Colloquium**: Math SIUC

Title: Analysis of Non-Negative Observations Subject to Two Factors Using Gamma Models

Speaker: Nabendu Pal, Professor, Department of Mathematics, University of Louisiana at Lafayette

(speaker’s website: https://www.ucs.louisiana.edu/~nxp3695/index.htm)

Date: 4-20-17

Time: 1:00-2:00pm (*unusual time)

Place: Neckers 156

Abstract: A two-factor analysis of variance (ANOVA) is widely used in design of experiments when experimental units are subjected to two factors (i.e., potential sources of variations). However, such an analysis, which uses the F-tests, is dependent on three critical assumptions, - (i) all the main and interaction effects as well as the unexplained error term are additive to explain the response variable; (ii) the errors

are all independent and follow a normal distribution; and (iii) the error variances, though unknown, are all equal (i.e., the errors are homoscedastic). In many engineering and biological studies, where the observations are non-negative to begin with, it is often found that one or more of the above assumptions is/are not tenable. Further, the observations tend to exhibit positively skewed distributions as seen from sample histograms. In such situations, the standard operating procedure (SOP) of the two-factor ANOVA calls for a suitable (Box-Cox type) transformation, so that the transformed observations can follow the aforementioned model assumptions. There are two practical difficulties faced by the researchers with the transformed observations: (a) the transformed observations lose their relevance to the original problem, and the resultant unit(s) of the transformed observations can be meaningless, and (b) it becomes a subjective call to come up with the most appropriate transformation of the data, i.e., one transformation can make the data adhere to one assumption while another transformation can make the data follow another assumption closely. Faced with such a dilemma we offer a completely new paradigm where the non-negative observations, influenced by two factors, are modeled by gamma distributions with unknown shape and scale parameters which are dependent on the corresponding factor levels. We then proceed with testing the main effects (whether the main effects of a factor are all equal or not) and interaction effects (whether the interactions exist or not). To test a null hypothesis against a suitable alternative, we first derive the likelihood ratio test (LRT) based on its asymptotic Chi-square distribution. But since the asymptotic LRT (henceforth called 'ALRT') may not work well for small to moderate sample sizes we then propose a parametric bootstrap (PB) test based on the LRT statistic which does not use the Chi-square distribution, rather finds its critical value automatically through simulation. The PB test using LRT statistic (henceforth called 'PBLRT') appears to work very well in terms of maintaining the nominal level as seen from our comprehensive simulation study. Further, we present some real-life datasets to buttress the applicability of our proposed PBLRT over the classical ALRT, and to show how the inferences may differ from the ones based on traditional ANOVA.

**Colloquium**: Math SIUC

Title: Modern Techniques in Password Cracking and Password Meters

Speaker: Shiva Houshmand, Assistant Professor, Department of Computer Science, SIUC

(Click here https://sites.google.com/site/shiva1houshmand/ to visit her website)

Date: 4-13-17

Time: 3:00-4:00pm

Place: Neckers 156

Abstract: Passwords are critical for security in many different domains such as social networks, emails, encryption of sensitive data and online banking. Human memorable passwords are thus a key element in the security of such systems. It is important for system administrators to have access to the most powerful and efficient attacks to assess the security of their systems more accurately. In this talk I describe the recent techniques for password cracking and assessing the strength of passwords. The probabilistic context-free grammar technique has been shown to be very effective in password cracking. In this approach, the system is trained on a set of revealed passwords and a probabilistic context-free grammar is constructed. The grammar is then used to generate guesses in highest probability order, which is the optimal off-line attack. I also describe how entropy measures and Markov models have been used as password-strength meters to analyze the strength of user chosen passwords. A new password meter will also be introduced that estimates the probability of passwords being cracked. The system modifies the weak password slightly and suggests a new stronger password to the user. By dynamically updating the grammar we make sure that the guessing entropy increases and the suggested passwords thus remain resistant to various attacks.

**Colloquium**: Math SIUC

Title: Quantifying Uncertainties in Inverse Problems: Meaning and Usefulness of Error Bars in Large-Scale Inversion

Speaker: Aaron Luttman, Manager, Diagnostic Research and Material Studies, Nevada National Security Site

Date: 3-30-17

Time: 3:00-4:00pm

Place: Neckers 156

Abstract: While the U.S. Department of Energy’s National Nuclear Security Administration (NNSA) has moved to a scientific paradigm driven by modeling and simulation and in which experimentation is motivated primarily by code validation, there is still much to be learned by analyzing data directly and extracting information from experimental data by solving inverse problems. In order to quantify the uncertainties associated with the solutions, however, it is necessary to use statistical approaches to formulating the inverse problems and to understand the nature of the uncertainties for which such formulations can correctly account. In this work we will present data from NNSA X-ray imaging experiments related to the stockpile stewardship program, some inverse problems whose solutions inform the evolution of our experiments and diagnostics systems, and the challenges associated with the Bayesian formalisms used to assign error bars to the information extracted. The discussion will include details of the experiments themselves, where mathematical data analysts fit into the experimental programs, the role of mathematical theory in development of analysis techniques, and results demonstrating the efficacy of solving statistical inverse problems to drive stockpile stewardship.

** Colloquium: **Math SIUC

Title: Finite Group Theory and Local Langlands Conjecture** ** Speaker: Kwangho Choiy, Assistant Professor, Department of Mathematics, SIUC

**Date: 2-23-17**

**Time: 3:00-4:00pm**

**Place: Neckers 156**

**Abstract: The local Langlands conjecture for p-adic groups partitions the infinite set of equivalence classes of irreducible smooth complex representations of the p-adic groups into finite subsets whose internal structures are conjecturally interpreted in terms of irreducible representations of certain finite groups (Sgroups). As a part of the local Langlands conjecture, decompositions of tempered parabolic inductions into irreducible constituents are governed by certain finite groups (R-groups). In this context, we shall discuss various roles of finite group theory in the far-reaching local Langlands conjecture for p-adic groups.**

**Colloquium:** Math SIUC

**Title:** Some New Results on Lyapunov-Type Diagonal Stability

**Speaker:** Mehmet Gumus, Graduate Student, Department of Mathematics, SIUC

**Date:** 12-1-16

**Time:** 3:00-4:00pm

**Place:** Neckers 156

**Abstract: ** In this talk, we present several recent developments regarding Lyapunov diag-onal stability. This type of matrix stability plays an important role in various applied areas such as population dynamics, systems theory, complex networks, and mathematical economics. First, we establish a necessary and suﬃcient condition, based on the Schur complement, for determining Lyapunov diagonal stability of a matrix. This condition reduces the problem to common diagonal Lyapunov solutions on two matrices of order one less. We develop a number of extensions to this result, and formulate the range of feasible diagonal Lya-punov solutions. In particular, we derive explicit algebraic conditions for a set of 2 × 2 matrices to share a common diagonal Lyapunov solution. Second, the connection between Lyapunov diagonal stability and P -matrix property under Hadamard multiplication is extended. We present a new characterization involv-ing Hadamard multiplications for simultaneous Lyapunov diagonal stability on a set of matrices. This development is based upon a recent result concerning si-multaneous Lyapunov diagonal stability and a new concept called P-sets, which is a generalization of P -matrices. Third, we consider various types of matrix sta-bility involving a partition α of {1, . . . , n}. We introduce the notions of additive H(α)-stability and P0(α)-matrices, extending those of additive D-stability and nonsingular P0-matrices. Several new results are developed, connecting additive H(α)-stability and the P0(α)-matrix property to the existing results on matrix stability involving α. The extensions of results related to Lyapunov diagonal stability, D-stability, and additive D-stability are discussed.

Poster Presentation Slides Video - Part One Video - Part Two

**Colloquium:** Math SIUC

**Title:** A Semiparametric Method for Estimating Nonlinear and Partial Linear Vector Autoregressive Time Series Models with Independent and Dependent Errors

**Speaker:** Mahtab Hajebi, Visitor at Department of Mathematics, SIUC

**Date:** 11-17-16

**Time:** 3:00-4:00pm

**Place:** Neckers 156

**Abstract:** A semiparametric method is proposed to estimate vector autoregressive function in the nonlinear and partially linear vector time series model. We consider a combination of parametric and nonparametric estimation approach to estimate the nonlinear vector autoregressive function for both independent and dependent errors. The multivariate Taylor series expansion is utilized to approximate the vector regression function up to the second order. After the unknown parameters are estimated by the maximum likelihood estimation procedure, the obtained nonlinear vector autoregressive function is adjusted by a nonparametric diagonal matrix. The proposed adjusted matrix is estimated using nonparametric kernel method.

Asymptotic consistency properties of the proposed estimators are established. Simulation studies are conducted to evaluate the performance of the proposed semiparametric method. Finally, we demonstrate the application of the proposed approach with an empirical example.

**Colloquium:** Math SIUC

**Title:** The Multivariate Percentile Power Method Transformation

**Speaker:** Jennifer Koran, Associate Professor, Department of Counseling, Quantitative Methods, and Special Education, SIUC

**Date:** 11-10-16

**Time:** 3:00-4:00pm

**Place:** Neckers 156

**Abstract:** The conventional power method transformation is a moment-matching technique that simulates non-normal distributions with controlled measures of skew and kurtosis. The percentile power method transformation is an alternative that uses the percentiles of a distribution in lieu of moments. This presentation covers the multivariate percentile power method transformation, which is used to simultaneously simulate several non-normal variates using percentiles and a specified correlation matrix. Empirical illustrations are provided, including demonstration of the percentile power method transformation using a publicly-available SAS macro. The macro and instructions for using it can be found at https://digitalcommons.wayne.edu/jmasm/vol15/iss1/42.

Poster Presentation Slides Video - Part One Video - Part Two

**Colloquium:** Math SIUC - Art, Math and Science: An Interdisciplinary Colloquium

**Title:** Art and Mathematical Instinct: The Relationship Between Art and Math

**Speaker: **Marie Bukowski, Professor, Director, School of Art and Design

**Date:** 10-20-16

**Time:** 3:30-4:30pm

**Place:** Neckers 240

**Abstract:** I believe that art making is a pioneering, transformative act that moves, often changes, and sometimes revolutionizes culture. To achieve this, I have become more aware, reflective, and adept, willing to expand skills and capacities and to place my own work within a creative inquiry that takes me more deeply into the nature and meaning of my work. I incorporate diverse, interdisciplinary perspectives into my art practice, and use them to create art that is truly innovative, has deep impact, or powerfully challenges personal or cultural perceptions. I cross disciplines by working with practicing scientists and researchers so that our journeys are enriched by multiple perspectives and disciplines. *Art & the Mathematical Instinct* will discuss the influence that mathematical and scientific events have had on my creative research.

Click here to visit Marie Bukowski's website

Poster Video - Part One Video - Part Two

**Colloquium:** Math SIUC

**Title: **Integral Quadratic Forms and Lattices Satisfying Regularity Conditions

**Speaker:** Andrew Earnest, Professor, Emeritus, Department of Mathematics

**Date:** 10-06-16

**Time:** 3:00pm

**Place:** Neckers 156

**Abstract:** In 1927, L.E. Dickson introduced the term ‘regular' to refer to a positive definite ternary integral quadratic form with the property that it represents all the positive integers not ruled out for representation by congruence conditions. In more modern terminology, the regular forms are those for which a local-global principle holds for the representation of integers. Since that time, quadratic forms and lattices with this property and various natural generalizations of it have been studied extensively. In this talk, we will give an overview of some of the main results that have been obtained, describe some recent advances, and indicate some remaining open problems on these interesting classes of lattices.

Poster Video - Part One Video - Part Two Power Points

**Colloquium:** Math SIUC

**Title:** A Variational Approach to Stochastic Problems

**Speaker:** H.R. Hughes

**Date:** 9-22-16

**Time:** 3:00pm

**Place:** Neckers 156

**Abstract:** A relationship between optimal control and calculus of variations problems is exploited to investigate variational formulations of several stochastic problems, including Brownian bridge and the stochastic linear regulator problem. Computational approaches are presented.

Poster Video - Part One Video - Part Two

**Colloquium:** Math SIUC

**Title:** Taylor Approximations and Sobolev Spaces

**Speaker:** Daniel Spector, Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan

**Date:** 9-8-16

**Time:** 3:00pm

**Place:** Neckers 156

**Abstract:** In this talk we will introduce the sometimes difficult to understand Sobolev spaces as a simple extension of the Taylor approximation of classically differentiable functions (C^{1}).

Poster Video - Part 1 Video - Part 2

**Colloquium:** Physics SIUC** Title:** Quantum Entanglement and Nonlocal Games

**Laura Mancinska**

Speaker:

Speaker:

**4-1-16**

Date:

Date:

**4:00pm**

Time:

Time:

**Neckers 440**

Place:

Place:

**Quantum entanglement is known to provide advantage in many nonlocal scenarios. However, in practice, finding the best entangled strategy is challenging and one is often forced to resort to ad hoc methods. In general, the mathematical structure of the set of entangled strategies is poorly understood and many basic questions remain open.**

Abstract:

Abstract:

One basic open question is whether a continuous payoff function should always achieve its maximum when optimized over the set of entangled strategies. A positive answer would alleviate the search of optimal entangled strategies while a negative one would give evidence of the hardness of this problem. In this work, we show that the answer can be negative even if the nonlocal task has classical inputs and outputs. In particular, we present a one-round two-party nonlocal game at which entangled quantum parties can perform increasingly better by sharing a quantum system of increasingly larger size. Although no error free strategy exists for this game, the players can succeed with probability arbitrarily close to one by using entangled states of increasingly larger dimension.

This is joint work with Thomas Vidick.

**Colloquium:** Math SIUC** Title:** Multiplicities in restriction of representations of p-adic groups

**Kwangho Choiy**

Speaker:

Speaker:

**3-3-16**

Date:

Date:

**3:00pm**

Time:

Time:

**Neckers 156**

Place:

Place:

**The multiplicity of an irreducible representation of a p-adic group, when restricted to its closed subgroup containing the derived group, yields arithmetic properties of the given representation. Starting to introduce basic notions and backgrounds, we discuss the case of discrete series representations of GL(m, D) when restricted to SL(m, D), where D is a central division algebra over a p-adic field of characteristic 0. The approach here is to use elementary facts in algebraic number theory and special properties in the local Langlands correspondence. We further extend this method to other p-adic groups with some assumptions and necessary modifications.**

Abstract:

Abstract:

**Colloquium:** Math SIUC** Title:** Bounded global Hopf branches for the Nicholson’s blowflies equation with stage structure

**Hongying Shu**

Speaker:

Speaker:

**2-4-16**

Date:

Date:

**3:00pm**

Time:

Time:

**Neckers 156**

Place:

Place:

**We investigate Nicholson’s blowflies model with natural death rate incorporated into the delay feedback. We consider the delay as a bifurcation parameter and examine the onset and termination of Hopf bifurcations of periodic solutions from a positive equilibrium. We show that the model has only a finite number of Hopf bifurcation values and we describe how branches of Hopf bifurcations are paired so the existence of periodic solutions with specific oscillation frequencies occurs only in bounded delay intervals. The bifurcation analysis guides some numerical simulations to identify ranges of parameters for coexisting multiple attractive periodic solutions.**

Abstract:

Abstract:

**Colloquium:** Math SIUC** Title:** Designing, fabricating, and characterization of devices and materials for resource-limited areas

**Punit Kohli**

Speaker:

Speaker:

**12-3-15**

Date:

Date:

**3:00pm**

Time:

Time:

**Neckers 156**

Place:

Place:

**In this talk, I will describe our recent experimental work on the design, fabrication, and characterization of devices for areas and countries with limited resources. The questions of empowering the local people through available materials, resources, and human power is discussed in this talk. I will attempt to demonstrate that through creative thinking, the use of common materials in house-hold can be used for the fabrication of high-tech devices (solar cells, lithography, oil-water separation).**

Abstract:

Abstract:

**Colloquium:** Math SIUC

**Title: **Realizations of simple Smale flows using n-band templates (n=3, 4)

**Speaker:** Kamal Adhikari

**Date: **11-19-15

**Time:** 3:00pm

**Place: **Neckers 156

**Abstract:** A simple Smale flow is a structurally stable flow which has one dimensional chain recurrent (invariant) set. When the flow has hyperbolic structure on its chain recurrent set, the chain recurrent set can be decomposed into finite number of basic sets which are disjoint, compact and have a dense orbit. Each basic set is either an attractor, a repeller or a saddle set. For the simple Smale flows on 3- manifolds, the attracting and repelling basic sets are single closed orbits and the saddle sets are single closed orbits or of chaotic nature. A chaotic saddle set can be modeled by a branched manifold called a template and the knot types of the periodic orbits can be studied within a template.

In the talk, we will mainly focus on the linking structure of attracting and repelling orbits using templates and discuss all possible realizations of the flow using 3-band and 4-band template models. This extends the work done by Prof. Michael Sullivan on the realization of Lorenz Smale flow and continues the work of Elizabeth Haynes on realizing simple Smale flow with a four band template on 3- sphere.

**Colloquium:** Math SIUC

**Title: **Pleasures, Challenges, and New Results on Polyhedra

**Speaker:** Wayne Deeter

**Date:** 11-5-15

**Time:** 3:00pm

**Place:** Neckers 156

**Abstract: **If we attempt to enclose a circle, or a sphere - or a hypersphere in any number of dimensions - with an intersection of planes or hyperplanes (in general terms, within a polyhedron), we will have only an approximation of a sphere. We ask instead, "How closely can any polyhedron-enclosure of the sphere fit?" How many of it's faces would be identical? How many different types of faces would this roundest polyhedron have? Today there are no known formulas to specify the roundest polyhedra.

**Colloquium:** Math SIUC

**Title:** Stability of host-parasitoid systems

**Speaker:** Dashun Xu

**Date:** 10-15-15

**Time:** 3:00pm

**Place:** Neckers 156

**Abstract:** Understanding the mechanisms driving predator-prey population dynamics and stability has been a central theme in the field of ecology. Although theoretical models developed over the past quarter century have demonstrated that predator-prey population dynamics can depend critically on age (stage) structure and duration and variability in development times of different life stages, unambiguous experimental support for this theory is nonexistent. We conducted an experiment with the cowpea weevil Callosobruchus maculatus, and its parasitoid Anisopteromalus calandrae, to test the prediction that increased variability in the development time of the host stage that is vulnerable to parasitism can promote interaction stability. In this talk, I am going to present first some stability results of host-parasitoid systems and then some model simulations by fitting to our lab data

**Colloquium:** Math SIUC

**Title:** A Tale of Three Groups: A Hitchhiker's Guide to Lorentz Boosts

**Speaker:** Jerzy Kocik

**Date:** 10-1-15

**Time:** 3:00pm

**Place:** Neckers 156

**Abstract:** A remarkably simple geometric diagrammatic method of relativistic composition of velocities is presented. It is derived from a homomorphism of three groups: the Moebius group of fractional linear transformations over complex numbers, quaternions and Clifford algebras, the group of reversions of sphere, and the Lorentz group restricted to isotropic vectors.

The talk will be friendly and graduate students are encouraged to attend.

**Colliquium:** Math SIUC

**Title:** Mathematics of Theoretical Machine Learning

**Speaker:** Wesley Calvert

**Date:** 9-17-15

**Time:** 3:00pm

**Place:** Neckers 156

**Abstract:** What can a computer learn? Since the 1960s, there have been mathematical models of this problem. The usual modern formulation allows for the computer to be given a sample of data, with each point labeled correct or incorrect. The computer is then asked to identify a rule which will, with high probability, be correct enough to decide whether a new point is correct or incorrect, with perhaps some small region of error. Some cases where this is possible are well-known. Other cases where this is impossible are also well-known. Other (even more well-known) cases are things that people try, and then let the market sort out whether it works well enough (think of Netflix, trying to learn what movies you'd enjoy).

The central problem of this talk is the difficulty of deciding whether something is learnable or not. Logicians have many tools for thinking about the "difficulty" of various problems, and I'll introduce some of them. Much of the real show, though, is in finding the right representations of the problem.

**Colloquium:** Math SIUC

**Title:** There and Back Again

**Speaker:** Daniel Spector

**Date:** 9-3-15

**Time:** 3:00pm

**Place:** Neckers 156

**Abstract:** In this talk I will report on the mathematical journey I have been on in the past several years away from SIUC. This journey begins in the calculus of variation, taking us to fractional PDE, to harmonic analysis, and not surprisingly returning to the calculus of variations. Results will be mentioned, but my hope is to give a motivation for why I began new projects as well as possible future directions.

**Colloquium:** Math SIUC** Title: **Fourier coefficients at Finite Cusps

**Joseph Hundley, Department of Mathematics, University at Buffalo (SUNY)**

Speaker:

Speaker:

**4-16-15**

Date:

Date:

**3:00pm**

Time:

Time:

**Neckers 156**

Place:

Place:

**Modular forms are venerable objects in Analytic Number Theory which attained particular notoriety in the 1990s, through their connection with Wiles’s proof of Fermat’s Last Theorem. They are functions on the complex upper half plane which satisfy a sort of generalized periodicity property in addition to having nice analytic properties. Generalized periodicity includes ordinary periodicity in the real coordinate, giving rise to a Fourier expansion. The number theory shows up in the sequence of Fourier coefficients. But generalized periodicity is more than ordinary periodicity, so in general one must also consider alternate Fourier expansions. We shall discuss cusps and Fourier expansions at them. From this point of view, expansion in the real direction will correspond to expansion around the “point at infinity” in the projective line. We will then discuss what nice properties of the expansion at infinity do and do not extend to the finite cusps. This talk reports on joint work with Dorian Goldfeld, Min Lee, and Qiao Zhang.**

Abstract:

Abstract:

**Colloquium:** Math SIUC** Title:** Mathematical and numerical analysis of the time-dependent Ginzburg-Landau superconductivity equations

**Buyang Li, Department of Mathematics, Nanjing University**

Speaker:

Speaker:

**4-9-15**

Date:

Date:

**3:00pm**

Time:

Time:

**Neckers 156**

Place:

Place:

**We prove well-posedness of time-dependent Ginzburg–Landau superconductivity equations in a nonconvex polygonal domain, and decompose the solution as a regular part plus a singular part. We see that the magnetic potential is not in $H^1$ in general, and the standard finite element method may give incorrect solutions. To remedy this situation, we reformulate the equations into an equivalent system based on the Hodge decomposition, which avoids direct calculation of the singular magnetic potential. The essential unknowns of the reformulated system admit $H^1$ solutions and can be solved correctly by the standard finite element methods. We then propose a decoupled and linearized FEM to solve the reformulated equations and prove the convergence of the numerical solution based on proved regularity of the solution.**

Abstract:

Abstract:

**Colloquium:** Math SIUC** Title:** Non-normal asymptotics of the mean-field Heisenberg model

**Kay Kirkpatrick, Department of Mathematics, UIUC**

Speaker:

Speaker:

**4-2-15**

Date:

Date:

**3:00pm**

Time:

Time:

**Neckers 156**

Place:

Place:

**I will discuss spin models of magnets and superconductors, with spins in the circle (XY model) and in the sphere (Heisenberg model) - with interesting phase transitions. I will discuss work with Elizabeth Meckes on the mean-field Heisenberg model and its non-normal behavior at the phase transition. There is much that is still unclear about these models; I'll mention work in progress with Tayyab Nawaz and Leslie Ross.**

Abstract:

Abstract:

**Colloquium:** Math SIUC** Title:** Zeros of L-functions

**Peter Cho**

Speaker:

Speaker:

**2-26-15**

Date:

Date:

**3:00pm**

Time:

Time:

**Neckers 156**

Place:

Place:

**In the 20th century, one of the most striking discoveries in number theory is Montgomery's pair-correlation. It says that pair-correlation of zeros of the Riemann zeta function is the same with that of eigenvalues of unitary matrices. In the 1990s, Rudnick, Katz and Sarnak studied the zeros of L-functions more systematically. Moreover, Katz and Sarnak proposed the n-level density conjecture which claims that distributions of low-lying zeros of L-functions in a camily is predicted by one of the compact matrix groups, which are U(N), SO(even), SO(odd), O(N), and Sp(2N). At the end of the talk, I will state an n-level density theorem for some families of Artin L-functions and talk about counting number fields with local conditions. I will start with a friendly definition of L-functions and give some examples. No background or knowledge for L-functions are required for this talk.**

Abstract:

Abstract:

**Colloquium:** Math SIUC

**Title:** Shahidi local coefficients and irreducibility results on coverings of p-adic SL(2).

**Speaker:** Daniel Szpruch

**Date:** 2-19-15

**Time:** 3:00pm

**Place:** Neckers 156

**Abstract:** The Langlands-Shahidi method has proven to be one of the most powerful tools to study automorphic L-functions. In this talk we shall survey the definition of Shahidi local coefficients for p-adic SL(2) and an application to a local irreducibility question. We will then present some new results and techniques regarding their metaplectic counterpart. No background on p-adic numbers and no knowledge on representation theory beyond basics are required for this talk. This is a joint work with David Goldberg.

**Colloquium:** Math SIUC

**Title:** Invariants of L-parameters between p-adic inner forms

**Speaker:** Kwangho Choiy, Department of Mathematics, Oklahoma State University

**Date:** 2-17-15

**Time:** 3:00pm

**Place:** Neckers 156

**Abstract:** The local Langlands correspondence predicts a relationship between irreducible complex representations and certain continuous homomorphisms, so-called L-parameters. The discovery of such a relationship provides new approaches to study the representations. After a tour of basic related theories, I will introduce the local Langlands correspondence for p-adic groups. Bringing in the notion of a p-adic inner form, I will then discuss some invariant properties governed by L-parameters between p-adic inner forms. At the end of the talk, I will describe my recent work with D. Goldberg on the invariance of R-groups for classical groups.

**Colloquium:** Math SIUC** Title: **Time series analysis for symbolic interval-valued data

**Speaker:**Yaser Samadi, Department of Mathematics, SIUC

**Date:**2-5-15

**Time:**3:00pm

**Abstract:**Symbolic values can be lists, intervals, frequency distributions, and so on. Therefore, in comparison with standard classical data, they are more complex and can have structures (especially internal structures) that impose complications that are not evident in classical data. In general, using classical analysis approaches directly lead to inaccurate results.

As a result of dependencies in time series observations, it is more difficult to deal with symbolic interval-valued time series data and take into account their complex structure and internal variability than for standard classical time series. In the literature, the proposed procedures for analyzing interval time series data used either midpoint or radius values that are inappropriate surrogates for symbolic interval variables. We develop a theory and methodology to analyze symbolic time series data (interval data) directly. Autocorrelation and partial autocorrelation functions are formulated, maximum likelihood estimators of the parameters of symbolic autoregressive processes are provided.

**Colloquium:** Math SIUC

**Title:** Variational method for the regular generalized fractional Sturm-Liouville problem

**Speaker:** Nimisha Pathak, Department of Mathematics, SIUC

**Date:** 1-22-15

**Time:** 3:00pm

**Abstract:** This talk will present a formulation and a solution of a regular generalized Sturm-Liouville problem using the variational method. The problem is formulated in terms of generalized operators introduced recently. Although, many different kernels can be considered, the kernels considered include fractional power kernel which lead to fractional integral and derivative operators; fractional power multiplied with exponential kernel which leads to generalized fractional integral and derivative operators with weights and scales, and some arbitrary kernels. In special cases, these operators reduce to Riemann-Liouville fractional integral and Riemann-Liouville and Caputo differential operators. The fractional power and the fractional power with exponential function kernels are singular kernels, and they lead to operators which satisfy semi-group properties. However, in general the generalized operators which are analogous to the fractional integral operators do not satisfy the semi-group property. Some properties of these operators are discussed.

Next, it will be demonstrated that the regular generalized Sturm-Liouville problem has infinite countable set of positive eigenvalues, and the eigenfunctions associated with distinct eigenvalues form a set of orthonormal bases for square integral functions. Thus, the regular generalized Sturm-Liouville problem considered here exhibit properties similar to Sturm-Liouville problems defined using integer order derivatives.

**Colloquium:** Math SIUC** Title:** Complexity of the isomorphism problem for subshifts

**John Clemens, Department of Mathematics, SIUC**

Speaker:

Speaker:

**12-4-14**

Date:

Date:

**3:00pm**

Time:

Time:

**Given a finite set A of symbols, we can form the Bernoulli shift on A. This is defined by equipping the set of all bi-infinite sequences from A with an appropriate topology, and considering the left-shift map S on these sequences. By a subshift we mean a subset of this space which is both topologically closed and invariant under the shift map. Subshifts form a rich class of dynamical systems which have been widely studied in symbolic dynamics. We say two subshifts are isomorphic if there is a homeomorphism between the underlying subsets which commutes with the shift map.**

Abstract:

Abstract:

In this talk, I will give an introduction to these systems, and then consider the problem of classifying subshifts up to isomorphism. We can use tools from descriptive set theory to give a precise gauge of the complexity of this problem, namely, we can show that the classification problem is of maximum complexity among equivalence relations with countable equivalence classes. I will also discuss free subshifts (those without any periodic orbits) and generalizations to subflows of other countable groups.

**Colloquium:** Math SIUC** Title:** A New Technique for Finding Small Kirkman Covering and Packing Designs; a KCD(11), a canonical KCD(13), and more examples

**John P. McSorley, Department of Mathematics, SIUC**

Speaker:

Speaker:

**11-20-14**

Date:

Date:

**Neckers A 156**

Place:

Place:

**3:00pm**

Time:

Time:

**We present a new technique which we call the 'type/unlabelled/labeled' technique for finding, or determining the non-existence of, small Kirkman covering and packing designs. Using this technique and different computational methods, we construct a new KCD(11), and a new canonical KCD(13), and make some progress on the existence question of a KPD(19,8).**

Abstract:

Abstract:

**Colloquium:** Math SIUC

**Title:** A 2-Ball Billiard Dynamical System Counts All Digits of $\pi$

**Speaker:** Gregory Galperin, Eastern Illinois University (formerly of Moscow State University)

**Date:** 11-6-14

**Place:** Neckers A 156

**Time:** 3:00pm

**Abstract:** In my talk I will tell how two massive colliding billiard particles (point-like balls) count all the decimal digits of the number $\pi$. While the formulation of the main theorem does not require any mathematics at all, its proof is subtle and tricky: it uses some knowledge form mechanics, geometry and calculus. If time allows, I will tell in the end of my talk two problems on billiards posed by the prominent mathematician Ya G. Sinai that were solved just recently. (Ya G. Sinai won the most prestigious award in mathematics, The Abel Prize, in May 2014).

The preliminary knowledge is more required. All interested in physics and mathematics are invited to the lecture, especially students of mathematics and physics majors.

**Colloquium:** Math SIUC

**Title:** Lyapunov Functional Technique and Global Asymptotic Stability of Delayed Epidemic Models

**Speaker:** Xiang-Sheng Wang, Southeast Missouri State University

**Date:** 10-16-14

**Place:** Neckers A 156

**Time:** 3:00pm

**Abstract:** In this talk, we start with a simple and fundamental epidemic model to illustrate the technique of Lyapunov functional in global stability analysis of equilibria for differential systems. Next, we introduce time delays to the model and state a notorious open problem related to the resulting delay differential system. We will discuss on the main difficulties and present some partial answers to this open problem.

**Colloquium: Math SIUC** Title: Some Aspects of Data Analysis Under Confidentiality Protection

Speaker: Professor Bimal Sinha, Presidential Research Professor, UMBC & Board of Regents Professor of the University System of Maryland

Date: 10-9-14

Place: Neckers A 156

Time: 3:00pm

Abstract: Statisticians working in most federal agencies are often faced with two conflicting objectives: (1) collect and publish useful data sets for designing public policies and building scientific theories, and (2) protect confidentiality of data respondents which is essential to uphold public trust, leading to better response rates and data accuracy. In this talk I will provide a survey of two statistical methods currently used at the U.S. Census Bureau: synthetic data and noise perturbed data.

**Colloquium: Math SIUC** Title: Flows on Three-Manifolds and Knotted Orbits

Speaker: Michael Sullivan, SIU Carbondale

Date: 9-4-14

Place: Neckers A 156

Time: 3:00pm

Abstract: We examine a class of structurally stable chaotic flows with one attracting and one repelling close orbit. We look at how the dynamics of the flow relate to the knotting and linking of these two orbits.

**Colloquium: Math SIUC** Title: A view of the Langlands Program

Speaker: David Goldberg, Purdue University

Date: 3-27-14

Place: Neckers 156

Time: 3:00pm

Abstract: A few years ago, I gave a colloquium motivating the Langlands program through examples, mostly taken in chronological order, and used this glossary of examples to formulate the framework of this wide reaching project. Here I will, instead, attempt to start the story closer to the end, with Wiles's proof of Fermat's Last Theorem, and use this as a case study for the power of the Langlands philosophy. We will certainly re-introduce some of the examples from the previous treatment, so there will be some overlap with the previous. I hope, however, those who saw that one will consider this a sequel, while those who did not can find it a suitable introduction.

**Colloquium: Math SIUC** Title: Admissibility Analysis and Synthesis of Singular Systems via Delta Operator Method

Speaker: Xin-zhuang Dong

Date: 3-20-14

Place: Neckers 156

Time: 3:00pm

Abstract: In this report, we present some of our research results about studying singular systems via delta operator method. The delta operator model is set up for a singular continuous system. It is obtained from the discrete model of the singular continuous system and will tend to the singular continuous system when the sampling period tends to zero. Thus, the delta operator model provides a unified description of a singular continuous system and its discrete model. Various necessary and sufficient admissibility conditions are given for singular delta operator systems and the relations among these conditions are also presented. Several sufficient conditions are derived to solve the problem of admissible control for singular delta operator systems and the design methods of an admissible controller are also given. Some examples are provided to illustrate the effectiveness of the above theoretical results.

** Colloquium: Math SIUC ** Title: On the structure of the degrees of relative provability: Why some functions are more complicated than others

Speaker: Steffen Lempp, University of Wisconsin, Madison

Date: 3-6-14

Place: Neckers 156

Time: 3:00pm

Abstract: Gödel's famous Incompleteness Theorem states that for any axiomatization of number theory, there is a true statement about the natural numbers which cannot be proved from these axioms.

We investigate how this theorem can be extended to proving the totality of computable functions: Not all total computable functions can be proved by a set of axioms to be total; and for some, totality is harder to prove than for others. We define the so-called "degrees of provability", which measure this is a precise way, and relate this to properties of functions, such as how fast a function is growing.

This is joint work with U. Andrews, M. Cai (who originally defined these degrees in his thesis), D. Diamondstone and J. Miller.

**Colloquium: Math SIUC**

Title: Formal Construction and Generation of Algorithms

Speaker:Haihe Shi (Jiangxi Normal University, Nanchang, China)

Date: 2-20-14

Place: Neckers 156

Time: 3:00pm

Abstract: Recently trustworthy software has been proposed and advocated by many countries and many academic communities. As the core of computer software, algorithm, especially its reliability and productivity, plays a critical role in both trustworthiness and application of software. Formal method and automation of algorithms have been shown to be important ways to improve the reliability and productivity of various algorithms. Yet, due to the creativity involved, algorithm formal method still remains to be one of the field’s most challenging problems. Its use so far within the software development community has not been commensurate with its potential. Therefore, it is necessary to explore the laws during algorithm design and to propose new techniques. Here series of our work will be presented, including a unified and practical formal approach and its supporting platform, algorithm development rules/strategies and prototype system, sorting algorithms via formal component product line assembly, and algorithm design through the optimization of reuse-based generation via category theoretical semantic. Also, some recent ongoing works will be introduced.

** Colloquium:** Math SIUC

**Title: Representations of covering groups**

**Speaker: Dubravka Ban**

**Date: 12-5-13**

**Place: Neckers 156**

**Time: 3:00pm**

**Abstract: Let F be a p-adic field, and let G be the group of F-points of an algebraic group defined over F. We will talk about n-fold topological coverings of G. In general, these groups are not algebraic. Still, we can use the structure of G to obtain important information about the structure of covering groups. This is a basis for developing representation theory for covering groups. Important examples of covering groups are metaplectic groups, which are n-fold covers of GL(k,F).**

**Colloquium:** Math SIUC

**Title:** On Simulation Methods for Random Vectors under Specified Dependence Structure

**Speaker:** Chul G. Park (Carleton University)

**Date:** 11-14-13

**Place:** Neckers 156

**Time:** 3:00pm

**Abstract:** Generation of dependent random variables is an important subject in studies involving repeated measurements, cluster data, clinical trials, system reliability, time series data, and so on. In non-normal case, statistical methods to analyze such data rely on asymptotic theories and their finite sample performances can be evaluated only by a simulation study. However, there is no nice way to specify the joint distribution of such dependent observations even under well specified marginal distributions and dependence measures. In this talk, first I will review basic simulation methods when distributions are completely specified. And then, some important multivariate simulation methods will be discussed for the case where only marginal distributions and correlations are specified.

**Colloquium:** Math SIUC

**Title:** Digital Tomosynthesis: Current Biomedical Imaging Research and Future Promising Directions

**Speaker:** Ying (Ada) Chen, Ph.D., Associate Professor, Department of Electrical and Computer Engineering, SIUC

**Date:** 10-31-13

**Place:** Neckers 156

**Time:** 3:00pm

**Abstract:** Digital tomosynthesis refers to a three-dimensional low-dose X-ray imaging technique that allows reconstruction of an arbitrary set of planes in the object from limited-angle series of projection images. In breast imaging fields, compared with standard mammography, digital breast tomosynthesis (DBT) improves conspicuity of structures by removing the visual clutter associated with overlying anatomy. In chest imaging fields, the technique has been commercially available. This talk focuses on image reconstruction algorithms and optimization for the digital breast tomosynthesis imaging technique to improve early breast cancer detection. Applications with pulmonary nodule detection and other potential clinical and industrial applications will also be discussed.

**Colloquium**: Math SIUC

**Title:** p-adic inner forms and invariants of Langlands parameters

**Speaker:** Kwangho Choiy | Website

**Date**: 10-17-13

**Place:** Neckers 156

**Time:** 3:00pm

Abstract: The local Langlands conjecture for a p-adic group predicts a relationship between irreducible complex representations of the group and certain homomorphisms from the local Langlands group into the Langlands dual group. The latter homomorphisms are called Langlands parameters, and the representations of the p-adic group are partitioned into finite sets, called L-packets, indexed by Langlands parameters.

It is natural to expect some properties that all members in an L-packet have in common. Also, it can be questioned what kinds of data can be preserved by inner twistings which define inner forms. This talk will focus on such invariants. We begin with background and basic concepts in the representation theory of p-adic groups, and survey some known cases on the local Langlands conjecture. We finally discuss the invariants of Langlands parameters.

**Colloquium:** Math SIUC

**Title:** Generalized Fractional Calculus and the Application to Oscillator Equations

Speaker: Yufeng Xu (Central South University, Changsha, China)

**Date:** 9-19-13

**Place:** Neckers 156

Time: 3:00pm

Abstract: Fractional Calculus has gained considerable development in the recent forty years, while in fact it is a subject of several hundred years as Calculus. Fractional integral and differential equations have been applied in many physical and engineering real-world problems, and have been verified as powerful tools in modeling particular phenomena with memory effect. In this talk, we will introduce the mathematical preliminaries of fractional calculus, including different definitions of fractional integrals and fractional derivatives, and some properties of fractional operators. Furthermore, we would like to introduce two types of generalized fractional operators, which contain all existing classical and fractional integrals and derivatives as special cases. Those generalized fractional operators are firstly proposed in 2010 and 2012, respectively. Nowadays it is opening some possible interests on fractional calculus. As an application, we finally discuss the dynamical behaviors of Harmonic oscillator and van der Pol oscillator with generalized fractional derivatives, which depends on different kernel functions. Many interesting dynamics may not appear in classical Harmonic and van der pol oscillators will be presented.

**Colloquium:** Math SIUC

**Title:** Lie Groups and Unitarity

Speaker: Joseph Hundley, SIUC

**Date:** 9-5-13

**Place:** Neckers 156

Time: 3:00pm

Abstract: This talk will begin with a survey-level discussion of Lie groups, their unitary representations, and why one might be interested in them. We will then delve a bit into the details of how Lie groups were classified, and how the five exceptional groups were seen to exist. We'll describe a conjectural structure to the class of unitary representations, and explain an approach to proving parts of these conjectures. Time permitting we'll report on some recent results with Stephen Miller of Rutgers on this problem.

**Colloquium**: Math SIUC

**Title:**Introduction to Topological Quantum Computing

**Speaker:** Louis H. Kauffman, UIC

**Date**: 3-27-13

**Place**: AG 102

**Time**: 3:00pm

Abstract: This talk will begin with an introduction to the general idea of quantum computing and quantum algorithms. Then we will discuss how there is the possibility of using topology to both investigate topology problems through quantum formulations and to use physical situations that involve topology to create quantum computers. The latter is an active area of research, due to surprising and sometimes simple relationships between topology and physics. For example, the algebra of fermion creation and annihilation operators is generated by a Clifford algebra of Majorana fermion operators. These operators (call them a, b and c)) satisfy a^2 = b^2 = c^2 = 1 and ab = -ba, ac = -ca, bc = - cb. Then the quaternions arise via I = ba, J = cb, K = ac with I^2 = J^2 = K^2 = IJK = -1 and if we define R = (1 + I)/sqrt(2), S = (1 + J)/sart(2) and T = (1 + K)/sqrt(2), then RSR = SRS, STS = TST,

RTR = TRT giving unitary braid group representations associated with fermions. Topology occurs naturally in basic quantum physics.