## Colloquium Series

**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: **http://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:http://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: http://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: http://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.

**______________________________________________________________________________________________________________________________________________________________________________________________**

**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 http://digitalcommons.wayne.edu/jmasm/vol15/iss1/42.

**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 Mathemaical 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, fidning 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 maxiumum 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 equiibrium. 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 drived 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 fracitonal 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 zeroes 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 Fidning 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/labelled' 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 nore 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. Poster

**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. Poster

**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.

**Poster.**

**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. Poster

** 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). Poster**

**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. Poster

**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. Poster

**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. Poster

**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.