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## Main Content

### The Langenhop Lectures are made possible by the generous funding from Carl E. Langenhop, Emeritus Mathematics Professor, SIUC.

#### An Elementary Introduction to Langlands Program | Freydoon Shahidi

Langenhop Lecture | May 16, 2016 | Guyon Auditorium, Morris Library | 4:00PM

Abstract: We use a simple counting function to introduce two different aspects of Langlands program through some basic special cases: Spectral theory of Maass forms and Artin reciprocity law. The talk is aimed at a general audience with some very basic mathematical familiarity. But no specialized knowledge of number theory is assumed.

#### The Role of Mathematics & Statistics in Science & Society | Lynne Billard

Langenhop Lecture | April 29, 2015 | Guyon Auditorium, Morris Library | 7:30PM

Abstract: Whatever our interests may be, whether that be the social sciences, medical sciences, history, physical sciences, mathematical sciences, and so on, statistics and statisticians have a rol to play in helping us decipher th einformation pertaining to those interests that surround us daily. Against the backdrop of a brief historical view of its applications, we illustrate the role of mathematics and statistics in a variety of situations, including cases where the obvious technique is not necessarily the best analysis to employ.

#### Patterns and Disorder | Bryna Kra

Langenhop Lecture | April 23, 2014 | Guyon Auditorium, Morris Library | 7:30PM

What does it mean for a mathematical object to be ordered? To be disordered? If we look at a set of numbers that is large in some sense, does it have to contain any patterns? How small can we make such a set, but still have it contain interesting configurations? We explore different notions of patterned and random sets, starting with ancient ideas and ending with still unsolved problems.

Poster for event. Video of Lecture

#### Introduction to Virtual Knot Theory | Louis H. Kauffman

Langenhop Lecture | 2013

Abstract: Virtual knot theory is a study of embeddings of circles in thickend orientable surfaces. This is a particularly interesting case of knots in arbitrary three-manifolds. In the case of virtual knot theory, there is a corresponding diagrammatic theory that is remarkably similar to the familiar theory of knot diagrams for classical knots and links. As a result, it is possible to use a mixture of geometric and combinatorial topology to study virtual knots. There are many interesting phenomena and it is the intent of this talk to introduce some of these and to show how the Jones polynomial and its relatives fit into the virtual context.

#### Number theory and the circle packings of Apollonius | Peter Sarnak

Langenhop Lecture | 2012

Abstract.

Like many problems in number theory, the questions that arise from packing the plane with mutually tangent circles are easy to formulate but difficult to answer. We will explain the basic features of such integral packings and how modern tools from number theory, group theory (symmetries) and combinatorics are being used to answer some of these old questions.

Peter Sarnak is a member of the permanent faculty at the School of Mathematics of the Institute for Advanced Study and has been Eugene Higgins Professor of Mathematics at Princeton University since 2002. He is a member of the National Academy of Sciences (USA) and a Fellow of the Royal Society (UK). He received numerous awards including the Polya Prize (1998) and the Frank Nelson Cole Prize (2005). Professor Sarnak’s interest in mathematics is wide-ranging. He has made major contributions to number theory, analysis, combinatorics and mathematical physics. Professor Sarnak is a colorful and engaging speaker, with a broad and deep command of a wide range of mathematical subjects, and an unsurpassed ability to convey the historical context and the big-picture significance of mathematical ideas.