Department of

Mathematics


Seminar Calendar
for Math 499: Introduction to Graduate Mathematics events the year of Sunday, September 24, 2017.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, January 23, 2017

4:00 pm in 245 Altgeld Hall,Monday, January 23, 2017

Problem-solving, question-asking and knowledge-finding

Bruce Reznick (Department of Mathematics, University of Illinois)

Abstract: Three of the most important activities that researchers perform are listed in the title. I will talk about practical techniques for improving your skills in these areas, using specific examples of mathematics from my own work and the work of my graduate students. My intention that most members of the audience will see at least a few objects which resonate with their own mathematical interests.

Monday, January 30, 2017

4:00 pm in 245 Altgeld Hall,Monday, January 30, 2017

What is a root system?

William Haboush (Department of Mathematics, University of Illinois)

Monday, February 6, 2017

4:00 pm in 245 Altgeld Hall,Monday, February 6, 2017

Some classical and exotic ruin problems

Shu Li (Department of Mathematics, University of Illinois)

Monday, February 13, 2017

4:00 pm in 245 Altgeld Hall,Monday, February 13, 2017

Geometric properties of Banach spaces and embeddability of graphs

Denka Kutzarova (Department of Mathematics, University of Illinois)

Monday, February 20, 2017

4:00 pm in 245 Altgeld Hall,Monday, February 20, 2017

Stuck in Traffic

Richard Sowers (Department of Mathematics, University of Illinois)

Abstract: Used Uber or Lyft lately? Been in a traffic jam lately? There is an increasing amount of interest and data in making 'cities' and 'mobility' smart. We take a look at some data and data reduction problems which we have been looking at for the past several months. We outline some current and new challenges. This is work with Professor Dan Work of Civil and Environmental Engineering, the PI4 program, and the IGL program.

Monday, February 27, 2017

4:00 pm in 245 Altgeld Hall,Monday, February 27, 2017

Algebra, Combinatorics, Geometry

Hal Schenck (Department of Mathematics, University of Illinois)

Abstract: I'll give an overview of the spectacular success of algebraic methods in studying problems in discrete geometry and combinatorics. First we'll discuss the face vector (number of vertices, edges, etc.) of a convex polytope and recall Euler's famous formula for polytopes of dimension 3. Then we'll discuss graded rings, focusing on polynomial rings and quotients. Associated to a simplicial polytope P (every face is "like" a triangle) is a graded ring called the Stanley-Reisner ring, which "remembers" everything about P, and gives a beautiful algebra/combinatorics dictionary. I will sketch Stanley's solution to a famous conjecture using this machinery, and also touch on connections between P and toric varieties, which are objects arising in algebraic geometry.

Monday, March 6, 2017

4:00 pm in 245 Altgeld Hall,Monday, March 6, 2017

Stability, Eigenvalues and Index Theorems

Jared Bronski (Department of Mathematics, University of Illinois)

Monday, March 13, 2017

4:00 pm in 245 Altgeld Hall,Monday, March 13, 2017

Farey statistics and applications

Florin Boca (Department of Mathematics, University of Illinois)

Monday, March 27, 2017

4:00 pm in 245 Altgeld Hall,Monday, March 27, 2017

Teleportation

Marius Junge (Department of Mathematics, University of Illinois)

Abstract: Teleportation is real, and has a clear mathematical explanation. Don't worry, nobody will be 'beamed up' and then 'lost in space' during this talk. Instead, we will study the nice collection of matrices responsible for teleportation and superdense coding. This will required us to dive into some aspects of quantum mechanics. The aim of this talk is to understand that there is plenty of abstract mathematics to be discovered in the interface of operator algebra theory and quantum information theory.

Monday, April 3, 2017

4:00 pm in 245 Altgeld Hall,Monday, April 3, 2017

Mobius transformations in Biology

Zoi Rapti (Department of Mathematics, University of Illinois)

Abstract: In this talk I will first introduce a few compartmental models based on differential equations that describe biological phenomena, such as animal dispersion and epidemics. I will then review the Mobius transformation and its properties. Finally, I will explain how such transformations arise in the stability analysis of steady states in the models. This is joint work with Jared Bronski.

Monday, April 10, 2017

4:00 pm in 245 Altgeld Hall,Monday, April 10, 2017

Vector bundles

Steve Bradlow (Department of Mathematics, University of Illinois)

Abstract: This will be an introductory talk. The goal is to give you an idea what vector bundles (or more generally fiber bundles) are and where they arise naturally.

Monday, April 17, 2017

4:00 pm in 245 Altgeld Hall,Monday, April 17, 2017

No lecture today

(Department of Mathematics, University of Illinois)

Monday, April 24, 2017

4:00 pm in 245 Altgeld Hall,Monday, April 24, 2017

Some algorithmic problems for presentations of groups

Sergei Ivanov (Department of Mathematics, University of Illinois)

Monday, August 28, 2017

4:00 pm in 245 Altgeld Hall,Monday, August 28, 2017

Organizational Meeting

Abstract: We will have a brief meeting about the semester plans for Math 499.

Monday, September 11, 2017

4:00 pm in 245 Altgeld Hall,Monday, September 11, 2017

To Be Announced

Alexandru Zaharescu   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Monday, September 18, 2017

4:00 pm in 245 Altgeld Hall,Monday, September 18, 2017

From Brownian motion to Levy processes

Renming Song   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: In this talk, I will briefly introduce Brownian motion and Levy processes, and their connections to analysis and PDE's.

Monday, September 25, 2017

4:00 pm in 245 Altgeld Hall,Monday, September 25, 2017

Rigidity in orbit equivalence via cost

Anush Tserunyan   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: The talk is tailored around the following basic question: Let $\mathbb{F}_n$↷$[0,1]$ and $\mathbb{F}_m$↷$[0,1]$ be free actions of the free groups on $n$ and $m$ generators and assume that these actions preserve the Lebesgue measure and are ergodic (a bunch of words you're not supposed to know—ignore). If these actions produce the same orbits (i.e. their orbit equivalence relations are equal), must it be that $n = m$? This is an instance of the more general question: how much of the group is "remembered" by the orbit equivalence relations of its free actions? The phenomenon of a weaker notion "remembering" a stronger one is referred to as rigidity. We will describe the answer to the initial question (due to D. Gaboriau) by introducing an invariant called cost, which is tied to measurable graphs and combinatorics, and even ideas from homology theory. I will only assume familiarity with the words graph and measure.

Monday, October 2, 2017

4:00 pm in 245 Altgeld Hall,Monday, October 2, 2017

How to recognize a metric space

Jeremy Tyson   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: An embedding of one metric space $X$ into another metric space $Y$ is a one-to-one continuous map with continuous inverse. We fix the target space $Y$, which may be a finite-dimensional Euclidean space or some other normed vector space. Natural classes of embeddings include isometric embeddings (distances are exactly preserved) and bi-Lipschitz embeddings (distances are distorted by at most a fixed multiplicative constant). In this talk, we'll discuss the existence of embeddings within a fixed class into a fixed target space. For instance, which metric spaces admit an isometric embedding into a finite-dimensional Euclidean space? To indicate the subtlety of the problem, note that every metric space with at most three points embeds isometrically in the plane, but there exist four-point metric spaces which do not embed isometrically into any Hilbert space. Rademacher's theorem on the almost everywhere differentiability of Lipschitz functions plays a starring role. We'll highlight the use of Rademacher-type differentiation theorems for Lipschitz mappings of metric measure spaces in the proof of bi-Lipschitz nonembeddability theorems. We'll also discuss several recent bi-Lipschitz embedding theorems proved by current and former graduate students in this department.

Monday, October 9, 2017

4:00 pm in 245 Altgeld Hall,Monday, October 9, 2017

Lie theory beyond Lie groups

Rui Fernandes   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: Symmetries of differential equations, symmetries of geometric structures (e.g., Riemannian metrics, symplectic stuctures, complex structures), symmetries of algebraic equations, etc., are classically described by Lie theory, which is the study of groups equipped with a smooth structure and their actions on manifolds. In recent times we have came to realize that in many situations one needs the more general concept of a Lie groupoid. This lecture will be a gentle introduction to Lie groupoids and some of their applications.

Monday, October 16, 2017

4:00 pm in 245 Altgeld Hall,Monday, October 16, 2017

To Be Announced

Partha Dey   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Monday, October 23, 2017

4:00 pm in 245 Altgeld Hall,Monday, October 23, 2017

Fractal solutions of dispersive PDE

Burak Erdoğan   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: We will discuss the fractal solutions of linear and nonlinear dispersive PDE such as the Schrodinger's equation and Korteweg de Vries equation.

Monday, October 30, 2017

4:00 pm in 245 Altgeld Hall,Monday, October 30, 2017

Symplectic non-squeezing and Beltrami equation

Alexander Tumanov   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: Gromov's Non-Squeezing Theorem is a remarkable result in symplectic geometry. It says that the ball $B^{2n}(r)$ of radius $r$ in ${\mathbb R}^{2n}$ can be symplectically embedded in the "cylinder" $B^2(R)\times {\mathbb R}^{2n-2}$ of radius $R$ only if $r\le R$. The proof uses so called J-complex (pseudoholomorphic) curves. We will describe a construction of J-complex disks based on the classical scheme for solving the Beltrami equation in complex analysis. We will discuss related results and open problems.

Monday, November 6, 2017

4:00 pm in 245 Altgeld Hall,Monday, November 6, 2017

Asymptotically optimal shapes: the drum with lowest n-th frequency, and the ellipse enclosing the most lattice points

Rick Laugesen   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: What shape of domain minimizes the n-th energy level (frequency) of the Laplacian, for large n? How is that connected to lattice point counting in ellipses? And why do right triangles behave differently?

Monday, November 13, 2017

4:00 pm in 245 Altgeld Hall,Monday, November 13, 2017

Signed Laplacians, What Are They Good For?

Lee DeVille   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: We will present results on the eigenvalues of the Laplacians of graphs that have (possibly) negatively-weighted edges, and motivate these results using models of opinion formation on social networks.

Monday, November 27, 2017

4:00 pm in 245 Altgeld Hall,Monday, November 27, 2017

Problem-solving, question-asking and knowledge-finding

Bruce Reznick   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: Three of the most important activities that researchers perform are listed in the title. I will talk about practical techniques for improving your skills in these areas, using specific examples of mathematics from my own work and the work of my graduate students. My intention that most members of the audience will see at least a few objects which resonate with their own mathematical interests.

Monday, December 4, 2017

4:00 pm in 245 Altgeld Hall,Monday, December 4, 2017

Discrete Differential Geometry

Anil Hirani   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: An overview of discrete differential geometry.