Department of

Mathematics


Seminar Calendar
for Graduate Student Colloquium events the year of Friday, April 21, 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.
      March 2017             April 2017              May 2017      
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                        30                                         

Wednesday, February 1, 2017

4:00 pm in 245 Altgeld Hall,Wednesday, February 1, 2017

Application of Stein's method in Spin Glass Systems

Tayyab Nawaz (UIUC Math)

Abstract: In 1960’s, Stein introduced a method to bound the distance between two probability distributions using a specific probability metric. For a large complex stochastic system, mean field theory is considered as a starting point to study its physical properties. In mean field theory we assume that each particle interacts with the rest of the system in a homogeneous 'average' way. In this talk, I will discuss how Stein’s method and mean field theory are used to study the energy minimization problem for spin-glass models in statistical mechanics. I will also discuss the idea of optimal Monte Carlo algorithms for solving energy minimization problem and related open problems.

Wednesday, March 1, 2017

4:00 pm in 245 Altgeld Hall,Wednesday, March 1, 2017

Convexity and curvature in space-time geometry

William Karr (UIUC Math)

Abstract: A space-time is said to satisfy $\mathcal{R} \geq K$ if the sectional curvatures of spacelike planes are bounded below by $K$ and the sectional curvatures of timelike planes are bounded above by $K$. Similarly, one can define $\mathcal{R} \leq K$ by reversing the inequalities. These conditions naturally generalize the notion of curvature bounds for Riemannian manifolds to the Lorentzian setting. We describe how these conditions can be used to construct two types of convex functions. We then describe two geometric consequences of space-times supporting these functions. One result establishes geodesic connectedness for a class of space-times satisfying $\mathcal{R} \geq 0$. Another result rules out submanifolds associated with black holes and wormholes in certain domains of space-times satisfying $\mathcal{R} \leq 0$. This is joint work with Stephanie Alexander.

Monday, March 27, 2017

2:00 pm in 245 Altgeld Hall,Monday, March 27, 2017

A Mathematical View of Biology and Diversification

Vanessa Rivera-Quiñones (Illinois Math)

Abstract: Have you ever wondered about the meaning of the phrase "survival of the fittest"? To an evolutionary biologist, fitness simply means reproductive success and reflects how well an organism is adapted to its environment. How systems adapt over time has been a central question in Biology and other Life-Sciences. While I will focus on the theory of Adaptive Dynamics, there are many areas of mathematics that have contributed to our understanding of adaptation. In this talk, I will give an overview of how we can use mathematical models to understand adaptation as an evolutionary process and its relationship to creating and preserving diversity. If time permits, I will also address the connections between this theory and my own research in disease modeling.

Wednesday, April 19, 2017

4:00 pm in 245 Altgeld Hall,Wednesday, April 19, 2017

An introduction to enumerative geometry

Yun Shi (UIUC Math)

Abstract: One important question in enumerative geometry concerns how many curves there are on a Calabi-Yau 3-fold. In this talk, I will present one of the approaches to the classical problem: there are 27 lines on a smooth cubic surface. Motivated by this approach, we will discuss the modern set-up to answer the curve counting questions, in particular its applications to Donaldson-Thomas theory.

Wednesday, September 6, 2017

4:00 pm in 245 Altgeld Hall,Wednesday, September 6, 2017

Truncation in Generalized Series Fields

Santiago Camacho (Illinois Math)

Abstract: Taylor polynomials are very useful for approximating analytic functions, nevertheless there is increasing interest in understanding so-called analyzable functions that are not necessarily analytic. For this reason fields of generalized series (Hahn fields) that extend Laurent series have been studied. A natural analogue of Taylor or Laurent polynomials in these series fields are truncated series. We explore some of the stability properties of truncation closed subsets of Hahn Fields.

4:00 pm in 245 Altgeld Hall,Wednesday, September 6, 2017

Truncation in Generalized Series Fields

Santiago Camacho (UIUC Math)

Abstract: Taylor polynomials are very useful for approximating analytic functions, nevertheless there is increasing interest in understanding so-called analyzable functions that are not necessarily analytic. For this reason fields of generalized series (Hahn fields) that extend Laurent series have been studied. A natural analogue of Taylor or Laurent polynomials in these series fields are truncated series. We explore some of the stability properties of truncation closed subsets of Hahn Fields.

Wednesday, October 4, 2017

4:00 pm in 343 Altgeld Hall,Wednesday, October 4, 2017

Enumerative Geometry and the Schubert Problem

Anna Weigandt (UIUC)

Abstract: How many lines meet four fixed lines in three space? This question has its roots in classical enumerative geometry. We will discuss the answer to the Schubert problem from the perspective of geometry, symmetric function theory, and combinatorics. This talk will be accessible for beginning graduate students.

Monday, November 6, 2017

4:00 pm in 141 Altgeld Hall,Monday, November 6, 2017

Higher Categories: What's up with that?

Nima Rasekh

Abstract: Upcoming!

Wednesday, November 29, 2017

4:00 pm in 245 Altgeld Hall,Wednesday, November 29, 2017

Randomness in number theory

Junxian Li