Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, February 13, 2018.

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Tuesday, February 13, 2018

11:00 am in 345 Altgeld Hall,Tuesday, February 13, 2018

Factorization homology and topological Hochschild cohomology of Thom spectra

Inbar Klang (Stanford)

Abstract: By a theorem of Lewis, the Thom spectrum of an n-fold loop map to BO is an E_n-ring spectrum. I will discuss a project studying the factorization homology and the E_n topological Hochschild cohomology of such Thom spectra, and talk about some applications, such as computations, and a duality between topological Hochschild homology and cohomology of certain Thom spectra. Time permitting, I will discuss connections to topological field theories. This talk will include an introduction to factorization homology via labeled configuration spaces.

1:00 pm in 345 Altgeld Hall,Tuesday, February 13, 2018

Topological dimension through the lens of Baire category

Anush Tserunyan (Illinois Math)

Abstract: In 1913, Brouwer proved that the topological dimension of $\mathbb{R}^n$ is $n$, which implies that there is no continuous injection of $\mathbb{R}^{n+1}$ into $\mathbb{R}^n$. More recently, Izzo and Li wondered if the last statement survives when the requirement of injectivity is relaxed to being injective on a large set. They showed in 2013 that the answer is negative when the largeness is measure-theoretic, i.e. when the continuous function is required to be injective only on a conull set. However, they conjectured that the answer should be positive for the notion of largeness provided by Baire category, namely: there does not exist a continuous function $\mathbb{R}^{n+1} \to \mathbb{R}^n$ that is injective on a comeager set. We will discuss this conjecture and its dramatic (for the speaker) resolution.

3:00 pm in 243 Altgeld Hall,Tuesday, February 13, 2018

A noncommutative McKay correspondence

Chelsea Walton (UIUC)

Abstract: The aim of this talk is two-fold-- (1) to recall the classic McKay correspondence in the commutative/ classic setting for group actions on polynomial rings, and (2) to present a generalization of the McKay correspondence in the noncommutative/ quantum setting of Hopf algebra actions on noncommutative analogues of polynomial rings. Many notions will be defined from scratch during the talk and pre-talk, and useful examples will be provided during the pre-talk.

3:00 pm in 241 Altgeld Hall,Tuesday, February 13, 2018

Proportional Choosability: A New List Analogue of Equitable Coloring

Jeffrey Mudrock (Department of Applied Mathematics, Illinois Institute of Technology)

Abstract: The study of equitable coloring began with a conjecture of Erdős in 1964, and it was formally introduced by Meyer in 1973. An equitable $k$-coloring of a graph $G$ is a proper $k$-coloring of $G$ such that the sizes of the color classes differ by at most one. In 2003 Kostochka, Pelsmajer, and West introduced a list analogue of equitable coloring, called equitable choosability. Specifically, given lists of available colors of size $k$ at each vertex of a graph $G$, a proper list coloring is equitable if each color appears on at most $\lceil |V(G)|/k \rceil$ vertices. Graph $G$ is equitably $k$-choosable if such a coloring exists whenever all the lists have size $k$. In this talk we introduce a new list analogue of equitable coloring which we call proportional choosability. For this new notion, the number of times we use a color must be proportional to the number of lists in which the color appears. Proportional $k$-choosability implies both equitable $k$-choosability and equitable $k$-colorability, and the graph property of being proportionally $k$-choosable is monotone. We will discuss proportional choosability of graphs with small order, completely characterize proportionally 2-choosable graphs, and illustrate some of the techniques we have used to prove results. This is joint work with Hemanshu Kaul, Michael Pelsmajer, and Benjamin Reiniger.

4:00 pm in Illini Hall 1,Tuesday, February 13, 2018

Introduction to Cohomological Field Theory

Sungwoo Nam (UIUC)

Abstract: Cohomological field theory(CohFT) was first introduced by Kontsevich and Manin to organize the data of Gromov-Witten theory and quantum cohomology into a list of axioms. Although its main model is Gromov-Witten theory, it has been also successful dealing with problems outside of Gromov-Witten theory. In this talk, I will introduce the notion of CohFT, Givental-Telemanís classification of semisimple CohFTs and some concrete examples. Basic knowledge of Gromov-Witten theory will be helpful, but it is not assumed in this talk.