Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, October 31, 2018.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, October 31, 2018

1:00 pm in 2 Illini Hall,Wednesday, October 31, 2018

#### Hodge theory and singularities II

###### Sungwoo Nam

Abstract: After motivating singularities, I’ll introduce Deligne's mixed Hodge structure, which, unlike pure Hodge structure, sees singularities. Then I’ll discuss(with examples of Riemann surfaces) how one can use it to study singularities. I’ll end by connecting it to an isolated singularity coming from a family, focusing on Lefschetz degeneration.

3:00 pm in 241 Altgeld Hall,Wednesday, October 31, 2018

#### $\ell^2$ Betti numbers of countable Borel equivalence relations: Part 1

###### Ruiyuan (Ronnie) Chen (UIUC Math)

Abstract: We will discuss Gaboriau's 2002 paper "Invariants $\ell^2$ de relations d'équivalence et de groupes" from a descriptive set-theoretic point of view. This first talk will consist of a survey of the main results, as well as a review of some relevant concepts from (ordinary and $\ell^2$) homology theory.

4:00 pm in 2 Illini Hall,Wednesday, October 31, 2018

#### Congruences of modular forms from an algebro-geometric perspective

###### Ningchuan Zhang (UIUC Math)

Abstract: In this talk, I’ll give an algebro-geometric explanation of congruences of normalized Eisenstein series following chapter 4 of Nicholas Katz’s paper “$p$-adic properties of modular schemes and modular forms”. The key idea in Katz’s paper is to establish a $p$-adic Riemann-Hilbert correspondence that can translate congruences of normalized Eisenstein series to that of continuous $\mathbb{Z}_p^\times$-representations in rank $1$ free $\mathbb{Z}_p$-modules. The latter is very easy to compute given that $\mathbb{Z}_p^\times$ is topologically cyclic when $p\neq 2$.

4:00 pm in 245 Altgeld Hall,Wednesday, October 31, 2018

#### Basics of Coding Theory and Some Applications

###### Xiao Li (UIUC Math)

Abstract: In this talk I will be presenting some basics of coding theory and some applications to error correcting code. I will then focus on algebraic coding theory and give some examples with interesting algebraic and combinatorial properties. If time permits, I will give some applications in distributed storage.