Department of

Mathematics


Seminar Calendar
for events the day of Friday, February 10, 2017.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, February 10, 2017

3:00 pm in 243 Altgeld Hall,Friday, February 10, 2017

The KP-CM correspondence

Matej Penciak (UIUC Math)

Abstract: In this talk I will describe how two seemingly unrelated integrable systems have an unexpected connection. I will begin with the classical story first worked out by Airault, McKean, and Moser. I will then describe a more modern interpretation of the relation due to Ben-Zvi and Nevins.

4:00 pm in 345 Altgeld Hall,Friday, February 10, 2017

On "Structurable equivalence relations" by R. Chen and A. Kechris: Characterization of elementary classes (3rd talk)

Anush Tserunyan (UIUC Math)

Abstract: In our previous talk, we proved that any elementary class of equivalence relations admits an invariantly injective universal element. This completes one direction of the characterization of elementary classes. In this third talk, we will prove the other direction of the characterization, as well as discuss other results of the paper if time permits.

4:00 pm in 241 Altgeld Hall,Friday, February 10, 2017

Opers and non-abelian Hodge theory

Georgios Kydonakis (UIUC Math)

Abstract: We will describe two different families of flat $G$-connections over a compact Riemann surface for a complex, simple, simply connected Lie group $G$. The first is the family of $G$-opers, which for $G=\text{SL(2}\text{,}\mathbb{C}\text{)}$ can be thought of as global versions of the locally defined second order Schrödinger operators. The second comes from a particular subfamily of solutions to the so-called $G$-Hitchin equations. The physicist Davide Gaiotto conjectured that for $G=\text{SL(}n\text{,}\mathbb{C}\text{)}$ the second family in a scaling limit converges to a limiting connection which has the structure of an oper. We will describe a proof of this conjecture. This is joint work with Olivia Dumitrescu, Laura Fredrickson, Rafe Mazzeo, Motohico Mulase and Andrew Neitzke.