Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, September 27, 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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Thursday, September 27, 2018

11:00 am in 241 Altgeld Hall,Thursday, September 27, 2018

#### Full-image p-adic Galois Representations and Galois Deformation Theory

###### Shiang Tang (Illinois Math)

12:30 pm in 464 Loomis,Thursday, September 27, 2018

#### Hecke Relations in Rational Conformal Field Theory

###### Jeffrey Harvey (U. of Chicago)

Abstract: Hecke operators that act on characters of rational conformal field theories are defined and we use these to show that many characters of different RCFTs are related by Hecke operators. These relations extend the previously studied Galois symmetry of the modular representations appearing in RCFT. Connections with modular linear differential equations will also be discussed.

2:00 pm in 241 Altgeld Hall,Thursday, September 27, 2018

#### alpha-odd continuation fractions

###### Claire Merriman (University of Illinois at Urbana-Champaign)

Abstract: Nakada’s alpha-expansions move from the regular continued fractions (alpha=1), Hurwitz singular continued fractions (obtained at alpha=little golden ratio), and nearest integer continued fractions (alpha=1/2). This talk will look at similar continued fraction expansions where all of the denominators are odd. I will describe how restricting the parity of the partial quotients changes the Gauss map and natural extension domain. This is join work with Florin Boca.

3:00 pm in 345 Altgeld Hall,Thursday, September 27, 2018

#### The Ruijsenaars-Schneider and 2D Toda lattice correspondence

###### Matej Penciak (UIUC)

Abstract: It has been known since the work of Airault, McKean, and Moser in 1977 that the time evolution of poles for meromorphic solutions to the Kadomtsev-Petviashvili (KP) equation are related to dynamics of Calogero-Moser (CM) particles. David Ben-Zvi and Tom Nevins proved a general result on a correspondence between the full KP and CM hierarchies in arXiv:math/0603720. Their approach is to identify the CM and KP phase spaces with algebro-geometric data on a cubic curve, and relate the two phase spaces via a Fourier-Mukai transform. In this talk I will describe ongoing work, joint with David and Tom, applying the same ideas to prove a correspondence between the Ruijsenaars-Schneider (RS) and 2D Toda lattice hierarchies. I will focus on giving an algebro-geometric description of the spectral curves of the RS system, the proof of which uses identities for theta functions known since the 19th century.

4:00 pm in 245 Altgeld Hall,Thursday, September 27, 2018

#### Fall Department Faculty Meeting

Abstract: The Fall Department Faculty Meeting will be held at 4 p.m. in 245 Altgeld Hall, followed by a reception in 239 Altgeld Hall.