Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, February 5, 2019.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, February 5, 2019

12:00 pm in 243 Altgeld Hall,Tuesday, February 5, 2019

Asymptotics of the expected diameter of translation surfaces

Anja Randecker (U Toronto)

Abstract: For the hyperbolic structure on a Riemann surface, Mirzakhani has proven asymptotics of the expected diameter for large genus surfaces. An abelian differential equips a Riemann surface with a translation structure. In joint work with Howard Masur and Kasra Rafi, we prove asymptotics for large genus translation surfaces of area 1. Unlike in the case of hyperbolic surfaces, the expected diameter goes to zero as the genus goes to infinity.

1:00 pm in 345 Altgeld Hall,Tuesday, February 5, 2019

Local Keisler Measures and NIP Formulas

Kyle Gannon (Notre Dame)

Abstract: The connection between finitely additive probability measures and NIP theories was first noticed by Keisler. Around 20 years later, the work of Hrushovski, Peterzil, Pillay, and Simon greatly expanded this connection. Out of this research came the concept of generically stable measures. In the context of NIP theories, these particular measures exhibit stable behavior. In particular, Hrushovski, Pillay, and Simon demonstrated that generically stable measures admit a natural finite approximation. In this talk, we will discuss generically stable measures in the local setting. We will describe connections between these measures and concepts in functional analysis as well as show that this interpretation allows us to derive a local approximation theorem.

2:00 pm in 243 Altgeld Hall,Tuesday, February 5, 2019

Fractalizers

Florian Pfender (University of Colorado Denver Math)

Abstract: A graph $H$ is a fractalizer if every graph $G$ maximizing the number of induced copies of $H$ is an iterated balanced blow-up of $H$. Fox, Hao and Lee, and independently Yuster, showed that almost every graph is a fractalizer considering random graphs. Nevertheless, no non-trivial explicit examples of fractalizers are known. We show that the cycle $C_5$ is almost a fractalizer, and conjecture that all longer cycles are fractalizers.

3:00 pm in 243 Altgeld Hall,Tuesday, February 5, 2019

Non-reduced Parabolic Group Schemes, II

William Haboush (UIUC Math)

4:05 pm in 243 AH,Tuesday, February 5, 2019

Backprop in NN and AD cont'd

George Francis   [email] (University of Illinois at Urbana)

Abstract: I will finish presenting some items in the handout last week. In particular I hope to explain just how Trask's updating the weights in his program for a machine to learn XOR might be derived from Pearlmutter&Siskind's reverse automatic differentiation recipe. This won't take the entire time, and I hope to answer questions and ask a few myself. There will no new items introduced and the seminar may end early. The temperature is forecasts to be 53F, but with showers.