Department of

# Mathematics

Seminar Calendar
for events the day of Monday, October 26, 2020.

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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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Monday, October 26, 2020

11:00 am in zoom,Monday, October 26, 2020

#### Real forms and Hamiltonian dynamics

###### Marine Fontaine (University of Antwerp)

Abstract: We present a theory of real forms for holomorphic Hamiltonian systems which behaves well under integrability: given a real analytic integrable system, one can (under some assumptions) complexify the system and obtain other real integrable systems on different real forms. These systems are dynamically different but they do share the same complexification. As an example, we explain how we can apply this theory and use hyperkähler geometry to find a compact integrable real form of the spherical pendulum on S2 x S2. This is based on joint work with P. Arathoon.

2:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Monday, October 26, 2020

#### An introduction to random walks in random environments

###### Jonathon Peterson (Purdue University)

Abstract: I will give an introduction to the model of random walks in random environments, paying particular attention to the one-dimensional case. I will give sketches of proofs for some of the basic results, including criteria for recurrence/transience, limiting velocity, and a central limit theorem.

3:00 pm in Zoom,Monday, October 26, 2020

#### Introduction to simplicial sets

###### Haoyuan Li (UIUC)

Abstract: This is an introduction to simplicial sets. I will first talk about the definition of simplicial sets and also some examples of simplicial sets. Then I will introduce the Kan complex and some of its properties. If time permits, I will talk a little bit about the homotopy groups of Kan complex. Please email vb8 at illinois dot edu for the zoom details.

5:00 pmMonday, October 26, 2020

#### Recovery

###### Marius Junge (UIUC Math)

Abstract: We will talk about Petz recovery maps, and new developments. Please email mjunge@illinois.edu for details.