Department of

Mathematics


Seminar Calendar
for events the day of Monday, December 4, 2017.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, December 4, 2017

3:00 pm in 141 Altgeld Hall,Monday, December 4, 2017

Oriented Ring Spectra and Formal Group Laws

Liz Tatum   [email] (UIUC)

Abstract: Each complex-oriented ring spectrum has a corresponding formal group law. I will discuss some properties of these formal group laws, and give some examples of how they are used for computations involving complex-oriented cohomology theories.

4:00 pm in 343 Altgeld Hall,Monday, December 4, 2017

Amenability of discrete groups and their actions

Kate Juschenko (Northwestern Math)

Abstract: The subject of amenability essentially begins in 1900's with Lebesgue. He asked whether the properties of his integral are really fundamental and follow from more familiar integral axioms. This led to the study of positive, finitely additive and translation invariant measure on reals as well as on other spaces. In particular the study of isometry-invariant measure led to the Banach-Tarski decomposition theorem in 1924. The class of amenable groups was introduced by von Neumann in 1929, who explained why the paradox appeared only in dimensions greater or equal to three, and does not happen when we would like to decompose the two-dimensional ball. In 1940's, M. Day formally defined a class of elementary amenable groups as the largest class of groups amenability of which was known to von Naumann. He asked whether there are other groups then that. Currently there are many groups that answer von Neumann-Day's question. However, in each particular case it is algebraically difficult to show that the group is not elementary amenable, and analytically difficult to show that it is amenable. The talk is aimed to discuss recent developments and approaches in the field. In particular, it will be shown how to prove amenability of all known non-elementary amenable groups using only one single approach. We will also discuss techniques coming from random walks of groups.

4:00 pm in 245 Altgeld Hall,Monday, December 4, 2017

Discrete Differential Geometry

Anil Hirani   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: An overview of discrete differential geometry.

5:00 pm in Altgeld Hall,Monday, December 4, 2017

Quantum Markov Seimgroups as Gradient Flows II

Li Gao   [email] (UIUC Math)

Abstract: We will continue to discuss Carlen and Maas' paper on gradient flow for quantum Markov Semigroup. We will talk about Fermionic and Bosonic Ornstein-Uhlenbeck semigroup as examples and also the connections to functional inequalities.