Department of

# Mathematics

Seminar Calendar
for events the day of Monday, October 21, 2019.

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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 21, 2019

3:00 pm in 441 Altgeld Hall,Monday, October 21, 2019

#### Topological Data Analysis: Theory and Applications

###### Daniel Carmody (UIUC Math)

Abstract: There are two algorithms which form the backbone of many applications of modern topological data analysis: the Mapper algorithm (Singh, Memoli, Carlsson), and persistent homology (Zomorodian, Carlsson). In this talk I'll introduce both algorithms, talk about the homotopy theory behind them, and give an application of each.

3:00 pm in 243 Altgeld Hall,Monday, October 21, 2019

#### Categories of equivariant bifurcation problems

###### Stef Klajbor-Goderich (Illinois)

Abstract: We present a framework for studying equivariant bifurcation from relative equilibria of dynamical systems with Lie group symmetries. We will explain how equivariant bifurcation problems from relative equilibria are objects of a category internal to the category of topological abelian groups, or equivalently they are part of a $2$-term chain complex of topological abelian groups. This category is topologically equivalent to a category of equivariant bifurcation problems from "honest" equilibria. Thus, generic equivariant bifurcation problems from relative equilibria are equivalent to generic equivariant bifurcation problems from equilibria. We conclude with some observations on one way an analogous approach to Hamiltonian bifurcation problems could proceed.

5:00 pm in 243 Altgeld Hall,Monday, October 21, 2019

#### Dixmier Trace

###### Haojian Li

Abstract: Diximer traces, heat kernel, and Zeta functions.