Department of

# Mathematics

Seminar Calendar
for events the day of Friday, October 29, 2021.

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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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Friday, October 29, 2021

2:00 pm in 347 Altgeld Hall,Friday, October 29, 2021

#### Localization and Laplacians

###### Gayana Jayasinghe (UIUC)

Abstract: Localization can be broadly described as a phenomenon where certain integrands turn out to only be supported near special points. The classic result of this form is stationary phase. I will talk about different instances of localization and the analysis involved. I'll begin with stationary phase and move onto Atiyah Bott localization, the Duistermaat-Heckman theorem, and Witten deformation. For more on Witten deformation, check out the Graduate Geometry and Topology Seminar this week.

3:00 pm in 243 Altgeld Hall,Friday, October 29, 2021

#### Connections between motivic and classical homotopy theory

###### Johnson Tan (UIUC Math)

Abstract: In the first part of this talk we will motivate the construction of the stable motivic homotopy category over the complex numbers through a non-standard construction of the stable homotopy category. After some comparisons between the motivic and classical theory, we will introduce the Chow t-structure and explain how it relates to some chromatic theory.

4:00 pm in Altgeld Hall 347,Friday, October 29, 2021

#### Witten Deformation, or Turning Critical Points into Cohomology

###### Gayana Jayasinghe (UIUC)

Abstract: Witten deformed the de Rham complex to relate critical points to harmonic representatives of cohomology. I will explain this relationship, and sketch out Witten's proof of the Morse inequalities. I will then try and explain how these ideas have been developed on infinite dimensional spaces.