Department of

# Mathematics

Seminar Calendar
for events the day of Friday, October 22, 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 22, 2021

3:00 pm in 243 Altgeld Hall,Friday, October 22, 2021

#### An introduction to equivariant motivic homotopy theory

###### Timmy Feng (UIUC Math)

Abstract: Equivariant motivic homotopy theory is the homotopy theory of motivic spaces and spectra with algebraic group actions. Following [Hoy17], I will introduce both the unstable and stable equivariant motivic homotopy ∞-category. I will also talk about the so called Ambidexterity Theorem which identifies the left and right adjoint of the pullback functor f* up to a suspension. Then I will show how to prove the Atiyah Duality by using the Ambidexterity and some other properties of these functors. [Hoy17] Marc Hoyois, The six operations in equivariant motivic homotopy theory.

4:00 pm in Altgeld Hall 347,Friday, October 22, 2021

#### The Alexander Polynomial, the Alexander Polynomial, and the Twisted Alexander Polynomial

###### Joseph Malionek (UIUC)

Abstract: The Alexander polynomial is a topological invariant of a space coming from a somewhat natural module structure on one of its covers. It was originally developed for knot exteriors, but since has been defined for more general topological spaces. This talk goes through the construction for knot exteriors, and then two levels of generalizations (As well as several examples). Some highlights: Covering spaces! Modules! T W I S T I N G. Familiarity with algebraic topology and a very small amount of module theory will be helpful.