Department of

# Mathematics

Seminar Calendar
for events the day of Friday, October 1, 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 1, 2021

2:00 pm in Altgeld Hall,Friday, October 1, 2021

#### How to not do analysis

Abstract: Today we’ll be making simple problems as difficult as possible.

3:00 pm in 243 Altgeld Hall,Friday, October 1, 2021

#### On the Lichtenbaum-Quillen conjectures in algebraic K theory

###### Likun Xie (UIUC Math)

Abstract: Starting with some motivations and brief expositions on algebraic K theory, I’ll introduce some early important computations of algebraic K theory, including computations of K theory of finite fields and of rings of integers for which I will briefly outline the proofs. Then we’ll move on to K theory with finite coefficients of separably closed fields. With the motivation of recovering some information of K theory of an arbitrary field from its separable closure, we introduce a few versions of the Lichtenbaum-Quillen conjectures as descent spectrum sequences of etale Cohomology groups. If time permits, I’ll mention relation to motivic Cohomology that a key tool is some “motivic-to-K-theory” spectral sequence.

4:00 pm in Altgeld Hall 347,Friday, October 1, 2021

#### Counting the number of essential surfaces in a 3-manifold

###### Chaeryn Lee (UIUC)

Abstract: Essential surfaces play an important role in understanding the nature of 3-manifolds. A natural question that may arise is to see how many distinct essential surfaces a 3-manifold has. In this talk we will look at a certain algorithm that enables us to count the number of isotopy classes of essential surfaces in 3-manifolds. In particular, we will count such surfaces in terms of their Euler characteristic to construct its generating function and then present results about this series.