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seminars:topsem

We meet **Thursdays** at **2:50–3:50 pm** in **Whitney Hall 100E**. This semester's organizer is Cary Malkiewich. The seminar has an announcement mailing list open to all.

Topics include: geometric group theory, differential geometry and topology, low-dimensional topology, algebraic topology, and homotopy theory.

**August 22nd**

Organizational meeting, meet in WH 100E at 2:50pm

**August 29th**

No seminar this week

**September 5th**

Speaker:**Ezekiel Lemann**(Binghamton University)

Title:**Scissors Automorphism Groups and Homological Stability***Abstract:*In this talk we will outline the proof of homological stability for scissors automorphism groups and highlight a number of consequences and related results. These include plus and group completion constructions for assembler K-theory, interpreting higher K-theory in terms of automorphism groups, and homology calculations for some scissors automorphism groups. The content of the talk is joint work with Kupers, Malkiewich, Miller, and Sroka.

**September 12th**

Speaker:**Kimball Strong**(Cornell University)

Title:**Strictification of $\infty$-groupoids***Abstract:*An $\infty$-groupoid is a mathematical object which generalizes a groupoid by possessing not just objects and morphisms, but also $2$-morphisms between morphisms, $3$-morphisms between $2$-morphisms, etc. Grothendieck conjectured that the category of $\infty$-groupoids up to homotopy was equivalent to the category of topological spaces up to homotopy, a still—unproven statement known as the “Homotopy Hypothesis.'' In this talk I will introduce a simpler object called a \textit{strict} $\infty$-groupoid, which encodes less information than an ordinary $\infty$-groupoid, but is easier to work with—much in the same way that homology groups are easier to work with than homotopy groups. I will then define a strictification functor that takes an ordinary $\infty$-groupoid and returns a strict $\infty$-groupoid, and prove that, up to homotopy, this functor can be used to encode the data of a topological space coalgebraically as a strict $\infty$-groupoid. Time permitting, I will discuss progress and open questions on generalizing this to $\infty$-categories.

**September 19th**

Speaker:**Chase Vogeli**(Cornell University)

Title:**The Galois-equivariant $K$-theory of finite fields***Abstract:*Abstract: Algebraic $K$-theory is an important invariant of rings defined using tools from homotopy theory. Recent progress in equivariant homotopy theory has enabled the study of equivariant algebraic $K$-theory for rings with actions by finite groups. In this talk, I will focus on the case of finite fields, where there is an action by their cyclic Galois groups. The nonequivariant $K$-groups of finite fields were computed by classical work of Quillen, and I will describe joint work with David Chan which extends this to a computation of the Galois-equivariant $K$-groups. In particular, we show the computation reduces to the well-studied coefficient groups of ordinary equivariant cohomology.

**September 26th**

Speaker:**Lorenzo Ruffoni**(Binghamton University)

Title:**TBA***Abstract:*TBA

**October 3rd**

No seminar this week (Rosh Hashanah/Fall break)

**October 10th**

Speaker:**Hanh Vo**(Arizona State University)

Title:**TBA***Abstract:*TBA

**October 17th**

Speaker:**Yu-Chan Chang**(Wesleyan University)

Title:**TBA***Abstract:*TBA

**October 24th**

Speaker:**Kate Ponto**(University of Kentucky)

Title:**TBA***Abstract:*TBA

**October 31st**

Speaker:**Danika Van Niel**(Binghamton University)

Title:**TBA***Abstract:*TBA

**November 7th**

Speaker:**Shuchen Mu**(Binghamton University)

Title:**TBA***Abstract:*TBA

**November 14th**

Speaker:**Ismael Sierra**(University of Toronto)

Title:**TBA***Abstract:*TBA

**November 21st**

Speaker:**Hari Rau-Murthy**(University of Rochester)

Title:**TBA***Abstract:*TBA

**November 28th**

No seminar this week (Thanksgiving break)

**December 5th**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

seminars/topsem.txt · Last modified: 2024/09/10 08:06 by malkiewich

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