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: Atoroidal surface bundles with zero signature

  Abstract: Hyperbolic geometry has been a powerful tool in the study of manifold topology. Beyond the classical theory of surfaces, Thurston showed that the family of surface bundles over the circle is a rich source of hyperbolic 3-manifolds. In dimension 4, the correct analogue is given surface bundles over surfaces. In order for such a bundle to admit a hyperbolic metric, it needs to satisfy some conditions, such as being atoroidal and having zero signature. Surprisingly enough, the first examples of atoroidal surface bundles over surfaces were constructed only a few months ago by Kent-Leininger. In this talk I’ll explain why these examples also have zero signature, meaning that they could admit hyperbolic metrics. This is joint work in progress with J-F. Lafont and N. Miller.
  

• 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