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.

• February 15th
  Speaker: Sebastian Hurtado (Yale University)
  Title: Groups with full Limit Set vs Lattices

  Abstract: We show the existence of an (infinitely generated) discrete subgroup of a Lie group (such as SL_n(R)) that has full limit set in its (Furstenberg) boundary and which is not a lattice, we also discuss the possibility of whether this is possible for finitely generated groups. All notions will be explained. Based on work in progress with Subhadip Dey.
  

• February 22nd
  Speaker: Nima Hoda (Cornell University)
  Title: Tree of graph boundaries of hyperbolic groups

  Abstract: Regular trees of graphs are inverse limits of particularly simple inverse systems of finite graphs. They form a 1-dimensional subclass of the Markov compacta: a class of finitely describable inverse limits of simplicial complexes, which includes all boundaries of hyperbolic groups. I will discuss upcoming joint work with Jacek Swiatkowski in which we use Bowditch's canonical JSJ decomposition to characterize the 1-ended hyperbolic groups whose boundaries are (regular) trees of graphs.
  

• February 29th
  Speaker: Xin Li (University of Glasgow) (virtual talk)
  Title: Ample groupoids, topological full groups, algebraic K-theory spectra and infinite loop spaces

  Abstract: Topological groupoids describe orbit structures of dynamical systems by capturing their local symmetries. The group of global symmetries, which are pieced together from local ones, is called the topological full group. This construction gives rise to new examples of groups with very interesting properties, solving outstanding open problems in group theory. This talk is about a new connection between groupoids and topological full groups on the one hand and algebraic K-theory spectra and infinite loop spaces on the other hand. Several applications will be discussed. Parts of this connection already feature in work of Szymik and Wahl on the homology of Higman-Thompson groups.
  

• March 7th
  No seminar this week (spring break)

• March 14th
  Speaker: Lucas Williams (Binghamton University)
  Title: Periodic Points and Equivariant Parameterized Cobordism

  Abstract: In this talk we investigate invariants that count periodic points of a map. Given a self map $f$ of a compact manifold we could detect $n$-periodic points of $f$ by computing the Reidemeister trace of $f^n$ or by computing the equivariant Fuller trace. In 2020 Malkiewich and Ponto showed that the collection of Reidemeister traces of $f^k$ for varying $k|n$ and the equivariant Fuller trace are equivalent as periodic point invariants, and they conjecture that for families of endomorphisms the Fuller trace will be a strictly richer invariant for $n$-periodic points.

  In this talk we will explain our new result which confirms Malkiewich and Ponto's conjecture. We do so by proving a new Pontryagin-Thom isomorphism between equivariant parameterized cobordism and the spectrum of sections of a particular parametrized spectrum and using this result to carry out geometric computations.
  

• March 21st
  Speaker: Lei Chen (University of Maryland)
  Title: TBA

  Abstract: TBA
  

• March 28th
  Speaker: Mark Pentigore (University of Virginia)
  Title: TBA

  Abstract: TBA
  

• April 4th
  Speaker: Giuseppe Martone (Sam Houston State University)
  Title: TBA

  Abstract: TBA
  

• April 11th
  PETER HILTON MEMORIAL LECTURE
  SPECIAL TIME AND LOCATION: April 11, 3pm, Lecture Hall 009
  Speaker: Alex Eskin (University of Chicago)
  Title: Polygonal Billiards and Dynamics on Moduli Spaces

  Abstract: Billiards in polygons can exhibit bizarre behavior, some of which can be explained by deep connections to several seemingly unrelated branches of mathematics. These include algebraic geometry, Teichmuller theory and ergodic theory on homogeneous spaces. The talk will be an introduction to these ideas, aimed at a general mathematical audience.
  

• April 18th
  Speaker: Alex Wright (University of Michigan)
  Title: TBA

  Abstract: TBA
  

• April 25th
  No seminar this week (Tuesday classes meet)

• May 2nd
  Speaker: Zhouli Xu (University of California San Diego)
  Title: TBA

  Abstract: TBA