We meet Thursdays at 2:50–3:50 pm in Whitney Hall 100E. This semester's organizers are James Hyde and Lorenzo Ruffoni. 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.

• January 23rd
  Organizational meeting, meet in WH 100E at 2:50pm

• January 30th
  Speaker: Matthew Zaremsky (University at Albany)
  Title: Progress around the Boone-Higman conjecture

  Abstract: The Boone-Higman conjecture (1973) predicts that every finitely generated group with solvable word problem embeds in a finitely presented simple group. There has been a flurry of recent activity around this conjecture, in particular relating it to the family of so called twisted Brin-Thompson groups. In this talk I will give some background on the conjecture, give a gentle introduction to twisted Brin-Thompson groups, and then discuss various recent results of mine, including some joint with combinations of Jim Belk, Collin Bleak, Francesco Fournier-Facio, James Hyde, and Francesco Matucci.
  

• February 6th
  Problem session
  

• February 13th
  No seminar
  

• February 20th
  No seminar
  

• February 27th
  Speaker: Valentina Zapata Castro (University of Virginia)
  Title: Monoidal complete Segal spaces

  Abstract: Viewing a monoid as a category with a single object allows us to encode the binary operation using the properties of composition and associativity inherent in any category. In this talk, we use this idea to explore the relationship between $(\infty,1)$-categories with a monoidal structure and $(\infty,2)$-categories with one object. This exploration relies on the model structure of simplicial and $\Theta_2$-spaces. The talk is designed to be self-contained, requiring no prior knowledge of the aforementioned categories.
  

• March 6th
  Speaker: Inhyeok Choi (Cornell University)
  Title: Genericity of pseudo-Anosovs and quasi-isometries

  Abstract: In this talk, I will explain a recent result that pseudo-Anosov mapping classes are generic in every Cayley graph of mapping class groups. If time permits, I will also explain why this strategy goes well with quasi-isometries and implies genericity of Morse elements for groups quasi-isometric to (many) 3-manifold groups and special cubical groups.
  

• March 13th
  Spring break

• March 20th
  Peter Hilton Memorial Lecture

• March 27th
  Speaker: Colby Kelln (Cornell University)
  Title: Coning off a hyperbolic manifold with totally geodesic boundary

  Abstract: Let $M$ be a compact hyperbolic manifold with totally geodesic boundary. If the injectivity radius of $\partial M$ is larger than an explicit function of the normal injectivity radius of $\partial M$, we show there is a negatively curved metric on the space obtained by coning each boundary component of $M$ to a point. Moreover, we give explicit geometric conditions under which a locally convex subset of $M$ gives rise to a locally convex subset of the cone-off. Group-theoretically, we conclude that the fundamental group of the cone-off is hyperbolic and the $\pi_1$-image of the locally convex subset is a quasi-convex subgroup.
  

• April 3rd
  Speaker: Theodore Weisman (University of Michigan)
  Title: Anosov representations of cubulated hyperbolic groups

  Abstract: An Anosov representation of a hyperbolic group $\Gamma$ is a representation which quasi-isometrically embeds $\Gamma$ into a semisimple Lie group - say, SL(d, R) - in a way which imitates the behavior of a convex cocompact group acting on a hyperbolic metric space. It is unknown whether every linear hyperbolic group admits an Anosov representation. In this talk, I will discuss joint work with Sami Douba, Balthazar Flechelles, and Feng Zhu, which shows that every hyperbolic group that acts geometrically on a CAT(0) cube complex admits a 1-Anosov representation into SL(d, R) for some d. Mainly, the proof exploits the relationship between the combinatorial/CAT(0) geometry of right-angled Coxeter groups and the projective geometry of a convex domain in real projective space on which a Coxeter group acts by reflections.
  

• April 10th
  Speaker: Marco Volpe (University of Toronto)
  Title: Fiberwise simple homotopy theory

  Abstract: Simple homotopy theory is, roughly speaking, the study of finite CW-complexes up to collapses and expansions. From its early stages, it has been observed that simple homotopy types are deeply connected to K-theory. This connection is realized through Wall's finiteness obstruction for finitely dominated complexes and the Whitehead torsion of a homotopy equivalence between finite complexes. One of Waldhausen's main contributions ('83) to simple homotopy theory was to incorporate both Wall's obstruction and the Whitehead torsion in the study of assembly maps in K-theory. Later on, Dwyer-Weiss-Williams ('03) have introduced “fiberwise” assembly maps associated to fibrations over a fixed base space, thereby providing a framework for understanding simple homotopy types varying in families.

  In this talk, we introduce a novel perspective on fiberwise assembly maps, developed via the infinity-category of sheaves of spectra on a topological space. Using this approach, we are able to simultaneously generalize both the recently announced (but as yet unpublished) work of Bartels-Efimov-Nikolaus and the topological Dwyer-Weiss-Williams index theorem ('03).

  This is a joint work with Maxime Ramzi and Sebastian Wolf.
  

• April 17th
  Speaker: Sayantika Mondal (CUNY)
  Title: TBA

  Abstract: TBA
  

• April 24th
  Speaker: Kasia Jankiewicz (UC Santa Cruz / IAS)
  Title: TBA

  Abstract: TBA
  

• May 1st
  Speaker: TBA (Institution)
  Title: TBA

  Abstract: TBA