Purdue Topology Seminar

In Fall 2026, the Purdue Topology Seminar will be held on Wednesdays 10:30am - 11:30am Eastern time in BRNG B212 (if we meet in person) unless otherwise noted. If you want to be added to our email list please contact Shawn Cui (shawn.cui at purdue.edu) or Manuel Rivera (manuelr at purdue.edu). 

Some recorded talks may be found on our YouTube Channel.

 

Fall 2026

September 2 (in-person)

Jeremy Miller (Purdue)

Title: Nontriviality of the Morita classes

Abstract: I will describe work in progress with Kupers and Patzt on the nontriviality of the Morita classes for \(\mathrm{Aut}(F_n)\).

 

September 9 (in-person)

Kevin Piterman (Purdue)

Title: Spherical complexes associated to buildings 

Abstract: The Solomon–Tits theorem states that a spherical building of dimension d has the homotopy type of a wedge of d-spheres. One proof of this theorem uses the natural CAT(1) metric on the building, under which each apartment is isometric to a unit sphere. In this talk, we will see how the intrinsic geometry of a building can be used to show that certain natural complexes associated to it are spherical, and how these complexes relate to familiar constructions in the GL_n case. In particular, I will propose definitions of a common basis complex and a partial decomposition complex for an arbitrary spherical building. Using the intrinsic metric, we will show that these two complexes are homotopy equivalent and that the latter is highly connected. This is joint work with J. Shareshian and V. Welker.

 

September 16 (in-person)

Lucas Williams (Purdue)

Title: Invariants for Families of Periodic Points

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.

Time permitting, we will discuss how this homeomorphism of a manifold gives rise to an element of the kernel of the ghost map on \pi_1(-) of topological restriction homology.

 

September 23 (in-person)

Sarah Anderson (Purdue)

 

October 7 (in-person)

Miguel Barata (Purdue)

 

October 21 (in-person)

Matthew Scalamandre (Toronto) 

 

October 28 (in-person)

Sam Nariman (Purdue)

 

November 4 (online)

Thomas Willwacher (ETH Zurich) 

 

Purdue topology group: