Skip to main content
Department of Mathematics

Purdue Topology Seminar

In Spring 2026, the Purdue Topology Seminar will be held on Wednesdays 10:20am - 11:20am Eastern time in DSAI 1004 (when 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.

 

Spring 2026

January 14 (in-person)

Eric Samperton (Purdue)

Title: Obstruction theory and counting complexity

Abstract: For a fixed finite group G, I will explain what it is known about how hard it is to count group homomorphisms from another group Γ to G.  To make things precise, one must specify how Γ is encoded.  On one hand, if Γ is a finitely presented group, then the counting problem is #P-hard as soon as G is non-abelian.  This follows as an easy corollary of major results of Bulatov and Dalmau on the computational complexity of counting CSPs (constraint satisfaction problems).  On the other hand, if G is class 2 nilpotent and Γ is either a finite group provided via a multiplication table or the fundamental group of a triangulated 3-manifold, then there exist efficient algorithms to compute this count.  The tension between the two theorems is resolved by understanding how easy/hard it is to access a triangulation of the three skeleton of the Eilenberg-MacLane space K(Γ, 1) from the given encoding of Γ.

I will introduce all of the complexity theory necessary, and I will also give some motivations coming from topological quantum computing.  This talk is based on joint work with Armin Weiss.

 

January 21 (online)

Benjamin McMillan (IBS Center for Complex Geometry)

Title: Foliation surgeries and Godbillon-Vey spheres

Abstract: I define a general procedure extending smooth manifold surgery to foliations or Haefliger structures. Thus, starting with a foliated manifold, one may be able to obtain a new foliation on the underlying surgered manifold. There is one potential obstruction to this surgery, but when it vanishes, the surgery can be chosen so that foliation characteristic class numbers (e.g., from Godbillon-Vey classes) are unchanged. For foliations of large codimension (roughly half of the manifold dimension), the surgery obstructions are determined by the normal bundle of the foliation, and so may be dealt with directly.

I will give an application of this to foliations constructed by Thurston, to describe in each codimension \( q \) families of foliations on the sphere \( S^{2q+1} \) whose Godbillon-Vey class numbers surject to \( \R \). This gives a new description of a surjection \( \pi_{2q+1}(F\Gamma_{q}) \to \R \), where \( F\Gamma_{q} \) is the classifying space for normally-trivial foliations.

 

February 11 (in-person) 

Pierre Godfard (University of North Carolina)

Title: Rigidity of some quantum representations of mapping class groups via Ocneanu rigidity.

Abstract: The property (T) conjecture predicts that finite-dimensional unitary representations of mapping class groups $\mathrm{Mod}(S_g)$ for $g \geq 3$ are rigid (in the sense that they admit no infinitesimal deformations). While extensively studied for finite image representations, where it is known as the Ivanov conjecture, much less is known for infinite image representations.

We establish rigidity of quantum representations arising from SU(2) and SO(3) modular categories, for closed surfaces of genus $g\geq 7$ and at levels $\ell=p-2$ where $p\geq 5$ is prime. These are natural infinite image examples arising via the Reshetikhin-Turaev construction from unitary modular fusion categories.

Our strategy exploits Ocneanu rigidity, which asserts that quantum representations cannot be deformed within the set of quantum representations. We prove that any infinitesimal deformation necessarily remains quantum, hence is trivial. The proof combines fusion rules of modular functors with Hodge theory on twisted moduli spaces of curves--certain Kähler compact orbifolds whose fundamental groups are quotients of mapping class groups.

February 18 (online) 

Nicolas Guès (Paris 13) 

Title: A homotopy-theoretic approach to representation stability

Abstract: In a series of papers from the 2010s, Church, Ellenberg and Farb developed the notion of representation stability, aimed at understanding the asymptotic behavior of natural sequences of representations of the symmetric groups S_n, particularly those arising from homological invariants. Such phenomena typically occur for FI-modules, i.e., functors from FI (the category of finite sets and injections) to abelian groups.

In this talk, I will propose a homotopical refinement of representation stability: a derived version adapted to (co)FI-spaces. This viewpoint sheds light on how the phenomenon of representation stability can arise from the high (co)cartesianity of certain cubical diagrams. With this point of view, I will show how one can deduce polynomial growth results for the homotopy groups of ordered configuration spaces on closed manifolds, recover the best known bounds on their cohomology, and generalize stability results of Palmer concerning moduli spaces of submanifolds of a fixed manifold.

 

March 5 (in-person, 1:30-2:30 BRNG 1243)

Note this is a Thursday and a nonstandard location 

Jennifer Wilson (University of Michigan)

Title: PL Morse theory and the Solomon--Tits theorem

Abstract: In the field of homological stability, proofs often hinge on determining the homotopy type of certain simplicial complexes associated to the spaces or groups of interest. In this mostly-expository talk, I will survey a general combinatorial technique that can be used to prove that a simplicial complex is homotopy equivalent to a wedge of spheres.  As an application we'll prove this statement for the Tits buildings associated to the special linear groups, a classical result that plays a key role in the theory of arithmetic groups.

 

 

March 11 (in-person) 

Peter Patzt (University of Oklahoma)

 

March 18 (online) 

Yasha Savelyev (University of Colima, Mexico)

 

March 25 (in-person) 

Yash Deshmukh (IAS)

 

April 1 (in-person) 

Tatiana Abdelnaim (University of Oklahoma)

 

April 22 (online) 

Kelly Wang (University of Cambridge)

 

Purdue topology group:

Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067

Phone: (765) 494-1901 - FAX: (765) 494-0548  Contact Us

© 2025 Purdue University | An equal access/equal opportunity university | Copyright Complaints | DOE Degree Scorecards | Accessibility