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)

Title: Stability Patterns for Spherical Braid Groups

Abstract: Stability patterns for the homology of configuration spaces has been studied for decades, starting with homological stability in the 1970's, then representation stability in 2010, and stable periodicity in 2015. When the configuration spaces are Eilenberg-MacLane spaces, these stability results extend to the group homology of surface braid groups. However, configuration spaces on S^2 and RP^2 are not Eilenberg-MacLane spaces and so the stability patterns for their group homology had not yet been established. In this talk, I will use a result from Fred Cohen and Jonathan Pakianathan as well as the theory of FI-homology to establish stability patterns for the group homology of braid groups on S^2 and RP^2. 

 

September 30 (in-person)

Sam Nariman (Purdue)

Title: The continuous cohomology of the diffeomorphism group of compact manifolds and a question of Bott and Haefliger

Abstract: For finite-dimensional Lie groups, there is an isomorphism due to van Est that identifies the continuous group cohomology of a Lie group G with the relative Lie algebra cohomology of the Lie algebra g relative to its maximal compact Lie group. The maximal compact Lie subgroup does not exist in general for diffeomorphism groups. Bott formulated a statement and stated it as a belief of his and Haefliger that identifies the continuous cohomology of the diffeomorphism group of compact manifolds as the real cohomology of the homotopy quotient of certain mapping space. We reinterpret the van Est isomorphism as "the homotopy quotient" of the Lie algebra cohomology to realize Bott-Haefliger's belief. 

October 7 (in-person)

Miguel Barata (Purdue)

Title: A new proof of Dunn-Lurie additivity and the Gray tensor product of operads

Abstract: An important tool in modern developments of homotopy theory is the notion of an operad, and among these the E_n-operad is of particular relevance. Roughly speaking, for each natural number n these correspond to a symmetric sequence of spaces interpolating between homotopy coherent associative and homotopy coherent commutative multiplications. Although originating many years ago through the study of iterated loop spaces, it has also had a recent meaningufl impact in areas such as higher algebra, (un)stable homotopy theory and the study of embedding spaces of manifolds. In this talk I want to present a new proof of Dunn-Lurie additivity, a cornerstone result in the operad theory which relates the E_n-operads for different balues of n. The main idea of the proof comes from a construction of a new tensor product for operads, using ideas of Balteanu, Fiedorowicz, Schwaenzl and Vogt. If time permits, I will explain how the formalism of dendroidal spaces can be used to prove this result in the derived setting of infinity-operads. Joint work with Ieke Moerdijk.

 

October 14 (online)

Rhuiadi Burke (Oxford) 

 

October 21 (in-person)

Matthew Scalamandre (Toronto) 

 

 

November 4 (online)

Thomas Willwacher (ETH Zurich) 

 

November 11 (in-person)

David Chan (Michigan State)

 

December 2 (in-person)

Urshita Pal (Michigan)

 

Purdue topology group: