Calendar

Posted September 10, 2025
Last modified December 2, 2025

Geometry and Topology Seminar Seminar website

Corey Bregman, Tufts University
Diffeomorphism groups of reducible 3-manifolds

 Let M be a smooth, compact, connected orientable 3-manifold. A classical result of Kneser and Milnor states that M admits a connected sum decomposition into prime factors, unique up to reordering.  We introduce a topological poset of embedded 2-spheres in M and use it to study the classifying space BDiff(M) for the diffeomorphism group of M.  We prove that if M is closed then BDiff(M) has finite type, and if M has non-empty boundary then BDiff(M rel ∂M) is homotopy equivalent to a finite CW complex.  The proof will take us on crash course through classical 3-manifold topology and geometrization. This is joint work with Rachael Boyd and Jan Steinebrunner.

Posted November 13, 2025
Last modified December 3, 2025

Colloquium Questions or comments?

Peter Bradshaw, University of Illinois Urbana-Champaign
Toward Vu's conjecture

In 2002, Vu conjectured that graphs of maximum degree $\Delta$ and maximum codegree at most $\zeta \Delta$ have chromatic number at most $(\zeta+o(1))\Delta$. Despite its importance, the conjecture has remained widely open. The only direct progress so far has been obtained in the "dense regime,'' when $\zeta$ is close to $1$, by Hurley, de Verclos, and Kang.

In this talk, I will discuss one of my recent results achieving the first major progress in the sparse regime where \zeta approaches 0, the case of primary interest to Vu. The result states that there exists $\zeta_0 > 0$ such that for all $\zeta \in [\log^{-32}\Delta,\zeta_0]$, the following holds: if $G$ is a graph with maximum degree $\Delta$ and maximum codegree at most $\zeta \Delta$, then $\chi(G) \leq (\zeta^{1/32} + o(1))\Delta$. This bound is derived from a more general result that assumes only that the common neighborhood of any $s$ vertices is bounded rather than the codegrees of pairs of vertices. The more general result also extends to the list coloring setting, which is of independent interest.

This talk is based on joint work with Dhawan, Methuku, and Wigal.

Posted August 27, 2025
Last modified November 26, 2025

Informal Geometry and Topology Seminar Questions or comments?

Krishnendu Kar, Louisiana State University
Khovanov Homology

Wrapping up our discussion on Khovanov Homology from this semester.

Posted December 3, 2025

Faculty Meeting Questions or comments?

Meeting of the Professorial Faculty

Posted November 12, 2025

Colloquium Questions or comments?

Iain Moffatt, Royal Holloway, University of London
Graphs in surfaces, their one-face subgraphs, and the critical group

Critical groups are groups associated with graphs. They are well-established in combinatorics; closely related to the graph Laplacian and arising in several contexts such as chip firing and parking functions. The critical group of a graph is finite and Abelian, and its order is the number of spanning trees in the graph, a fact equivalent to Kirchhoff’s Matrix--Tree Theorem.

What happens if we want to define critical groups for graphs embedded in surfaces, rather than for graphs in the abstract?

In this talk I'll offer an answer to this question. I'll describe an analogue of the critical group for an embedded graph. We'll see how it relates to the classical critical groups, as well as to Chumtov's partial-duals, Bouchet's delta-matroids, and a Matrix--quasi-Tree Theorem of Macris and Pule, and describe how it arises through a chip-firing process on graphs in surfaces.

This is joint work with Criel Merino and Steven D. Noble.

Posted July 22, 2025
Last modified November 13, 2025

Control and Optimization Seminar Questions or comments?

Javad Velni, Clemson University
Optimal Supplemental Lighting in Controlled Environment Agriculture: Data-driven and Model-based Perspectives

This seminar presents one aspect of my lab’s research focused on developing optimal supplemental lighting control strategies using LED lamps in controlled environment agriculture. The work aims to minimize electricity costs associated with supplemental lighting by integrating model-based optimization techniques with advanced machine learning methods, such as deep neural networks and Markov chains, used to predict uncertain environmental variables. Several scenarios are explored, ranging from a baseline optimal lighting approach for a single crop to more complex settings involving large-scale greenhouses with multiple crops and spatial light distribution considerations. Experimental results from a research greenhouse, where an Internet of Agricultural Things (IoAT) system was developed to grow lettuce, are presented and discussed. The seminar concludes with a roadmap highlighting several emerging research directions inspired by these findings.

Posted December 2, 2025

Combinatorics Seminar Questions or comments?

Kevin Grace, University of South Alabama
Matroid Adjoints, Minors, and Matrix Patterns

The notion of an adjoint of a matroid M arises from the attempt to attach a matroid to the lattice-theoretic dual of the lattice of flats of M. More precisely, a simple matroid M’, with the same rank as M, is an adjoint of M if there is an inclusion-reversing injective map from the lattice of flats of M into the lattice of flats of M’ that bijectively maps the hyperplanes of M onto the points of M’. Not all matroids have adjoints; however, in this talk, I will present a proof that the class of matroids that do have adjoints is minor-closed. If time permits, I will also discuss related work from the field of combinatorial matrix theory. In this related work, joint with Louis Deaett, we explore connections between the notion of an adjoint of a matroid and the minimum rank of matrices with a given zero-nonzero pattern.

Posted November 13, 2025
Last modified November 16, 2025

Colloquium Questions or comments?

Sean Cotner, University of Michigan
Propagating congruences in the local Langlands program

The Langlands program is a vast generalization of quadratic reciprocity, aimed at understanding the algebraic field extensions of the rational or p-adic numbers. In this talk, I will describe a biased and incomplete history of the classical local Langlands program; recent developments in making it categorical, integral, and modular; and joint work-in-progress with Tony Feng concerned with patching together the modular theory to understand the classical theory.