Calendar

Posted November 12, 2025

Colloquium Questions or comments?

Quanjun Lang, Duke University
To be announced

Posted November 12, 2025

Colloquium Questions or comments?

Benjamin Zhang, University of North Carolina at Chapel Hill
To be announced

Posted November 12, 2025

Colloquium Questions or comments?

Colleen Robichaux, University of California, Los Angeles
Deciding Schubert positivity

We survey the study of structure constants in Schubert calculus and its connection to combinatorics and computational complexity.

Posted November 12, 2025

Colloquium Questions or comments?

Keegan Kirk, George Mason University
To be announced

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.