Events

Title: A Proof of Nash-Williams’ Conjecture

Abstract: A central open question in extremal design theory is Nash-Williams’ Conjecture from 1970, namely that every triangle-divisible graph on n vertices (for n large enough) with minimum degree at least 0.75n has a triangle decomposition. In this talk, we discuss the history of the problem and our recent resolution of this conjecture, as well as other applications in design theory. We also overview the proof, highlighting the new techniques we developed to resolve the fractional version as well as the full conjecture. Joint work with Michelle Delcourt.

Acyclic List Colouring Locally Planar Graphs

Massimo Vicenzo | University of Waterloo

Abstract: A (vertex) colouring of graph is acyclic if it contains no bicoloured cycle. In 1979, Borodin proved that planar graphs are acyclically 5-colourable. In 2010, Kawarabayashi and Mohar proved that locally planar graphs are acyclically 7-colourable. In 2002, Borodin, Fon-Der-Flaass, Kostochka, Raspaud, and Sopena proved that planar graphs are acyclically 7-list-colourable. In this talk we discuss our result that locally planar graphs are acyclically 9-list-colourable—no bound for acyclic list colouring locally planar graphs for any fixed number of colours was previously known.

This is joint work with Luke Postle and Evelyne Smith-Roberge. 

Seminar: Algebraic and Enumerative Combinatorics Seminar
Date: Thursday, September 17, 2026
Time: 2:30 PM
Location: MC 5417
Speaker: Mike Zabrocki
Affiliation: York University
Title: Characters of the rook monoid
Abstract:

The partial permutations form a monoid known in different contexts as either the “symmetric inverse semigroup” or the “rook monoid.” In this talk I will define a family of symmetric functions that evaluate to the character values of the irreducible representations of the monoid. The basis also connects to the representation theory of the Schur-Weyl duality with the “propagating partition algebra.” Moreover, the structure coefficients of this basis interpolate between the Kronecker coefficients and the Littlewood-Richardson coefficients and we use it to develop some of the combinatorics of the connection.

This is joint work with Rosa Orellana and Alex Wilson.

There will be a pre-seminar presenting relevant background at beginning graduate level starting at 1:30pm in MC 5417.

 

Abstract: The mirror of a smooth Fano toric variety is a Laurent polynomial, and this Laurent polynomial encodes interesting enumerative data of the toric variety.  For example, the Jacobian ring of the Laurent polynomial is isomorphic to the small quantum cohomology ring of the toric variety. In this talk, I’ll describe this aspect of the (now basically classical) toric mirror theorem, and explain how this picture is expected to extend to other smooth Fano varieties. The Grassmannian’s strong combinatorial structure  makes it one of the nicest examples of non-toric Fano varieties to study in this context. I’ll present several mirror constructions for the Grassmannian that each reflect a different perspective on its geometry. Finally, I’ll discuss some extensions of these constructions to generalizations of the Grassmannian. 

For this term's reading group we will be hosting a study group on quantum tools in cryptography. For the first week, we start with a motivation on quantum computing including the basic definitions and discussion on complexity classes. This will serve as a elementary foundation for the rest of the reading group. A week-by-week plan outline.

Abstract: On-shell forms are differential forms on the Grassmannian which arise in particle physics. They are defined using bipartite graphs with n distinguished boundary vertices. Mathematical investigation of on-shell forms has largely focused on the case of planar graphs, where one can use tools developed by Postnikov in the study of the totally nonnegative Grassmannian. In this talk we develop the mathematics of nonplanar on-shell forms, and explain how they arise in physics and math. For certain forms on the Grassmannian Gr(2,n), we prove a determinantal formula appearing in the physics literature, and give a connection to the hypertree divisors of Castravet and Tevelev.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.

Abstract: Various notions of negative dependence arise naturally and/or are desirable in various random processes and randomized algorithms. We survey how to generate and utilize a few such notions of negative dependence, and sketch applications to concentration inequalities, fairness, and approximation algorithms.