Current students

Abstract: I will go over the recent paper by Sahil Singla proving Matroid Secretary Conjecture.

Abstract: Pure quantum states describe systems whose preparation is known exactly, but realistic quantum information often involves uncertainty, inaccessible subsystems, and interactions with the environment. In this talk, we introduce density operators as a general framework encompassing both pure and mixed states. We then discuss quantum channels, which model physical transformations and common forms of noise affecting quantum systems. Finally, we introduce classical and quantum entropy as measures of uncertainty and information, and explain how these ideas provide basic intuition for quantum cryptographic security.

Abstract: I will introduce a family of commuting derivations on the ring of symmetric polynomials. Using this family I will then define an apparently-novel family of symmetric functions that is vertical-strip LLT positive and relates directly to the Theta operators of D'Adderio–Iraci–Vanden Wyngaerd. Finally I'll discuss some consequences for the "higher order" Macdonald positivity conjecture of Dołęga. This is joint work with Jim Haglund.

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

Abstract: For positive integers $s$ and $n$, let $f_{s}(n)$ denote the maximum $k$ such that every $n$-vertex $K_{s+1}$-free graph contains an induced $K_s$-free subgraph with $k$ vertices. These are the Erd\H{o}s-Rogers functions, introduced by Erd\H{o}s and Rogers in 1962, and are generalizations of Ramsey numbers.

In this talk we survey recent progress, culminating with the recent result of Morris, Saharasbudhe which finally determines the order of magnitude of the Erd\H{o}s-Rogers functions.

Joint work with Rob Morris and Julian Saharasbudhe.

Abstract: Much like matroids, oriented matroids can be defined on finite ground sets using a set of circuit axioms. Oriented matroid duality is an important property which is difficult to maintain in the infinite setting. One way to define infinite oriented matroids in a way that preserves duality is using signed set orthogonality. This allows for the notion of finitary and cofinitary oriented matroids. An oriented matroid is called finitary if all of its circuits have finite support, and cofinitary if it is the dual of a finitary oriented matroid. It has recently been shown that cofinitary oriented matroids do not necessarily satisfy the circuit axioms. In the finite setting, there are many ways to define oriented matroids which are equivalent to the circuit axioms. Here, we prove that some of these definitions still hold for cofinitary oriented matroids, even when the circuit axioms fail.

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.

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: 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. 

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.