Algebraic and Enumerative Combinatorics Seminar

Sep 17Thursday

Next Seminar

Mike Zabrocki, Characters of the rook monoid

Abstract

The partial permutations form a monoid known in different contexts as either as 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.

Sep 24

Lizzie Pratt, On-shell Forms and Hypertree Divisors

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 $\mathrm{Gr}(2,n)$, we prove a determinantal formula appearing in the physics literature, and give a connection to the hypertree divisors of Castravet and Tevelev. This is joint work with Artyom Lisitsyn, Melissa Sherman-Bennett, and Jaroslav Trnka.

Oct 1

Vasu Tewari

Oct 8

Jun Yan, Exact enumeration of lozenge tilings of a triangular region

Oct 15

No seminar during reading week.

Oct 22

Patty Commins

Oct 29

Shao Yuan Lin

Nov 5

Sophie Rehberg

Nov 12

Andy Zucker

Nov 19

Nov 26

Houcine Ben Dali

Dec 3

URA Day

About the Seminar

This is the website for the Algebraic and Enumerative Combinatorics Seminar at the University of Waterloo. We view algebraic combinatorics broadly, explicitly including algebraic enumeration and related asymptotic and bijective combinatorics as well as algebraic combinatorics as it appears in pure algebra and in applications outside mathematics.

We usually meet on Thursdays in MC 5417 using a pre-seminar and seminar format. Anyone is welcome to attend either or both sessions.

At 1:30 PM, we begin with a 45-minute pre-seminar designed to get participants up to speed on useful and interesting background for the talk, at a level accessible to beginning graduate students or researchers working in different areas. The format may be an introductory lecture, a problem session, or a mix of both. After the pre-seminar, there is a short coffee break.

At 2:30 PM, we resume with the main seminar: a 50-minute talk, plus 10 minutes for questions. Our audience consists primarily of combinatorics faculty and grad students.