The seminar meets Tuesdays 4:00 - 5:00 pm in (PIMS) ESB 4133. The seminar is preceded with coffee and cookies at 3:30.
For any questions please contact the organizers Nicolle Gonzalez ( nicolle [at] math [dot] ubc [dot] ca ), Joshua Turner ( jpturner [at] math [dot] ubc [dot] ca), or Steph van Willigenburg.
Sept 15, 2026:
Speaker: Jinting Liang (UBC)
Title: Log-Concavity and Log-Convexity via Distributive Lattices
Abstract: The FKG inequality is a powerful tool for proving inequalities in distributive lattices. We show how a special case, which we call the Order Ideal Lemma, can be used to demonstrate a wide array of log-concavity and log-convexity results in a combinatorial manner. We use the Order Ideal Lemma to prove log-concavity and log-convexity of various sequences involving binomial coefficients, Catalan numbers, Fibonacci numbers, Stirling numbers of the second kind, order polynomials, and more. In the process we define some new and interesting distributive lattices. This is joint work with Bruce Sagan.
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Sept 22, 2026:
Speaker: John Lentfer (UC San Diego)
Title: Type B bosonic-fermionic coinvariant rings
Abstract: In the 1990's Garsia and Haiman introduced the diagonal coinvariant ring, which generalizes the classical coinvariant ring (the cohomology ring of the flag variety) to two sets of commuting variables. Since then, there has been much interest in studying generalizations with k sets of n commuting variables and j sets of n anticommuting variables, called a bosonic-fermionic coinvariant ring R_n^{(k,j)}, for various choices of small k and j. There is also an analogous story for the Weyl group of type B_n (the hyperoctahedral group); denote the type B bosonic-fermionic coinvariant ring by R_{B_n}^{(k,j)}.
In this talk, we will learn about the history of these families of coinvariant rings, paying attention to when the story is the same in both types A and B, and when they diverge. New results include an explicit formula for the GL(2) x B_n module structure of R_{B_n}^{(0,2)}, the sign character of R_{B_n}^{(0,3)}, and the standard characters in types A and B. This is based on joint work with Yuhan Jiang (UC Berkeley).
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Sept 29, 2026:
Speaker: Josh Turner (UBC)
Title: A filtered basis for Haiman ideals
Abstract: We will talk about the ideal J generated by antisymmetric polynomials in two sets of variables and its powers, and discuss how these Haiman ideals are connected to link homology, geometry, and other combinatorial objects of interest (including diagonal coinvariants and q,t-Catalan numbers). We will then show how to reinterpret recursions for computing link homology into a method for constructing a free, filtered basis for J^d over C[y].
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Oct 6, 2026:
Speaker: Shubham Sinha (UBC)
Title: TDB
Oct 13, 2026:
Oct 20, 2026:
Oct 27, 2026:
Nov 3, 2026:
Nov 10, 2026: Midterm Break (no seminar)
Nov 17, 2026:
Nov 24, 2026:
Dec 1, 2026: