SEMINARS, HARVARD-MIT COMBINATORICS
March 8, 2023 4:15 pmStanley's chromatic symmetric function is a generalization of the chromatic polynomial of a graph that encodes coloring information for graphs. One open conjecture is that non-isomorphic trees have different chromatic...
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SEMINARS, HARVARD-MIT COMBINATORICS
November 16, 2022 4:15 pmI will discuss joint work with Christin Bibby, Nir Gadish, and Claudia Yun. The historical antecedents are in earlier work of Billera-Holmes-Vogtmann around 2000 and others, who study an interesting space of metric...
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SEMINARS, HARVARD-MIT COMBINATORICS
November 9, 2022 4:15 pmA hyperplane arrangement of braid type is a collection of hyperplanes in R^n of the form {x_i-x_j=s}, where i,j are indices in [n] and s is an integer. Classical families...
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SEMINARS, HARVARD-MIT COMBINATORICS
November 2, 2022 4:15 pmThe wonderful variety of a realizable matroid and its Chow ring have played key roles in solving many long-standing open questions in combinatorics and algebraic geometry. Yet, its $K$-rings are...
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SEMINARS, HARVARD-MIT COMBINATORICS
October 28, 2022 3:00 pmWe discuss recent joint work with Kyle Binder on defining the unipotent fundamental group of tropical varieties. This fundamental group arises from the Tannakian formalism using tropical vector bundles with...
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SEMINARS, HARVARD-MIT COMBINATORICS
May 4, 2022 4:15 pmHelly's theorem is a fundamental statement in discrete and convex geometry that relates the intersection of a family of convex sets to the intersections of its subfamilies. This talk surveys...
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SEMINARS, HARVARD-MIT COMBINATORICS
April 22, 2022 3:30 pmThe Eulerian idempotents of the symmetric group generate a family of representations—the Eulerian representations—that have connections to configuration spaces, equivariant cohomology, and Solomon's descent algebra. These representations are defined in...
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SEMINARS, HARVARD-MIT COMBINATORICS
April 20, 2022 4:15 pmWe prove that with high probability $G^{(3)}(n,n^{-1+o(1)})$ contains a spanning Steiner triple system. We also prove the analogous result for spanning Latin squares. This threshold is sharp up to a...
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HARVARD-MIT COMBINATORICS
April 6, 2022 4:15 pmConsider the Gibbs distribution of the hardcore model over all independent sets of a given graph, where the probability density of each independent set J is proportional to lambda^|J| where...
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SEMINARS, HARVARD-MIT COMBINATORICS
March 2, 2022 4:15 pmThe Newell-Littlewood numbers are defined in terms of the Littlewood-Richardson coefficients. Both arise as tensor product multiplicities for a classical Lie group. A. Klyachko connected eigenvalues of sums of Hermitian...
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