SEMINARS, HARVARD-MIT COMBINATORICS
May 17, 2023 3:00 pmLet S be a subset of the Boolean cube that is both an antichain and a distance-r code. How large can S be? I will discuss the solution to this...
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SEMINARS, HARVARD-MIT COMBINATORICS
May 17, 2023 3:00 pmLet S be a subset of the Boolean cube that is both an antichain and a distance-r code. How large can S be? I will discuss the solution to this...
Read more
SEMINARS, HARVARD-MIT COMBINATORICS
May 10, 2023 4:15 pmThe chromatic symmetric function (CSF) of Dyck paths of Stanley and its Shareshian Wachs q-analogue (q-CSF) have important connections to Hessenberg varieties, diagonal harmonics and LLT polynomials. In the, so...
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SEMINARS, HARVARD-MIT COMBINATORICS
May 3, 2023 4:15 pmA great tool in the arsenal of combinatorialists is modeling problems as counting the lattice points of some convex polytope. Let $P\subseteq\R^d$ be a rational convex polytope, that is, a...
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SEMINARS, HARVARD-MIT COMBINATORICS
April 28, 2023 3:00 pmGiven a fixed angle alpha and growing dimension n, what is the maximum number of lines in n dimensions, all pairs of which meet at the same angle alpha? In...
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SEMINARS, HARVARD-MIT COMBINATORICS
April 26, 2023 4:15 pmThe resonance varieties are cohomological invariants that are studied in a variety of topological, combinatorial, and geometric settings. I will describe several conditions that ensure the reducedness of the associated...
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SEMINARS, HARVARD-MIT COMBINATORICS
April 21, 2023 4:15 pmChip-firing games on finite graphs provide a combinatorial analog of the theory of special divisors on algebraic curves. Each chip configuration determines two numbers: the degree and rank, analogous to...
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SEMINARS, HARVARD-MIT COMBINATORICS
April 19, 2023 4:15 pmLascoux, Leclerc, and Thibon defined a remarkable family of symmetric functions that are $q$-deformations of products of skew Schur functions. These LLT polynomials $G_{\lambda}(x;q)$ can be indexed by a tuple...
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SEMINARS, HARVARD-MIT COMBINATORICS
April 12, 2023 4:15 pmTorus equivariant rank r vector bundles on a toric variety (toric vector bundles) were famously classified by Klyachko (1989) using certain combinatorial data of compatible filtrations in an r-dimensional vector...
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SEMINARS, HARVARD-MIT COMBINATORICS
April 5, 2023 4:15 pmWe will discuss enumerative and structural properties of two families of standard Young tableaux, the realizable rectangular tableaux and the realizable staircase tableaux. The realizable rectangular tableaux come from tropical...
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