Seminar meets on Thursdays 10:10-11:00AM CT in Vincent 570
Organizers: Vic Reiner and Anna Weigandt
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Related Seminars
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Title: Adjacency spectra for once and twice punctured hypercubes
Abstract: The eigenspaces for the adjacency matrices of hypercube graphs are well-understood. After reviewing that story, will explain how to extend it to the graphs obtained by removing a vertex or antipodal pair of vertices. This was motivated by a conjecture on zonotopes arising in the UMN Senior Honors Thesis of Laura Schoenzeit, and whose last remaining proof piece was provided by a query to ChatGPT.
(Based on arxiv:2608.27887, joint with Jang Soo Kim and Laura Schoenzeit.)
Title: Symplectic Bumpless Pipe Dreams
Abstract: Bumpless pipe dreams are combinatorial objects in bijection with alternating sign matrices. Double Grothendieck polynomials can be expressed as weighted sums over bumpless pipe dreams, a perspective that has led to many advances in the combinatorics of Schubert calculus and integrable systems. We introduce symplectic bumpless pipe dreams and present an analogous formula for symplectic Grothendieck polynomials, which represent the equivariant $K$–theoretic classes of $\mathrm{Sp}_{2n}$–orbit closures in the flag variety. To prove this result, we construct an analogue of Lascoux’s inflation on these objects, providing a combinatorial realization of the symplectic transition equations that appear in work of the first author, Marberg, and Pawlowski.
This is joint work with Zachary Hamaker.
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