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Logistics
Seminar meets on Thursdays 10:10-11:00AM CT in Vincent 570
Organizers: Shiyun Wang and Anna Weigandt
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Related Seminars
Schedule
Schedule
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January 29 - Nursel Erey (Minnesota / Gebze Technical University)
January 29 - Nursel Erey (Minnesota / Gebze Technical University)
Title: Linear quotients of powers of edge ideals
Abstract: The edge ideal $I(G)$ of a finite simple graph $G$ is the squarefree quadratic monomial ideal generated by monomials corresponding to the edges of $G$. Nevo and Peeva conjectured that if $G$ is gap-free, then $I(G)^s$ has a linear resolution for all sufficiently large $s$. In this talk, we explore the linear quotients property and discuss recent progress on this conjecture.
Joint work with S. Faridi, T. Ha, T. Hibi, S. Kara and S. Morey.
February 5 - Jack Chen-An Chou (Florida)
February 5 - Jack Chen-An Chou (Florida)
Title: A positive combinatorial formula for the double Edelman-Greene coefficients
Abstract: Lam, Lee, and Shimozono introduced the double Stanley symmetric functions in their study of the equivariant geometry of the affine Grassmannian. They proved that the associated double Edelman--Greene coefficients, the double Schur expansion coefficients of these functions, are positive, a result later refined by Anderson. They further asked for a combinatorial proof of this positivity. In this paper, we provide the first such proof, together with a combinatorial formula that manifests the finer positivity established by Anderson. Our formula is built from two combinatorial models: bumpless pipedreams and increasing chains in the Bruhat order. The proof relies on three key ingredients: a correspondence between these two models, a natural subdivision of bumpless pipedreams, and a symmetry property of increasing chains. This is based on joint work with Tianyi Yu.
February 12 - Vic Reiner (Minnesota)
February 12 - Vic Reiner (Minnesota)
Title: Invariant theory and wreath products
Abstract: Invariant theory starts with a group G acting on a polynomial algebra via linear substitutions of the variables, and tries to describe the subalgebra of G-invariant polynomials. The theory is particularly well-developed when the group G is finite and the polynomial algebra has coefficients in a field of characteristic zero.
After reviewing this, we will explain how certain data (Hilbert series) for the G-invariant polynomials determines the same data for the S_n[G]-invariant polynomials for all n. Here S_n[G] is the wreath product group G wr S_n acting on n sets of the original variables, with the symmetric group S_n swapping the variable sets. This then suggests a structural result: one can collate the direct sum on n of the S_n[G]-invariants into one big graded ring with a shuffle product, and this big ring ends up being a "superpolynomial algebra" (=symmetric tensor exterior algebra) generated by the G-invariants.
(Based on arXiv:2503.19323 with Trevor Karn).
February 19 - Brendon Rhoades (UCSD)
February 19 - Brendon Rhoades (UCSD)
Title: TBA
Abstract: TBA
February 26 - TBA
February 26 - TBA
Title: TBA
Abstract: TBA
March 5 - Ethan Partida (Brown)
March 5 - Ethan Partida (Brown)
Title: TBA
Abstract: TBA
March 12 - Spring Break
March 12 - Spring Break
March 19 - TBA
March 19 - TBA
Title: TBA
Abstract: TBA
March 26 - TBA
March 26 - TBA
Title: TBA
Abstract: TBA
April 2 - Moriah Elkin (Cornell)
April 2 - Moriah Elkin (Cornell)
Title: TBA
Abstract: TBA
April 9 - Ariana Chin (UCLA)
April 9 - Ariana Chin (UCLA)
Title: TBA
Abstract: TBA
April 16 - Joshua Swanson (University of Southern California)
April 16 - Joshua Swanson (University of Southern California)
Title: TBA
Abstract: TBA
April 23 - TBA
April 23 - TBA
Title: TBA
Abstract: TBA
April 30 - TBA
April 30 - TBA
Title: TBA
Abstract: TBA
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