URiCA

URiCA

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Saturday May 3rd, 2025

Registration/Poster Setup/Opening Remarks

Speaker: Xianlong Ni

Title: TBA

Abstract: TBA

Speaker: Anastasia Nathanson

Title: Permutation action on chow rings of matroids

Abstract: Given a matroid with a symmetry group, we study the induced group action on the Chow ring of the matroid with respect to symmetric building sets. This turns out to always be a permutation action. Work of Adiprasito, Huh and Katz showed that the Chow ring satisfies Poincar\'e duality and the Hard Lefschetz theorem. We lift these to statements about this permutation action, and suggest further conjectures in this vein.

Poster Session

Lunch

Speaker: Karthik Ganapathy

Title: TBA

Abstract: TBA

Speaker: Feiyang Lin

Title: Balanced+balanced splitting loci have rational singularities

Abstract: Whenever there is a vector bundle on a P^1-bundle, the base is stratified by how the vector bundle splits when it is restricted to the fibers. The strata that arise this way are called splitting loci. In this talk, I will explain how splitting loci are defined and explain why they arise naturally. Then I will give an outline of the proof that certain splitting loci have rational singularities. The key ingredient is the construction of a modular resolution of singularities for all splitting loci, and cohomology vanishing for certain tautological bundles on Quot schemes on P^1.

Turbo Talks

Sunday May 4th, 2025

Coffee

Speaker: Caitlin Davis

Title: Weighted rational curves and the (nonstandard) Koszul property

Abstract: (Joint work with Ola Sobieska.) The rational normal curve is a well-understood projective variety whose coordinate ring has many nice algebraic properties. We consider an analogous family of curves in weighted projective space, and we show that this family of curves has many of the same algebraic properties as the rational normal curve. In this talk, I will introduce the weighted rational curves as a case study for the (nonstandard) Koszul property.

Speaker: Bek Chase

Title: TBA

Abstract: TBA

Speaker: Nawaj KC

Title: TBA

Abstract: TBA

Closing Remarks