Seminar on Commutative Algebra and Algebraic Geometry

Semester (e.g. Spring 2024)

Time and Place (e.g. Tuesdays 4-6, Evans 939)

All semesters: Spring 2025, Fall 2024 , Spring 2024, Fall 2023, Spring 2023, Fall 2022

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1/20 Shubham Sinha Intersection theory of Hyperquot schemes on curves Hyperquot schemes parameterize chains of successive quotients of a fixed vector bundle V on a smooth projective curve C. When V is trivial, Hyperquot schemes provide a compactification of the space of morphisms from C to a partial flag variety. I will present a formula for computing intersection numbers on Hyperquot schemes. Our result generalizes the Vafa–Intriligator formula, proved by Marian–Oprea, for computing intersection numbers on Quot schemes. I will also discuss conditions under which our formulas yield enumerative counts of maps to flag varieties. This talk is based on joint work with R. Ontani and W. Xu.
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1/27 Cameron Chang Title 1 Abstract 1
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2/3 Shang Xu Title 1 Abstract 1
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2/10 Joe Hlavinka Title 1 Abstract 1
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2/17 Speaker 1 Title 1 Abstract 1
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2/24 Daksh Aggarwal Title 1 Abstract 1
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3/3 Speaker 1 Title 1 Abstract 1
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3/10 Bernd Sturmfels Title 1 Abstract 1
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