Seminar on Commutative Algebra and Algebraic Geometry

Semester Fall 2026

Time and Place Tuesday 4-6 unless otherwise noted

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

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August 25 Speaker 1 Title 1 Abstract 1
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September 1 Speaker 1 Title 1 Abstract 1
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September 8 Reginald Anderson (4:10-4:30) Stability conditions on abelian categories We recall the definition of a stability condition on an abelian category.
Reginald Anderson (4:45-5:35) Rationality of Pandharipande-Thomas descendent generating series for superpositive curve classes on smooth projective complex 3-folds Let X be a nonsingular quasi-projective 3-fold, and fix beta as an element of the second integral homology of X. In 2007, Pandharipande-Thomas conjectured that any descendent generating series of Pandharipande-Thomas stable pair invariants with curve class beta forms the Laurent expansion over the rational numbers of a rational function in a single formal variable q. In 2017, Pandharipande conjectured that moreover, this series is the Laurent expansion of a rational function with poles only at q=0 and at certain roots of unity bounded in order by the divisibility of beta in second integral homology of X, modulo torsion. While counterexamples are known for the second conjecture in Picard rank greater than 1, we prove rationality of the Pandharipande-Thomas descendent generating series for the case of superpositive curve classes on connected smooth complex projective 3-folds and show poles only at q=0 and at roots of unity. We also prove analogous conjectures in G-equivariant cohomology for the case of a linear algebraic complex group G acting on X which acts trivially on the second integral homology of X and on a certain quotient of the first Chow group. Our proof approach uses Joyce's theory of wall-crossing from Donaldson-Thomas invariants to Pandharipande-Thomas stable pair invariants. This is based on joint work with Dominic Joyce at Oxford University in arXiv: 2604.05664.
September 15 Speaker 1 Title 1 Abstract 1
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September 22 Speaker 1 Title 1 Abstract 1
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September 29 Speaker 1 Title 1 Abstract 1
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October 6 Speaker 1 Title 1 Abstract 1
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October 13 Speaker 1 Title 1 Abstract 1
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October 20 Speaker 1 Title 1 Abstract 1
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October 27 Speaker 1 Title 1 Abstract 1
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November 3 Speaker 1 Title 1 Abstract 1
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November 10 Speaker 1 Title 1 Abstract 1
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November 17 Speaker 1 Title 1 Abstract 1
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November 24 Speaker 1 Title 1 Abstract 1
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December 1 Speaker 1 Title 1 Abstract 1
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December 8 Speaker 1 Title 1 Abstract 1
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