Auburn Algebra Seminar
Spring 2026
Schedules from past semestersSeminars will be held in Parker 354 on Tuesdays from 2:30 to 3:20, unless otherwise noted.
Schedule:
January 13: Michael Brown (local)Title: The BGG correspondence for toric varieties, Part 1
Abstract: The Bernstein-Gel'fand-Gel'fand (BGG) correspondence gives an equivalence between the derived category of projective space and the singularity category of an exterior algebra. Recent work of mine with Daniel Erman ("Tate resolutions on toric varieties") suggested what a generalization of this theorem for toric varieties might look like. I will talk about ongoing work toward proving such a generalization.
January 20: Michael Brown (local)
Title: The BGG correspondence for toric varieties, Part 2
Abstract: This is a continuation of last week's talk.
January 27: Hal Schenck (local)
Title: Chow rings in toric geometry
Abstract: We discuss an intersection theory computation in toric geometry that exhibits why exponential formulas appear in algebraic geometry.
February 3: Anirban Bhaduri (University of South Carolina)
Title: Orlov Spectrum for Weighted Projective Line
Abstract: One way to measure the complexity of a triangulated category is through its Orlov spectrum, defined as the set of all possible generation times of strong generators. There are very few cases where the Orlov spectrum has been explicitly computed; one example is the bounded derived category of coherent sheaves on the projective line over a field. In this talk, we discuss explicit generation times for certain strong generators and establish bounds for others, thereby fully determining the Orlov spectrum of the weighted projective line of type (2) over a field. We also explore possible generalization to the case of weighted Projective line of type (n). This talk is based on a joint work with Matthew Ballard.
February 10:
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February 17:
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February 24:
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March 3: Justin Lyle (Auburn)
Title: Derived Complete Intersections
Abstract: A classical result of Gulliksen characterizes complete intersection rings as those for which the Betti numbers of any module have polynomial growth. In this talk, we extend this line of investigation to DG-algebras, and give a characterization of those DG-algebras over which any DG-module has polynomial growth of Betti numbers, ultimately concluding that, up to derived equivalence, these are exactly the finitely generated polynomial algebras (in the DG sense) over a regular base. This talk is based on joint work with Michael Brown.
March 17:
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March 24:
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March 31: Arik Wilbert (University of South Alabama)
Title: Two-row Delta Springer varieties
Abstract: Springer fibers play an important role in geometric representation theory. These algebraic varieties naturally arise as the fibers of a resolution of singularities of the nilpotent cone and can be used to geometrically classify the irreducible representations of Weyl groups. In this talk, I will discuss the geometry and topology of a certain family of so-called Delta Springer varieties from an explicit, combinatorial point of view. These singular varieties were introduced by Griffin--Levinson--Woo in 2021 in order to give a geometric realization of an expression that appears in the t=0 case of the Delta conjecture of Haglund--Remmel--Wilson. In the two-row case, Delta Springer varieties generalize both ordinary Springer fibers as well as Kato's exotic Springer fibers. Moreover, the homology of two-row Delta Springer varieties has a diagrammatic description and can be equipped with an action of the degenerate affine Hecke algebra. This recovers and upgrades the action of the symmetric group obtained by Griffin--Levinson--Woo and yields a skein theoretic description of said action. This is joint work with A. Lacabanne and P. Vaz.
April 7: Andrew Soto Levins (Texas Tech University)
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April 14:
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April 21:
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