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Wednesday, September 3
Speaker: Aryaman Maithani (Utah)
Title: Polynomial invariants of GL₂: Conjugation over finite fields
Abstract: Consider the conjugation action of GL₂(K) on the polynomial ring K[X₂ₓ₂]. When K is an infinite field, the ring of invariants is a polynomial ring generated by the trace and the determinant. We describe the ring of invariants when K is a finite field, and show that it is a hypersurface. -
Wednesday, September 10
Speaker: Vignesh Jagathese (UIC)
Title: Quasi-F-Purity and F-pure Thresholds
Abstract: A weakening of Frobenius splitting, Quasi-F-Splittings have proven to be a vital invariant in the study of varieties in positive characteristic, with numerous applications to birational geometry and singularities. In this talk I'll provide an overview of Quasi-F-Splittings and introduce a local analogue, Quasi-F-Purity, and discuss its various permanence properties. I will also discuss how quasi-F-pure hypersurfaces are "as close to being F-pure as possible" by computing the F-pure Threshold of an arbitrary quasi-F-pure hypersurface. This talk includes joint work with JJ Garzella. -
Wednesday, September 24
Speaker: Manav Batavia (Purdue)
Title: The arithmetic rank of residual intersections of a complete intersection ideal
Abstract: The arithmetic rank of a variety is the minimal number of equations needed to define it set-theoretically, i.e., the smallest number of polynomials generating the defining ideal upto radical. Computing this invariant is notoriously difficult: the minimal generators up to radical often bear little relation to the given ideal generators and can vary unpredictably across characteristics.Residual intersections provide a natural extension of the classical notion of algebraic links. We establish a general upper bound for the arithmetic rank of any residual intersection of a complete intersection ideal in an arbitrary Noetherian ring, and we show that this bound is sharp under specific characteristic assumptions. This work is joint with Kesavan Mohana Sundaram, Taylor Murray, and Vaibhav Pandey.
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Wednesday, October 1
Speaker: Reinold Huebl (Regensburg)
Title: TBA
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Wednesday, October 8
Speaker: Kangjin Han (DGIST, Korea)
Title: TBA
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Wednesday, October 15
Speaker: Joel Castillo Rey (BCAM, Basque)
Title: TBA
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Wednesday, October 22
Speaker: TBA
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Wednesday, October 29
Speaker: TBA
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Wednesday, November 5
Speaker: TBA
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Wednesday, November 12
Speaker: Dale Cutkosky (Missouri)
Title: TBA
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Wednesday, November 19
Speaker: TBA
Title: TBA
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Wednesday, December 3
Speaker: TBA
Title: TBA
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Wednesday, December 10
Speaker: TBA
Title: TBA
Abstract: TBA