| Date: | August 18, 2020 |
| Time: | 10:00pm |
| Location: | zoom |
| Speaker: | J. Zuiddam, Courant |
| Title: | Combinatorics, Tensors and Geometry |
| Abstract: | There is a widely studied family of open problems in extremal combinatorics that can naturally be phrased in terms of tensors. This family includes the cap set problem and the sunflower problem.
We present a geometric approach to this kind of problems, called Geometric Rank (Kopparty–Moshkovitz–Zuiddam, 2020). Geometric Rank is a natural extension of matrix rank to tensors that is different from previously known notions of rank for tensors.
I will conclude with an informal exploration of a totally different potential approach to these problems that is in line with the celebrated Lovász theta function.
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| Date: | October 28, 2020 |
| Time: | 11:00pm |
| Location: | zoom |
| Speaker: | JM Landsberg, TAMU |
| Title: | A technical lemma of Friedland |
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| Date: | November 4, 2020 |
| Time: | 11:00pm |
| Location: | zoom |
| Speaker: | R. Geng, TAMU |
| Title: | The variety of commuting matrices and geometric rank |
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| Date: | November 6, 2020 |
| Time: | 10:00pm |
| Location: | zoom |
| Speaker: | JM Landsberg, TAMU |
| Title: | Mukai: moduli of rank 2 vector bundles on curves I |
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| Date: | November 11, 2020 |
| Time: | 11:00pm |
| Location: | zoom |
| Speaker: | JM Landsberg, TAMU |
| Title: | Mukai: moduli of rank 2 vector bundles on curves II |
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| Date: | November 13, 2020 |
| Time: | 10:00pm |
| Location: | zoom |
| Speaker: | A. Huang, TAMU |
| Title: | Def. theory, curves of genus 0 and 1. |
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| Date: | November 18, 2020 |
| Time: | 11:00pm |
| Location: | zoom |
| Speaker: | JM Landsberg, TAMU |
| Title: | The substitution method and linear sections of spaces of matrices of bounded rank |
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| Date: | November 23, 2020 |
| Time: | 10:00pm |
| Location: | zoom |
| Speaker: | A. Harper, TAMU |
| Title: | Def theory: the road to stacks |
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| Date: | November 25, 2020 |
| Time: | 11:00am |
| Location: | zoom |
| Speaker: | F. Gesmundo, MPI Leipzig |
| Title: | cubics with Hilbert function 1771 |
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| Date: | November 29, 2020 |
| Time: | 10:00am |
| Location: | zoom |
| Speaker: | A. Huang, TAMU |
| Title: | Introduction to minimal free resolutions |
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| Date: | December 3, 2020 |
| Time: | 10:45am |
| Location: | zoom |
| Speaker: | JM Landsberg, TAMU |
| Title: | Introduction to Bott-Borel-Weil Thm. |
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| Date: | December 8, 2020 |
| Time: | 10:00am |
| Location: | zoom |
| Speaker: | Chia-Yu Chang, TAMU |
| Title: | Minimal components of the quot scheme I |
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| Date: | December 9, 2020 |
| Time: | 09:00am |
| Location: | zoom |
| Speaker: | A. Pal, TAMU |
| Title: | Tensors of minimal border rank |
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| Date: | December 16, 2020 |
| Time: | 10:00am |
| Location: | zoom |
| Speaker: | Tomasz Mandzuik, U. Warsaw |
| Title: | Limits of ideals of points in projective space |
| Abstract: | The notion of the border rank of a homogeneous polynomial is related, by border apolarity, to ideals that are limits of ideals of points in general position in projective space. I will discuss some conditions for an ideal to be such a limit. For projective plane I will present a sufficient condition and for projective space of arbitrary dimension I will give a necessary condition.
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| Date: | December 29, 2020 |
| Time: | 10:00am |
| Location: | zoom |
| Speaker: | Amy Huang, TAMU |
| Title: | Minimal Set of Generators of Ideals Defining Nilpotent Orbit Closures |
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| Date: | December 30, 2020 |
| Time: | 10:00am |
| Location: | zoom |
| Speaker: | Arthur Bik, U. Bern |
| Title: | Strength of polynomials via polynomial functors |
| Abstract: | The strength of a homogeneous polynomial is a subadditive invariant determined by defining a polynomial to have strength 1 when it is reducible and nonzero. It has been defined by Ananyan and Hochster in their paper proving Stillman's conjecture and has appeared in various works since. The goal of this talk is prove that the set of homogeneous polynomials of degree d in n variables of strength at most r is not always Zariski-closed. The proof involves techniques from the geometry of polynomial functors, which we will define.
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