Home /  Commutative Algebra + Algebraic Geometry Seminar: "Taylor Polynomials of Rational Functions" & "The Dual of the Canonical Module and Applications"

Seminar

Commutative Algebra + Algebraic Geometry Seminar: "Taylor Polynomials of Rational Functions" & "The Dual of the Canonical Module and Applications" January 16, 2024 (04:00 PM PST - 06:00 PM PST)
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Location: UCB, Evans Hall, Rm 748
Speaker(s) Hailong Dao (University of Kansas), Bernd Sturmfels (University of California, Berkeley; Max-Planck-Institut für Mathematik in den Naturwissenschaften)
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"Taylor Polynomials of Rational Functions" - Bernd Sturmfels

Abstract: A Taylor variety consists of all fixed order Taylor polynomials of rational functions, where the number of variables and degrees of numerators and denominators are fixed. In one variable, this leads us to Padé approximation and rank constraints on Hankel matrices. We study the dimension and defining ideals of Taylor varieties. In three and more variables, there exist defective Taylor varieties, and we explain this with Fröberg's Conjecture in commutative algebra. This is joint work with Aldo Conca, Simone Naldi and Giorgio Ottaviani.

 

"The Dual of the Canonical Module and Applications" - Hailong Dao

Abstract:  Let R be a Noetherian ring with canonical module W. We will use the R-dual of W to define new invariants of R. We will discuss some surprising connections of these invariants to additive number theory and extremal components of  Hilbert schemes.  

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