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Seminar

Fellowship of the Ring, National Seminar: Symbolic powers, interpolation and related problems April 22, 2021 (01:30 PM PDT - 03:00 PM PDT)
Parent Program: --
Location: MSRI: Online/Virtual
Speaker(s) Paolo Mantero (University of Arkansas)
Description

To attend this seminar, you must register in advance, by clicking HERE.

Video
Abstract/Media

To attend this seminar, you must register in advance, by clicking HERE.

Abtract: Interpolation problems are classical problems arising in several areas of mathematics. Broadly speaking, they ask to determine specific information about the set of all hypersurfaces passing through a given set of points X with given multiplicities.

By a classical theorem of Zariski and Nagata, these questions translate into questions about symbolic powers of ideals of points, e.g. determining the initial degrees of the symbolic powers of an ideal defining a set of points, or their Hilbert functions.

In the first part of the talk we present a few known results, including a celebrated theorem by Alexander and Hirschowitz, and some of the many  related conjectures and open questions. In the second part of the talk, we discuss recent results and advances providing partial answers to some of these questions.

Part of this talk is based on a joint work with T. Ha, and prior joint work with L. Fouli and Y. Xie. 

Asset no preview Notes 8.85 MB application/pdf

Symbolic Powers, Interpolation and Related Problems