Commutative Algebra seminar
Speaker: Vaibhav Pandey (Purdue University, West Lafayette, USA)
Host: Sudhir R. Ghorpade
Title: The optimal number of equations needed to define a variety: Connections with invariant theory
Time, day and date: 5:0:00 PM – 6:00:00 PM, Friday, August 08
Venue: Ramanujan Hall
Abstract: The arithmetic rank of a variety is the smallest number of equations needed to define it, i.e., the number of hypersurfaces needed to cut out the given variety. In general, this number turns out to be notoriously difficult to compute.
This talk will shed light on the interplay between classical and modern techniques in algebra. We will begin with a quick introduction to classical invariant theory and its role in laying some of the groundwork for modern algebra. We will focus on the classical representations of linear algebraic groups and explicitly compute the arithmetic ranks of their `nullcone variety' (introduced by Hilbert) in all characteristics.
This is ongoing work with Jack Jeffries, Anurag Singh, and Uli Walther.