Department of Mathematics

Virtual Commutative Algebra Seminar.

Speaker: Saugata Basu,
  Purdue University, West Lafayette, IN, USA
Date/Time: 10 February 2023, 6:30pm
(joining time 6:20 pm IST)

Gmeet link: meet.google.com/ujm-mmpg-ckq [1]

Title: Homology of symmetric semi-algebraic sets
Abstract: Studying the homology groups of semi-algebraic subsets of 
$\mathbb{R}^n$ and obtaining upper boundson the Betti numbers has been a 
classical topic in real algebraic geometry beginning with the work of 
Petrovskii and Oleinik, Thom, and Milnor. In this talk I will consider 
semi-algebraic subsets of $\mathbb{R}^n$ which are defined by symmetric 
polynomials and are thus stable under the standard action of the 
symmetric group $\mathfrak{S}_n$ on $\mathbb{R}^n$. The homology groups 
(with rational coefficients) of such sets thus acquire extra structure 
as $\mathfrak{S}_n$-modules leading to possible refinements on the 
classical bounds. I will also mention some connections with a 
homological stability conjecture.

Joint work (separately) with Daniel Perrucci and Cordian Riener.

For more information and links to previous seminars, visit the website 
of VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar