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