BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Saugata Basu (Purdue University\, West Lafayette\, IN\, USA) DTSTART:20230210T130000Z DTEND:20230210T140000Z DTSTAMP:20260423T021053Z UID:VCAS/174 DESCRIPTION:Title: H omology of symmetric semi-algebraic sets\nby Saugata Basu (Purdue Univ ersity\, West Lafayette\, IN\, USA) as part of IIT Bombay Virtual Commutat ive Algebra Seminar\n\n\nAbstract\nStudying the homology groups of semi-al gebraic subsets of $\\mathbb{R}^n$ and obtaining upper bounds\non the Bett i numbers has been a classical topic in real algebraic geometry beginning with the\nwork of Petrovskii and Oleinik\, Thom\, and Milnor. In this talk I will consider semi-algebraic\nsubsets of $\\mathbb{R}^n$ which are defi ned by symmetric polynomials and are thus stable under the\nstandard actio n of the symmetric group $\\mathfrak{S}_n$ on $\\mathbb{R}^n$.\nThe homolo gy groups (with rational coefficients) of such sets\nthus acquire extra st ructure as $\\mathfrak{S}_n$-modules leading to\npossible refinements on t he classical bounds. I will also mention some \nconnections with a homolog ical stability conjecture.\n \nJoint work (separately) with Daniel Perruc ci and Cordian Riener.\n LOCATION:https://researchseminars.org/talk/VCAS/174/ END:VEVENT END:VCALENDAR