BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yuri Berest (Cornell) DTSTART:20211027T200000Z DTEND:20211027T210000Z DTSTAMP:20260423T021043Z UID:MITLie/39 DESCRIPTION:Title: Topological realization of rings of quasi-invariants of finite reflection groups\nby Yuri Berest (Cornell) as part of MIT Lie groups seminar\n\n \nAbstract\nQuasi-invariants are natural geometric generalizations of clas sical invariant polynomials of finite reflection groups. They first appear ed in mathematical physics in the early 1990s\, and since then have found applications in a number of other areas (most notably\, representation the ory\, algebraic geometry and combinatorics).\n\nIn this talk\, I will expl ain how the algebras of quasi-invariants can be realized topologically: as (equivariant) cohomology rings of certain spaces naturally attached to co mpact connected Lie groups. Our main result can be viewed as a generalizat ion of a well-known theorem of A. Borel that realizes the algebra of invar iant polynomials of a Weyl group W as the cohomology ring of the classifyi ng space BG of the corresponding Lie group G. Replacing equivariant cohomo logy with equivariant K-theory gives a multiplicative (exponential) analog ues of quasi-invariants of Weyl groups. But perhaps more interesting is th e fact that one can also realize topologically the quasi-invariants of som e non-Coxeter groups: our `spaces of quasi-invariants' can be constructed in a purely homotopy-theoretic way\, and this construction extends natural ly to (p-adic) pseudoreflection groups. In this last case\, the compact Li e groups are replaced by p-compact groups (a.k.a. homotopy Lie groups). Th e talk is based on joint work with A. C. Ramadoss.\n LOCATION:https://researchseminars.org/talk/MITLie/39/ END:VEVENT END:VCALENDAR