BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Kamil Rychlewicz (Institute of Science and Technology Austria) DTSTART:20231106T080000Z DTEND:20231106T093000Z DTSTAMP:20260422T155807Z UID:HKUST-AG/25 DESCRIPTION:Title: Cohomology theories and rings of functions\nby Kamil Rychlewicz (Ins titute of Science and Technology Austria) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 5560.\n\nAbstract\nExtending the c lassical Poincare-Hopf theorem\, the work of Akyildiz\, Carrell\, Lieberma nn\, Sommese shows how to recover the cohomology ring of a smooth projecti ve variety from isolated zeros of a vector field. Thirty years later\, Bri on and Carrell showed how to find the spectrum of the torus-equivariant co homology as a geometrically defined scheme\, provided that the Borel of SL _2 acts with a single fixed point of the regular unipotent. In a joint wor k with Tamas Hausel we demonstrate how to see the spectrum of G-equivarian t cohomology\, if G is a linear group acting with similar assumptions. Thi s condition covers many interesting cases\, including flag varieties and B ott–Samelson resolutions. I will present this work and also show how to see the equivariant cohomology rings of spherical varieties as rings of fu nctions on non-affine schemes. Besides\, there are a lot of new directions and open questions I would like to advertise. This in particular concerns general\, potentially singular varieties\, as well as other equivariant c ohomology theories.\n LOCATION:https://researchseminars.org/talk/HKUST-AG/25/ END:VEVENT END:VCALENDAR