BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Pavel Etingof (MIT) DTSTART:20201109T160000Z DTEND:20201109T165000Z DTSTAMP:20260421T093710Z UID:icra2020/1 DESCRIPTION:Title: Symmetric tensor categories I\nby Pavel Etingof (MIT) as part of ICRA 2020\n\n\nAbstract\nLecture 1: Algebra and representation theory without vector spaces.\n\nA modern view of representation theory is that it is a s tudy not just of individual representations (say\, finite dimensional repr esentations of an affine group or\, more generally\, supergroup scheme G o ver an algebraically closed field k ) but also of the category Rep(G) form ed by them. The properties of Rep(G) can be summarized by saying that it i s a symmetric tensor category (shortly\, STC) which uniquely determines G . A STC is a natural home for studying any kind of linear algebraic struct ures (commutative algebras\, Lie algebras\, Hopf algebras\, modules over t hem\, etc.)\; for instance\, doing so in Rep(G) amounts to studying such s tructures with a G -symmetry. It is therefore natural to ask: does the stu dy of STC reduce to group representation theory\, or is it more general? I n other words\, do there exist STC other than Rep(G) ? If so\, this would be interesting\, since algebra in such STC would be a new kind of algebra\ , one “without vector spaces”. Luckily\, the answer turns out to be “yes”. I will discuss examples in characteristic zero and p>0 \, and a lso Deligne’s theorem\, which puts restrictions on the kind of examples one can have.\n LOCATION:https://researchseminars.org/talk/icra2020/1/ END:VEVENT END:VCALENDAR