BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tudor Padurariu (MIT) DTSTART:20200623T191500Z DTEND:20200623T194500Z DTSTAMP:20260424T133919Z UID:GRT-2020/16 DESCRIPTION:Title: K-theoretic Hall algebras\nby Tudor Padurariu (MIT) as part of Geome tric Representation Theory conference\n\n\nAbstract\nGiven a quiver with p otential\, Kontsevich-Soibelman constructed a Hall algebra on the cohomolo gy of the stack of representations of $(Q\,W)$. In particular cases\, one recovers positive parts of Yangians as defined by Maulik-Okounkov. For gen eral $(Q\,W)$\, the Hall algebra has nice structure properties\, for examp le Davison-Meinhardt proved a PBW theorem for it using the decomposition t heorem.\n\nOne can define a $K$-theoretic version of this algebra using ce rtain categories of singularities that depend on the stack of representati ons of $(Q\,W)$. In particular cases\, these Hall algebras are positive pa rts of quantum affine algebras. We show that some of the structure propert ies in cohomology\, such as the PBW theorem\, can be lifted to $K$-theory\ , replacing the use of the decomposition theorem with semi-orthogonal deco mpositions.\n LOCATION:https://researchseminars.org/talk/GRT-2020/16/ END:VEVENT END:VCALENDAR