BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jenna Rajchgot (University of Saskatchewan) DTSTART:20200623T180000Z DTEND:20200623T190000Z DTSTAMP:20260424T133602Z UID:GRT-2020/15 DESCRIPTION:Title: Type D quiver representation varieties\, double Grassmannians\, and symm etric varieties\nby Jenna Rajchgot (University of Saskatchewan) as par t of Geometric Representation Theory conference\n\n\nAbstract\nSince the 1 980s\, mathematicians have found connections between orbit closures in typ e $A$ quiver representation varieties and Schubert varieties in type $A$ f lag varieties. For example\, singularity types appearing in type $A$ quive r orbit closures coincide with those appearing in Schubert varieties in ty pe $A$ flag varieties (Bobinski-Zwara)\; combinatorics of type $A$ quiver orbit closure containment is governed by Bruhat order on the symmetric gro up (follows from work of Zelevinsky\, Kinser-R.)\; and multiple researcher s have produced formulas for classes of type $A$ quiver orbit closures in equivariant cohomology and $K$-theory in terms of Schubert polynomials\, G rothendieck polynomials\, and related objects.\n \nAfter recalling some of this type $A$ story\, I will discuss joint work with Ryan Kinser on type $D$ quiver representation varieties. I will describe explicit embeddings w hich completes a circle of links between orbit closures in type $D$ quiver representation varieties\, $B$-orbit closures (for a Borel subgroup $B$ o f $GL_n$) in certain symmetric varieties $GL_n/K$\, and $B$-orbit closures in double Grassmannians $Gr(a\, n) \\times Gr(b\, n)$. I will end with so me geometric and combinatorial consequences\, as well as a brief discussio n of joint work in progress with Zachary Hamaker and Ryan Kinser on formul as for classes of type $D$ quiver orbit closures in equivariant cohomology .\n LOCATION:https://researchseminars.org/talk/GRT-2020/15/ END:VEVENT END:VCALENDAR