BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ben Davison (Edinburgh) DTSTART:20201026T141500Z DTEND:20201026T151500Z DTSTAMP:20260423T005737Z UID:OxGeom/1 DESCRIPTION:Title: C oproducts in the cohomological DT theory of 3-Calabi-Yau completions\n by Ben Davison (Edinburgh) as part of Oxford Geometry and Analysis Seminar \n\n\nAbstract\nGiven a suitably friendly category D we can take the 3-Cal abi Yau completion of D and obtain a 3-Calabi-Yau category E. The archetyp al example has D as the category of coherent sheaves on a smooth quasiproj ective surface\, then E is the category of coherent sheaves on the total s pace of the canonical bundle - a quasiprojective 3CY variety. The moduli s tack of semistable objects in the 3CY completion E supports a vanishing cy cle-type sheaf\, the hypercohomology of which is the basic object in the s tudy of the DT theory of E. Something extra happens when our input categor y is itself 2CY: examples include the category of local systems on a Riema nn surface\, the category of coherent sheaves on a K3/Abelian surface\, th e category of Higgs bundles on a smooth complete curve\, or the category o f representations of a preprojective algebra. In these cases\, the DT coho mology of E carries a cocommutative coproduct. I'll also explain how this interacts with older algebraic structures in cohomological DT theory to pr ovide a geometric construction of both well-known and new quantum groups.\ n LOCATION:https://researchseminars.org/talk/OxGeom/1/ END:VEVENT END:VCALENDAR