BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Arkadij Bojko (Oxford) DTSTART:20201112T133000Z DTEND:20201112T143000Z DTSTAMP:20260423T005800Z UID:notts_ag/34 DESCRIPTION:Title: Orientations for DT invariants on quasi-projective Calabi-Yau $4$-folds< /a>\nby Arkadij Bojko (Oxford) as part of Online Nottingham algebraic geom etry seminar\n\n\nAbstract\nDonaldson-Thomas type invariants in complex di mension $4$ have attracted a lot of attention in the past few years. I wil l give a brief overview of how one can count coherent sheaves on Calabi-Ya u $4$-folds. Inherent to the definition of DT4 invariants is the notion of orientations on moduli spaces of sheaves/ perfect complexes. For virtual fundamental classes and virtual structure sheaves to be well-defined\, one needs to prove orientability. The result of Cao-Gross-Joyce does this for projective CY $4$-folds. However\, computations are more feasible in the non-compact setting using localization formulae\, where the fixed point lo ci inherit orientations from global ones\, and orientations of the virtual normal bundles come into play. I will explain how to use real determinant line bundles of Dirac operators on the double of the original Calabi-Yau manifold to construct orientations on the moduli stack of compactly suppor ted perfect complexes\, moduli schemes of stable pairs and Hilbert schemes . These are controlled by choices of orientations in K-theory and satisfy compatibility under direct sums. If time allows\, I will discuss the conne ction between the sings obtained from comparing orientations and universal wall-crossing formulae of Joyce using vertex algebras.\n LOCATION:https://researchseminars.org/talk/notts_ag/34/ END:VEVENT END:VCALENDAR