BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dougal Davis DTSTART:20200811T090000Z DTEND:20200811T100000Z DTSTAMP:20260423T052927Z UID:Freemath/15 DESCRIPTION:Title: Surface singularities and their deformations via principal bundles on el liptic curves\nby Dougal Davis as part of Free Mathematics Seminar\n\n \nAbstract\nIt is well known that du Val (aka simple\, Kleinian\, ADE\, .. .) singularities of algebraic surfaces are classified by Dynkin diagrams o f type ADE. A geometric link between the singularity and the Lie algebra o f the same type was given by Brieskorn in the 70s\, who showed that the si ngularity can be recovered by intersecting the nilpotent cone inside the L ie algebra with a transversal slice through a subregular nilpotent element . Brieskorn's construction also realises the entire transversal slice as t he total space of a miniversal deformation of the singularity. In this tal k\, I will discuss an elliptic version of this story\, where the Lie algeb ra is replaced with the stack of principal bundles on an elliptic curve. T here is still a notion of subregular slice in this stack\, and one gets a singular surface by intersecting such a thing with the locus of unstable b undles. I will explain which surfaces arise in this way\, and in what sens e the subregular slice is still the total space of a miniversal deformatio n. Time permitting\, I will also touch on how the BCFG types are related t o the ADE ones (in a different way to the story for Lie algebras!)\, and o n some questions about Poisson structures and their quantisations.\n LOCATION:https://researchseminars.org/talk/Freemath/15/ END:VEVENT END:VCALENDAR