BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tim Logvinenko (Cardiff) DTSTART:20200423T120000Z DTEND:20200423T130000Z DTSTAMP:20260423T041352Z UID:notts_ag/1 DESCRIPTION:Title: CANCELLED - Skein-triangulated representations of generalised braids\ nby Tim Logvinenko (Cardiff) as part of Online Nottingham algebraic geomet ry seminar\n\n\nAbstract\nOrdinary braid group $\\mathrm{Br}_n$ is a well- known algebraic structure which encodes configurations of n non-touching s trands ("braids") up to continuous transformations ("isotopies"). A classi cal result of Khovanov and Thomas states that there is a natural categoric al action of $\\mathrm{Br}_n$ on the derived category of the cotangent bun dle of the variety of complete flags in $\\mathbb{C}^n$.\nIn this talk\, I will introduce a new structure: the category $\\mathrm{GBr}_n$ of general ised braids. These are the braids whose strands are allowed to touch in a certain way. They have multiple endpoint configurations and can be non-inv ertible\, thus forming a category rather than a group. In the context of t riangulated categories\, it is natural to impose certain relations which r esult in the notion of a skein-triangulated representation of $\\mathrm{GB r}_n$.\nA decade-old conjecture states that there a skein-triangulated act ion of $\\mathrm{GBr}_n$ on the cotangent bundles of the varieties of full and partial flags in $\\mathbb{C}^n$. We prove this conjecture for $n = 3 $. We also show that any categorical action of $\\mathrm{Br}_n$ can be lif ted to a skein-triangulated action of $\\mathrm{GBr}_n$\, which behaves li ke a categorical nil Hecke algebra. This is a joint work with Rina Anno an d Lorenzo De Biase.\n LOCATION:https://researchseminars.org/talk/notts_ag/1/ END:VEVENT END:VCALENDAR