BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Timothy Logvinenko (Cardiff University) DTSTART:20201008T153000Z DTEND:20201008T163000Z DTSTAMP:20260423T021440Z UID:ZAG/56 DESCRIPTION:Title: Ske in-triangulated representations of generalised braids\nby Timothy Logv inenko (Cardiff University) as part of ZAG (Zoom Algebraic Geometry) semin ar\n\n\nAbstract\nOrdinary braid group Br_n is a well-known algebraic stru cture which encodes configurations of n non-touching strands (“braids” ) up to continious transformations (“isotopies”). A classical result o f Khovanov and Thomas states that there is a natural categorical action of Br_n on the derived category of the cotangent bundle of the variety of co mplete flags in C^n.\nIn this talk\, I will introduce a new structure: the category GBr_n of generalised braids. These are the braids whose strands are allowed to touch in a certain way. They have multiple endpoint configu rations and can be non-invertible\, thus forming a category rather than a group. In the context of triangulated categories\, it is natural to impose certain relations which result in the notion of a skein-triangulated repr esentation of GBr_n.\nA decade-old conjecture states that there a skein-tr iangulated action of GBr_n on the cotangent bundles of the varieties of fu ll and partial flags in C^n. We prove this conjecture for n = 3. We also s how that any categorical action of Br_n can be lifted to a skein-triangula ted action of GBr_n\, which behaves like a categorical nil Hecke algebra. This is a joint work with Rina Anno and Lorenzo De Biase.\n LOCATION:https://researchseminars.org/talk/ZAG/56/ END:VEVENT END:VCALENDAR