Manchester Geometry Seminar - Timothy Logvinenko
| Dates: | 17 March 2025 |
|---|
| Times: | 15:00 - 16:00 |
|---|
| What is it: | Seminar |
|---|
| Organiser: | Department of Mathematics |
|---|
| Who is it for: | University staff, External researchers, Current University students |
|---|
|
Speaker: Dr Timothy Logvinenko (Cardiff)
Title: Skein-triangulated representations of generalised braids
Abstract:
There are many examples where the braid group Br_n acts on the derived category of an algebraic variety: the minimal resolutions of Kleinian singularities, the cotangent bundles of flag varieties, etc.
In this talk, I will report on a long-running project with Rina Anno (Kansas) where we 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. We consider these strands embedded in a ribbon graph, and allow ribbon twists.
For triangulated categories, it is natural to impose certain relations which result in the notion of a skein-triangulated representation of GBr_n. These relations generalise the famous skein relation used to define oriented link invariants such as Jones polynomial. We give two examples of skein-triangulated actions of GBr_n: on the cotangent bundles of flag varieties and on categorical nil-Hecke algebras. The latter example shows that any categorical action of Br_n can be lifted to a skein-triangulated action of GBr_n, generalising a result of Ed Segal that all autoequivalences are spherical twists.
Travel and Contact Information
Find event
Frank Adams Room 1
Alan Turing Building
Manchester
