Organized by Fan Zhou, Cailan Li and Alvaro Martinez. Please email Cailan at ccl2166@columbia.edu to join the mailing list.
This is a learning seminar on representation theory, often with an eye towards categorification. There will be talks relating to quantum groups, Hecke algebras, symmetric functions, diagram algebras, and (in some cases) their categorifications.
Talks will roughly be 45 minutes followed by a 5 minute break followed by 45 more minutes. Please email Cailan at ccl2166@columbia.edu if you'd like to give a talk.
| Thu Sep 7 |
Fan Zhou The nilBrauer algebra and semi-highest weight theory Abstract: We discuss a modification of highest weight theory, “stratification theory”, introduced by Brundan-Stroppel, as well as the closely related theory of graded triangular bases, and discuss the nilBrauer algebra as an application of this theory. We also discuss some work-in-progress on the BGG resolution in this context. Notes. |
| Thu Sep 14 |
Fan Zhou Stratification and recollement of (stable infinity) categories and the "reconstruction philosophy" of BGG resolutions Abstract: This very general talk, while foreshadowed by the last talk, will be independent. We discuss stratifications of (stable infinity, but one can pretend triangulated more or less) categories first in great generality and then applied to recollements of representation categories. We then discuss how this can be used to give BGG-resolution-type results. Time permitting, we may discuss some more work-in-progress that we didn't get to discussing last time. Notes. |
| Thu Sep 21 |
Alvaro Martinez The dg trace Abstract: To a braid, one can associate a complex of certain bimodules over a polynomial ring, called Soergel bimodules. The algbraic counterpart of 'closing up the braid' is taking the 'trace' of this category, a general algebraic construction. In this talk, we will explain how this trace category fails to meet expectations and why, instead, we need a certain dg structure for things to work. Notes. |
| Thu Sep 28 |
Alvaro Martinez The dg trace (continued) Abstract: TBD Notes. |
| Thu Sep 28 |
Nicolas Jaramillo Torres TBD Abstract: TBD Notes. |