Representation Theory, Categorification, and Geometry Seminar (Fall 2026)
This is a seminar on the intersection of the subjects in the title. The seminar will be centered around the relationship between category O/Soergel calculus, KLR algebras, and Fukaya categories, as well as their applications to link homology. We also intend to discuss some algebraic geometry, for example coherent sheaves and Hodge theory. This is essentially a research seminar.
Talks will roughly be 1.25-1.5 hours, e.g. 45 minutes followed by a 5 minute break, followed by 45 more minutes. Please email Fan or Felix at fz2326@columbia.edu or fr2588@columbia.edu if you'd like to give a talk!
- Organizers: Felix Roz, Fan Zhou
- When: Thursday 05:00pm -- 06:30pm
- Where: Math Room 622
Schedule
- 09/10
- Speaker: n/a
- Title: Organizational
Abstract: Organizational meeting
- 09/17
- Speaker: Fan
- Title: Crash course in KLR
Abstract: We give a crash course in KLR algebras. We will define the KLR algebra, discuss its categorification properties, and describe the faithful action on polynomials. Time permitting we may say something about its representation theory.
- 09/24
- Speaker: Fan
- Title: The coherent KLR sheaf
Abstract: We give a coherent sheaf on a projective space recovering the KLR algebra on an affine chart. This recovers many structures of KLR, most notably the sl_2-action of Elias-Qi. Based on joint work with Matthew Hase-Liu.
- 10/01
- Speaker: Yifan
- Title: Hodge theory a la deCataldo-Migliorini
Abstract: This talk is an AG precursor to Felix's later talk, focusing on papers by deCataldo-Migliorini.
- 10/08
- Speaker: Ryan
- Title: Crash course in Soergel bimodules
Abstract: This talk is a Soergel precursor to Felix's later talk.
- 10/15
- Speaker: Felix
- Title: Hodge theory of Soergel bimodules
Abstract:
Syllabus
We intend to have the following talks, which will be distributed at the organizational meeting.
- Fukaya categories and their relationship to KLR/Soergel, 3-4 talks
- Hodge theory of Soergel bimodules, 1-2 talks
- Coherent sheaf theory of KLR algebras, 1-2 talks
- Applications to webs/link homology, 1-2 talks
- Categorification of Cartan algebras via coherent sheaves and plethysms, 1-2 talks
- Whatever introductory talks are necessary, depending on audience background, 0-2 talks
After the organizational meeting, we've decided to have the following talks in addition to the scheduled ones. We will schedule these as they draw closer.
- Homological knot invariants from mirror symmetry by Aganagic (Peter)
- Webs and foams and categorification (Felix)
- KLRW and tilting generators (Yousif)
- Fukaya talks (Elise)
- Plethysms and categorification of Cartan (Alvaro)
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