Welcome to the Berkeley Informal String-Math Seminar
Spring 2025
Organized by Mina Aganagic, Sujay Nair, Peng Zhou and Jasper van de Kreeke. Weekly on Mondays 2:10 PM (PT) at 402 Physics South. You are invited for lunch on the 4th floor of Physics South before the seminar. Subscribe to the mailing list. Join via zoom. Youtube video archive
| Date | Speaker | Title |
|---|---|---|
| Feb 3 | Paul Wedrich | A braided monoidal (∞,2)-category from link homology |
| Feb 24 | Joerg Teschner | |
| Mar 3 | Cheuk-Yu Mak | |
| Mar 10 | ||
| Mar 17 | Andrei Okounkov | |
| Mar 24 | Merlin Christ | |
| Mar 31 | Ben Davison | |
| Apr 7 | Yalong Cao / Yehao Zhou | |
| Apr 14 | ||
| Apr 21 | Sam DeHority | |
| Apr 28 | ||
| May 5 | Yanki Lekili | |
| May 12 | Alex Weekes |
Seminar archive:Fall 2024 Spring 2024, Fall 2023, Spring 2023, Fall 2022, Spring 2022, Fall 2021, Spring 2021, Fall 2020, Summer 2020, Spring 2020, Fall 2019, Spring 2019, Fall 2018, Fall 2017, Spring 2017, Fall 2016
A note to the speakers: This is a research seminar, intended for mathematicians and physicists. For the speaker to successfully reach the audience in both fields, it is important to explain, as clearly as possible: the motivations for the work, questions addressed, key ideas. The audience may fail to appreciate the glory of the result, otherwise.
Feb 3rd, Paul Wedrich (Univ. Hamburg)
A braided monoidal (∞,2)-category from link homology
An early highlight of quantum topology was the observation that the Jones polynomial — and many other knot and link invariants — arise from braided monoidal categories of quantum group representations. In hindsight, this can be understood as underlying reason for the existence of associated topological quantum field theories (TQFTs) in 3 and 4 dimensions.
Not much later, Khovanov discovered a link homology theory that categorifies the Jones polynomial. It associates graded chain complexes to links, from which the Jones polynomials can be recovered. It was therefore speculated that Khovanov homology and its variants may themselves be expressible in terms of certain braided monoidal 2-categories and that there should exist associated TQFTs in 4 and 5 dimensions that may be sensitive to smooth structure.
A major challenge in fully realizing this dream is the problem of coherence: Link homology theories live in the world of homological algebra, where constructing a braided monoidal structure in principle requires an infinite amount of higher and higher homological coherence data. In this talk, I will sketch a proposed solution to this problem, joint with Leon Liu, Aaron Mazel-Gee, David Reutter, and Catharina Stroppel, and explain how we use the language of infinity-categories to build an E2-monoidal (∞,2)-category which categorifies the Hecke braided monoidal category underlying the HOMFLYPT link polynomial.