Organized by Mina Aganagic, Ivan Danilenko, Andrei Okounkov, and Peng Zhou

Weekly on **Mondays 2:10 PM** (Pacific Time)

Meetings are in-person, at **402** Physics South

We have a lunch on the 4th floor of Physics South before the seminar

If you want to be added to the seminar **mailing list**, use this link https://forms.gle/Qk7Vpz4Uxv7rSyWaA

For those joining us remotely, we have a Zoom link: https://berkeley.zoom.us/j/99373923587?pwd=SUhXamdtbHhJMUJERlJ4NVJHL1Jtdz09

Jan 17, 12:30PM* |
Roman Bezrukavnikov | Microlocal sheaves on homogeneous affine Springer fibers and quantum groups | Video |

Jan 23 | No Seminar |
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Jan 30 | Wenjun Niu | Quantum-supergroup-extensions of \(U_q^H(\mathfrak{sl}(2))\) at the fourth root of unity | |

Feb 6 | Constantin Teleman | TBA | |

Feb 13 | |||

Feb 20 | No Seminar |
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Feb 27 | No Seminar |
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Mar 6 | Pavel Putrov | TBA | |

Mar 13 | Lev Rozansky | TBA | |

Mar 20 | Jonathan Heckman | TBA | |

Mar 27 | No Seminar |
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Apr 3 | |||

Apr 10 | |||

Apr 17 | Andrei Negut | TBA | |

Apr 24 | Sergey Cherkis | TBA | |

May 1 |

*Special Day/Time/Location.

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.

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

I will report on a joint work in progress with Pablo Boixeda Alvarez, Michael McBreen and Zhiwei Yun where categories of microlocal sheaves on some affine Springer fibers are described in terms of the Langlands dual group. In particular, in the slope 1 case we recover the regular block in the category of (graded) modules over the small quantum groups. Assuming a general formalism connecting microlocal sheaves to Fukaya categories, this yields new examples of homological mirror symmetry, including the mirror dual to \(T^*(G/B)\).

In work to appear with Ballin-Creutzig-Dimofte, we constructed vertex operator algebras associated to A and B twists of 3d N=4 abelian gauge theories. These are boundary VOAs supported on holomorphic boundary conditions of Costello-Gaiotto. For the B twist, the vertex algebra \(V_B\) is a simple current extension of an affine Lie superalgebra, and using the work of Creutzig-Kanade-McRae, we can study its representation theory using this simple current extension. An analogous extension procedure for quantum groups was developed by Creutzig-Rupert. I will explain how to apply their strategy to \(U_q^H(\mathfrak{sl}(2))\), the unrolled restricted quantum group at 4-th root of unity, and obtain a quantum supergroup whose category of representations is equivalent to that of \(V_B\). This is joint work in progress with T. Creutzig and T. Dimofte.