Organized by Mina Aganagic, Ivan Danilenko, 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://groups.google.com/g/berkeley-string-math

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

Aug 28 | Yin Lee | Hypertoric convolution algebras as Fukaya categories | Video |

Sept 4 | No Seminar |
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Sept 11 | No Seminar |
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Sept 18 | Sujay Nair | The SCFT/VOA correspondence for twisted class S | |

Sept 25 | No Seminar |
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Oct 2 | Justin Hilburn | TBA | |

Oct 9 | Alexei Oblomkov | TBA | |

Oct 16 | Niklas Garner | TBA | |

Oct 23 | Shaoyun Bai | TBA | |

Oct 30 | Nathan Haouzi | TBA | |

Nov 6 | |||

Nov 13 | |||

Nov 20 | No Seminar |
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Nov 27 | Mykola Dedushenko | TBA | |

Dec 4 |

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.

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

Given a polarized hyperplane arrangement, Braden-Licata-Proudfoot-Webster defined two convolution algebras: A & B. We show that both of them can be realized as Fukaya categories of hypertoric varieties. This proves a conjecture of Braden-Licata-Phan-Proudfoot-Webster in 2009 and gives a geometric interpretation of the Koszul duality between A & B. The proof relies on the construction of non-commutative vector fields on Fukaya categories (Abouzaid-Smith), the surgery quasi-isomorphism for singular Legendrians (Asplund-Ekholm), and the cobar interpretation of the Chekanov-Eliashberg DGA (Ekholm-Lekili). Time permitted, I'll also talk about the homological mirror symmetry for hypertoric varieties and the relation to knot Floer homology. This is based on joint works in progress with Sukjoo Lee, Siyang Liu and Cheuk Yu Mak.

In 2013, Beem-Lemos-Liendo-Peelaers-Rastelli-van Rees constructed a correspondence between four dimensional N=2 SCFTs, a certain kind of supersymmetric quantum field theory, and vertex algebras. When applied to the theories of class S, one obtains a rich family of vertex algebras which furnish novel representations of critical level, affine Kac-Moody algebras. Moreover, these vertex algebras satisfy an intricate set of gluing relations, arising from the geometric origins of class S.

I will review a construction of this family, due to Arakawa. Then I will explain an extension of this work to the setting of twisted class S, where modules of two different affine Kac-Moody algebras are sewn together. This talk is based on joint work with Christopher Beem.