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Адрес: 119048, Москва,
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тел. (495) 916-89-05
тел. (495) 772-95-90 *12720
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E-mail: math@hse.ru

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mathstudyoffice@hse.ru
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Руководство
Заместитель декана по учебной работе Артамкин Игорь Вадимович
Заместитель декана Кузнецова Вера Витальевна
Заместитель декана по науке Фейгин Евгений Борисович

Учебный семинар Михаила Хованова по категорификации по четвергам

We announce a new learning seminar on categorification. Our first meeting will occur at 1:00 pm Eastern Time (= 20:00 Moscow Time) on Thursday May 21st and will continue at this time every week for the remainder of the summer.  The first two lectures, on May 21st and 28th will be given by Gregoire Naisse (MPIM) on "Odd Khovanov homology for tangles " (full abstract included below).

- Talks will be 50 minutes + 10 minutes of questions, but feel free to stay afterwards to chat if you'd like. 

- The first 60 minutes of our meetings will be recorded so that those who can't make it to the live meeting can still watch the talks. We plan on making these videos available online.

- We plan to follow the usual Zoom etiquette: Keep your microphone muted during the talk. If you have questions, please type them into the chat, and one of the organizers will notify the speaker of questions during a natural pause.


If you are interested in participating and would like to receive the weekly Zoom links and information please fill in the sign-up sheet below: 

Sign up here

 

Our first 2 talks (Thursday, on May 21st and 28th) are to be given by Grégoire Naisse (MPIM). The title and abstract are below:
Title: Odd Khovanov homology for tangles

Abstract: Khovanov categorified the Jones polynomial by constructing a corresponding link homology. His construction admits an anticommutative version (referred to as 'odd') that was developed by Ozsváth, Rasmussen and Szabó. The usual (or 'even') construction extends to tangles, taking the form of the homotopy type of a complex of bimodules over the arc algebra. The 'odd' equivalent to the arc algebra is non-associative, making it not clear what a bimodule over it should be. In the first part of the talk, I'll explain how ORS construction works in the context of chronological cobordisms, as introduced by Putyra. Then, I'll sketch how to extend this to tangles by using an odd version of arc algebras. We will quickly see that it is not naively possible to use it to construct an odd invariant, mainly because the odd arc algebra is not associative. In the second part of the talk, I'll explain how, by changing the monoidal category of vector spaces we work in, we can solve the non-associativity issue of the arc algebra. Then, we will sketch how to use it to construct an odd version of Khovanov invariant for tangles. This is a joint work with Krzysztof Putyra.

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