[geometry-ml:04187] Series of lectures by Professor Todor Milanov

[Kohei_Iwaki]

皆様

来週に以下の連続講演 (online) が予定されております。
世話人である Satoshi Nawata氏 (Fudan University) からの依頼により代理で投稿させて頂きます。
Zoom ID や パスワードは以下のサイトにも情報が掲載されていますのでご確認下さい。

https://researchseminars.org/seminar/Milanov <https://researchseminars.org/seminar/Milanov>

どうぞよろしくお願いします。

東京大学大学院数理科学研究科
岩木耕平


> 転送されたメッセージ:
> 
> 差出人: Satoshi Nawata <snawata ＠ gmail.com <mailto:snawata ＠ gmail.com>>
> 件名: can you share this info in math community?
> 日付: 2020年11月14日 23:25:56 JST
> 宛先: Kohei_Iwaki <iwaki ＠ ms.u-tokyo.ac.jp <mailto:iwaki ＠ ms.u-tokyo.ac.jp>>
> 
> Dear Kohei, 
> 
> I wonder if you could share a lecture series by Milanov in Japanese math community. Thanks in advance. 
> 
> Speaker: Todor Milanov (IPMU)
> Title: Towards Hirota Bilinear Equations in Gromov--Witten theory
> Time: 15:30--17:00, Nov 16-20 (Mon-Fri)
> Zoom ID: 9383671691 Password: 123456
> 
> If the quantum cohomology of a smooth projective variety X, or more generally a projective variety with an orbifold structure, is semisimple, then Dubrovin and Zhang have constructed an integrable hierarchy that governs the Gromov--Witten (GW) invariants of X. The main motivation for the work that I would like to present is to construct an infinite dimensional Grassmannian that parametrizes the solutions of the Dubrovin--Zhang hierarchies. Similar description was proposed first by Mikio Sato for the KP hierarchy and it is very useful, because it allows us to study integrable hierarchies via the methods of representation theory of infinite dimensional Lie algebras. Based on ideas of Givental, I developed a method for proving that the generating function of GW invariants satisfies a given system of Hirota Bilinear Equations (HBEs). This is exactly what I am planning to talk about in my lectures. Note however, that the existence of the HBEs is still not clear. Based on joint work with B. Bakalov, I can only speculate that the HBEs, if they exist at all, should come from the representation theory of a certain class of lattice vertex algebras, i.e., in principal, we have reduced the problem of constructing HBEs in GW theory to a problem about lattice vertex algebras. Our ideas with Bakalov should be tested in an interesting example, such as, X=CP^2 or X= orbifold structure on P^1 with negative orbifold Euler characteristics. At this point I am not ready to lecture about the relation to lattice VOA, but if time permits, I will try to say something. Here is a list of topics that I am planning to cover 
> 
> 1. Frobenius manifolds and quantum cohomology 
> 
> 2. Givental's higher genus reconstruction 
> 
> 3. Quantization formalism 
> 
> 4. Vertex operators and phase factors 
> 
> 5. Hirota Bilinear Equations: an example.
> 
> Best,
> Satoshi


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