|Speaker:||Daniele Faenzi (Bourgogne U) and Zhen Hua (HKU)|
|Title:||(Daniele Faenzi) Homological projective duality for determinantal varieties (Zheng Hua) Some geometric problems associated to the elliptic sklyanin algebras|
|Date (JST):||Mon, Jul 06, 2015, 10:00 - 11:45|
|Place:||Seminar Room A|
(Daniele Faenzi) Homological projective duality for determinantal varieties Abstract. I will discuss an instance of Kuznetsov's homological projective duality, providing a categorical version of the classical duality of matrices of given rank and corank. If time allows I will discuss some work in progress on application of the same approach to Grassmannian / Pfaffian duality. In collaboration with M. Bernardara and M. Bolognesi.
(Zheng Hua) In the first part of the talk, I will survey two constructions of the elliptic sklyanian algebras. The first one is due to Artin, Tate and Van den Bergh. It is from the point of view of noncommutative deformation of projective space. The second one is due to Sklyanin, Cherednik, Feigin-Odesskii. It is from the point of view of quantum integrable system. After that, I will explain how to view sklyanin algebras as quantisation of certain moduli spaces on elliptic curves.
In the second part of the talk, I will explain some details about the last part of the first talk and introduce a geometric interpretation of the Yang-Baxter equation due to Polishchuk.
|Remarks:||10:00-10:45, Faenzi Part I
11:00-11:45, Hua Part I