Dear all, 

I would like to announce the following Mathematics and String theory seminar at IPMU:

Speaker: Jorgen Rennemo (ASC Oxford)
Date&Time: 2016, Jan 12 (Tue), 13:15--14:45
Place: Kavli IPMU, Seminar Room A

Title: Homological projective duality for Sym^2 P^n

Abstract: A famous theorem of Bridgeland says that if X and Y are Calabi-Yau 3-folds, then "X birational to Y" implies "the derived categories of X and Y are equivalent". The converse does not hold, and a few years ago Hosono and Takagi gave one example, when they proved that a certain pair of Calabi-Yau 3-folds X and Y have equivalent derived categories, but are not birational. Only a handful of such pairs are known.

In their example, X is a complete intersection of divisors in Sym^2(P^4). The derived category of such a complete intersections may often be understood via Kuznetsov's theory of homological projective duality. With Hosono & Takagi's example as motivation, we find a description of the "homological projective dual" of Sym^2(P^n) for any n. As a corollary, this gives a partial computation of derived categories of complete intersections in Sym^2(P^n), and in particular recovers Hosono & Takagi's theorem when n = 4. I will explain this result and its proof, which is based on rephrasing the problem in terms of categories of matrix factorisations and then applying a variation of GIT stability.

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Todor Eliseev Milanov
Associate Professor 
Kavli IPMU,  Japan

todor.milanov at ipmu.jp