## Algebraic Geometry Seminar

Man-Wai (Mandy) Cheung

Harvard

Batyrev-Borisov construction for cluster varieties

**Abstract:**Cluster varieties are blow up of toric varieties. They come in pairs (A,X), with A and X built from dual tori. Compactifications of A, studied by Gross, Hacking, Keel, and Kontsevich, generalize the polytope construction of toric varieties while the compactifications of X, studied by Fock and Goncharov, generalize the fan construction. The conjecture is that the A and the X cluster varieties are mirrors to each other. Together with Tim Magee, we have shown that there exists a positive polytope for the type A cluster varieties which give us a hint to the Batyrev-Borisov construction.

Wednesday March 6, 2019 at 4:00 PM in 427 SEO