Mikhail Kapranov 氏 (Kavli IPMU)
『 Lie algebras from secondary polytopes 』

The secondary polytope of a point configuration in the Euclidean space was introduced by Gelfand, Zelevinsky and the speaker long time ago in order to understand discriminants of multi-variable polynomials.
These polytopes have a remarkable factorization (or operadic) property: each face of any secondary polytope is isomorphic to the product of several other secondary polytopes.

The talk, based on joint work in progress with M. Kontsevich and Y. Soibelman, will explain how the factorization property can be used to construct Lie algebra-type objects: L¥infty and A¥infty-algebras.
These algebras turn out to be related to the problem of deformation of triangulated categories with semiorthogonal decompositions.