Exterior algebras and local mirror symmetry

Abstract: The exterior algebra plays an important role in mirror symmetry, as the Floer algebra of a Lagrangian torus bounding no holomorphic discs and as the Ext-algebra of the corresponding smooth point on the mirror. In the presence of holomorphic discs one obtains an A-infinity deformation of this picture, and I'll explain how to classify such deformations under a monotonicity hypothesis. This leads to a simple proof that the Floer algebra of a monotone torus is the endomorphism algebra of the expected matrix factorization of its superpotential, as well as a purely algebraic result generalizing the classification of Clifford algebras by quadratic forms

Mathematics

Audience: researchers in the topic

Rutgers symplectic geometry seminar

Series comments: Please contact the organizers for zoom link Soham Chanda, Yuhan Sun, Chris Woodward