Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Topological quantum field theory and dualities.

Many interesting algebraic and symplectic invariants, such as Gromov-Witten invariants, can be extracted from topological quantum fields theories naturally associated with geometry. I will introduce the requisite formalism and will explain how these invariants capture quantum correlators and will show how non-commutative Hodge structures help us reconstruct higher genus invariants out of categorical data and genus zero invariants. The reconstruction process is based on a classification of cohomological field theories and a Torelli type theorem in non-commutative Hodge theory. This is a joint work with L.Katzarkov and M.Kontsevich.