Relative non-commutative Calabi-Yau structures and shifted Lagrangians

          @misc{ scivideos_PIRSA:16040079,
            doi = {10.48660/16040079},
            url = {https://pirsa.org/16040079},
            author = {Brav, Christopher},
            keywords = {Mathematical physics},
            language = {en},
            title = {Relative non-commutative Calabi-Yau structures and shifted Lagrangians},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2016},
            month = {apr},
            note = {PIRSA:16040079 see, \url{https://scivideos.org/pirsa/16040079}}
          }
          

Abstract

We give a definition of relative Calabi-Yau structure on a dg functor f: A --> B, discussing a examples coming from algebraic geometry, homotopy theory, and representation theory. When A=0, this returns the usual definition of Calabi-Yau structure on a smooth dg category B. When A itself is endowed with a Calabi-Yau structure and relative Calabi-Yau structure on f is compatible with the absolute structure on A, then we sketch the construction of a shifted symplectic structure on the derived moduli space M_A of pseudo-perfect A-modules, as well as the construction of a Lagrangian structure on the induced map f* : M_B --> M_A of derived moduli. This is joint work with Tobias Dyckerhoff.