Northern California Symplectic Geometry Seminar: Symplectic structures in derived algebraic geometry

Seminar | April 1 | 2:30-3:30 p.m. | 740 Evans Hall

 Gabriele Vezzosi, University of Florence

 Department of Mathematics

After sketching the basics of derived algebraic geometry, I will explain how to define symplectic and lagrangian structures in this setting. A derived symplectic structure has a “shift” (or degree) that is zero for usual symplectic structures. This degree allows us a greater freedom, e.g. it leads to the fact that the derived intersection of two usual lagrangians is symplectic with a $-1$ shift. I will describe the basic existence theorems for symplectic structures on derived moduli spaces.