Gabriele Vezzosi

Vezzosi earned an MS degree in Physics at the University of Florence, under the supervision of Alexandre M. Vinogradov, and a PhD in Mathematics at the Scuola Normale Superiore in Pisa, under the supervision of Angelo Vistoli.

His first papers dealt with differential calculus over commutative rings, intersection theory, (equivariant) algebraic K-theory, motivic homotopy theory, and existence of vector bundles on singular algebraic surfaces.

More recently, Vezzosi together with Tony Pantev, Bertrand Toën and Michel Vaquié defined a derived version of symplectic structures[7] and studied important properties and examples (an important instance being Kai Behrend's symmetric obstruction theories); further together with Damien Calaque these authors introduced and studied a derived version of Poisson and coisotropic structures[8] with applications to deformation quantization.

[10][11][12] Vezzosi also defined a derived version of quadratic forms, and in collaboration with Benjamin Hennion and Mauro Porta, proved a very general formal gluing result along non-linear flags[13] with hints of application to a yet conjectural Geometric Langlands program for varieties of dimension bigger than 1.

Together with Benjamin Antieau, Vezzosi proved a Hochschild–Kostant–Rosenberg theorem (HKR) for varieties of dimension p in characteristic p.[14] In 2015 he organised the Oberwolfach Seminar on Derived Geometry[15] at the Mathematical Research Institute of Oberwolfach in Germany, and is an organiser of the one-semester thematic program at Mathematical Sciences Research Institute in Berkeley, California in 2019 on Derived algebraic geometry.