Gabriele Vezzosi "An overview of derived algebraic geometry"

Gabriele Vezzosi (IMJ Paris 7)
An overview of derived algebraic geometry

Derived algebraic geometry is a generalization of algebraic geometry where commutative rings are replaced by 'commutative rings' having an intrinsic homotopy theory (e.g simplicial commutative rings and commutative differential graded algebras). I will motivate and introduce derived stacks, give some examples and sketch applications to obstruction theories and quantization of moduli problems.