Topology Seminar by Joana Cirici

Topology Seminar

Speaker: Joana Cirici

Title: Rational homotopy of complex algebraic verieties

Abstract: The Formality Theorem of Deligne, Griffiths, Morgan and Sullivan states that the rational homotopy type of every smooth projective complex variety is entirely determined by its cohomology ring. In this talk, I will explain a generalization of this result to possibly singular varieties: for every complex algebraic variety there is a multiplicative spectral sequence encoding the rational homotopy type of its underlying topological space. I will then focus on particular simple examples and exploit this result to prove that large families of complex varieties, such as varieties with ordinary multiple points and hypersurfaces with isolated singularities, are formal topological spaces. I may even compute the rational homotopy groups of some threefolds if I have time.