Seminar on operads and algebraic geometry

Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn
Organizers: Pedro Boavida de Brito, Geoffroy Horel, Marcy Robertson

15:00 - 16:00 Marco Robalo: K-theoretic Gromov-Witten invariants and derived geometry

Abstract: In this talk I will explain the idea of brane actions for operads and how it recovers the formalism of K-theoretic Gromov-Witten invariants of Givental-Lee. I will explain how the lax structure obtained through this process is related to h-descent in derived algebraic geometry. This is a joint work with Etienne Mann.

15:00 - 16:00 Joana Cirici: Rational homotopy of complex algebraic varieties

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.