## University College London, 25/02/2014

#### Rahul Pandharipande

“Counting curves on K3 surfaces: the Katz-Klemm-Vafa formula.”

I will explain our recent proof (with R. Thomas) of the KKV formula governing higher genus curve counting in arbitrary classes on K3 surfaces. The subject intertwines Gromov-Witten, Noether-Lefschetz, and Donaldson-Thomas theories. A tour of these ideas will be included in the talk.

#### Ivan Smith

“Lagrangian immersions of exotic spheres.”

We study Lagrangian immersions into Euclidean space which have a single double point. A rigidity theorem for such immersions has applications to Arnold’s nearby Lagrangian submanifold conjecture. This talk reports on joint work with Tobias Ekholm.

#### Jean-Yves Welschinger

“Expected topology of random real algebraic submanifolds.”

Given a smooth projective manifold defined over the reals, what is the expected topology of a codimension k submanifold chosen at random? (as the vanishing locus of a random section of some rank k holomorphic vector bundle). I will explain how the L^2 estimates of Hörmander make it possible to tackle this question asymptotically and in particular to estimate its Betti numbers. This is a joint work with Damien Gayet.