All talks will take place in room B3.02 of the Mathematics Institute at the University of Warwick.

Lecture notes of Marcos Mariño's talks can be found here.

Boris Dubrovin: Frobenius manifolds and integrable hierarchies


Claus Hertling: tt* geometry and oscillating integrals

tt* geometry is a generalization of variation of Hodge structures. It was considered first by Cecotti, Vafa and Dubrovin. An important case where it turns up are functions with isolated singularities on affine manifolds (Landau-Ginzburg models) and their oscillating integrals. In the lectures I will present a frame for tt* geometry, called TERP-structures, and I will discuss the realization via oscillating integrals. Then I will talk about nilpotent orbits and classifying spaces, which generalize work of Schmid, Griffiths, Cattani and Kaplan. In the irregular case the interplay with Stokes data is important. Relations to harmonic bundles and to recent work of Sabbah and T. Mochizuki will also be discussed.

Marcos Mariño: Topological Strings, Matrix Models, and Nonperturbative Effects [lecture notes]

In these lectures I will explain the connection between topological string theory on toric Calabi-Yau manifolds and random matrices. I will start by reviewing the basics of topological strings, local mirror symmetry, and random matrices. Then I will explain the basic conjectures and work out some illustrative examples. Finally, I will explain how this connection makes possible to compute instanton effects for this class of topological string theories, and sketch some connections between topological strings and the theory of resurgent functions.

Johannes Walcher: B-model Fusion

These lectures will cover a variety of topics that form the background for current understanding of B-model topological string on Calabi-Yau manifolds.

Physics: Origin of topological-antitopological fusion in twisted N=2 theories; D-branes in N=2 theories; special geometry and holomorphic anomaly equation; superpotentials and holomorphic Chern-Simons theory.

Mathematics: Variation of Hodge structure; normal functions and their infinitesimal invariants; matrix factorizations.