Abstract Duco van Straten

Duco van Straten will speak on

Elliptic modular surfaces via Langlands correspondence and congruence differential equations.

Abstract: Beyond hypergeometric or more generally rigid local systems, it is hard to characterise those that have a geometrical origin. On the level of differerential equations it is the classical problem of accessory parameters. I will describe joint work in progress with G. Golyshev, which shows that a Langlands approch via an explicit description of a Hecke-algebra given by Kontsevich, combined with the new idea of a "congruence sheaf" leads to a practical approach in the rank two case. This leads to a new approach to the Apery-Beukers-Zagier operators of the Beauville list of elliptic modular surfaces.