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Speaker:

D. van Straten
Date:

Mon, 15/09/2014 - 15:00 - 16:00
Location:

MPIM Lecture Hall Pencils of Calabi-Yau threefolds give rise to local systems and differential operators with very strong arithmetical properties. One interesting source of examples come from regularised quantum cohomology D-modules of Fano varieties. Although no classification is known, one may hope to characerise and construct such operators from first principles. I will describe joint work in progress with V. Golyshev and A. Mellit, 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 obtain the Apery-Beukers-Zagier operators of the Beauville list of elliptic modular surfaces.

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