Posted in

Speaker:

Slawek Cynk
Affiliation:

Jagiellonian University/MPIM
Date:

Wed, 2020-03-18 14:30 - 15:30
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar I will discuss modularity of a Calabi-Yau threefold $X$ with Hodge numbers of $H^3(X)$ equal to (1,1,1,1).

The restriction of the Galois representation on $H^3(X)$ decomposes over $Q(\sqrt{2})$ into the direct sum of

the Galois representation for a Hilbert modular form of weight [4,2] and its conjugate.

The Calabi-Yau threefold $X$ is defined as a resolution of singularities of a double covering of $P^3$ branched

along a union of eight planes. The proof is based on a careful study of geometry of $X$, which allows us to find a

rational map on $X$ acting as a multiplication by $\pm\sqrt{2}$ on the middle cohomology.

This is a joint work with M. Schütt and D. van Straten.

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