Speaker
Description
The theme of this talk is to use a combinatorial approach, namely the diagonal coefficients of powers of a given polynomial, to infer arithmetic and analytic properties of the corresponding hypersurface; in the case where the hypersurface has degree equal to the number of variables (Calabi-Yau condition). Firstly, I will recall how the number of points over Fp can be read off, modulo p, from a single diagonal coefficient. I will then discuss a generalization to prime powers (joint work with Francis Brown). In the second part of the talk, I will discuss how the Apery limits of the sequence of diagonal coefficients furthermore encode the periods of the complement of the hypersurface relative to the coordinate simplex. I will illustrate all these phenomena with examples from Feynman integrals, i.e. hypersurfaces associated to graphs, using previous joint work with Karen Yeats.
