Project Details
Projekt
Computational aspects of motivic Hadamard products
Applicant
Professor Dr. Michael Dettweiler
Subject Area
Mathematics
Term
from 2010 to 2015
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 171743955
The usual Hadamard product f * g of two power series f and g is well known to be related to the convolution on the multiplicative group of the complex numbers. If f and g are motivic power series in the sense that they describe the variation of periods of cohomology groups of two family of varieties, then also f * g is motivic by twisting the original families over the square of the multiplicative group. In this way one obtains families of Hadamard product motives which are important for many applications in mathematics and physics. The following motives occur as Hadamard products and illustrate the importance of this class: Motives of generalized hypergeometric differential equations, playing a role in the two-body problem in quantum mechanics, and motives of families of Calabi-Yau-varieties occurring in the mirror symmetry conjecture of string theory. The latter motives also play an important role in the recent proof of the Sato-Tate conjecture. The aim of this proposal is the development and the implementation of algorithms for the computation of the monodromy, Hodge Type and Galois representations for Hadamard product motives. The resulting programs should be applied among others on modularity questions of (rigid) Calabi-Yau varieties and the study of polylogarithms and Feynman integrals.
DFG Programme
Priority Programmes
