Mixed Hodge numbers and factorial ratios

Abstract: The factorial ratios of the title are numbers such as $\frac{(30n)!n!}{(6n)!(10n)!(15n)!}$ considered by Chebyshev in his work on the distribution of prime numbers, which are integral for all n in a non-obvious way. I will discuss how integrality is related to the lack of interior points of the first few dilations of an associated polytope and the vanishing of certain Hodge numbers of associated varieties. This work is an offshoot of an ongoing project on hypergeometric motives joint with D. Roberts and M. Watkins.

number theory

Audience: researchers in the topic

EIMI Number Theory Seminar

Series comments: Password: the number of quadratic nonresidues modulo 23