Hypergeometric motives for rigid hypergeometric Calabi-Yau threefolds

Speaker: 

Wadim Zudilin

Affiliation: 

Radboud University Nijmegen (Netherlands) and the University of Newcastle (NSW, Australia)

Date: 

Wed, 16/08/2017 - 2:00pm

Venue: 

RC-4082, The Red Centre, UNSW

Abstract: 

In 2003, Fernando Rodriguez-Villegas conjectured fourteen congruences modulo $p^3$ that relate hypergeometric sums truncated at $p-1$ to the Fourier coefficients $a(p)$ of weight 4 modular forms. Such "supercongruences" are now understood as particular instances of hypergeometric motives (HGMs). In my talk I will review some ingredients of the theory of HGMs and illustrate its features on the fourteen examples of the underlying rigid Calabi-Yau threefolds. I will further outline some ideas in the proofs of Villegas's conjectures given recently in my joint work with Ling Long, Fang-Ting Tu and Noriko Yui.

School Seminar Series: