Mathematics Department Colloquium: Identities for $1/\pi ^2$ and special hypergeometric motives

Colloquium | September 26 | 4:10-5 p.m. | 60 Evans Hall

 John Voight, Dartmouth College

 Department of Mathematics

More than a century ago, Ramanujan discovered remarkable formulas for $1/\pi $. Inspired by these discoveries, similar Ramanujan-like expressions for $1/\pi ^2$ have been uncovered recently by Guillera. We explain the provenance of these formulas: we recognize certain special hypergeometric motives as arising from Hilbert modular forms in an explicit way. This is joint work with Lassina Dembélé, Alexei Panchishkin, and Wadim Zudilin.