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Event Type:

Number Theory Seminar

Date/Time:

Tuesday, May 26, 2020 - 10:00 to 11:00

Location:

zoom (ID via Canvas page, or request)

Local Speaker:

Abstract:

In the late 1990's, Rodriguez Villegas observed strong structural connections between hypergeometric series arising as periods of certain abelian varieties and modular forms. In particular, he conjectured 14 congruences between truncations of certain hypergeometric series and Fourier coefficients of certain modular forms. These were proven piecemeal by several authors, culminating in 2017 with Long, Tu, Yui, and Zudilin devising an approach which proved all 14 of Rodriguez Villegas' conjectures. We give a brief summary of this approach, and present work towards generalizing this approach to construct and prove further such congruences, focusing specifically on a handful of congruences conjectured recently by Long.

Host: