Maxson Lecture Series

Date: April 23, 2018

Time: 3:00PM - 4:00PM

Location: Blocker 117

Speaker: Fernando Rodriguez-Villegas, The Abdus Salam International Centre for Theoretical Physics

Title: Maxson Lecture I: Hypergeometric functions and L-series

Abstract: The classical one-variable hypergeometric functions _nF_n-1 with rational parameter has a geometric origin. This means that they arise from a one-parameter family of motives. In particular, for each rational value of the parameter we obtain an L-function of rank n. For example ₂F₁(1/2,1/2;1,t) corresponds in this way to the Legendre family of elliptic curves E_t: y²=x(x-1)(x-t). For each rational number t≠0,1 the rank 2 L-function is that of E_t.
Hypergeometric motives represent a class of motives that is accessible for detail study and still large enough to cover a wide range of features. The talk will focus on the explicit calculation of their L-functions.