AAG Seminar: Differential equations, hypergeometric families, and Beilinson's conjectures

Abstract: The Beilinson Conjectures relate an analytic quantity (determinant of a matrix of regulator-periods attached to algebraic cycles on a variety X/Q) to a number-theoretic one (special value of an L-function of X/Q); this is a massive generalization of the class-number formula of Dirichlet.  What is new here is a method for generating algebraic cycles (or really normal functions) on hypergeomtric families of Calabi-Yau varieties and calculating their regulators.  (The method of generating normal functions is related to toric geometry and mirror symmetry, and was motivated by work of Morrison and Walcher.)  With this in hand one can numerically check BC for countably many fibers in such a family.