Computational Algebra Seminar: Watkins -- Hypergeometric Motives

Speaker: Mark Watkins (University of Sydney)
Title: Hypergeometric motives
Time & Place: 3:05-4pm, Thursday 25 October, Carlaw 535.

Abstract:
Hypergeometric differential equations (dating to Gauss and before)
are example of Fuchsian equations; their only singularities are
regular at 0, 1, and infinity. A theorem of Pochhammer relates their
monodromy to a group-theoretic question regarding pseudo-reflections,
which was answered by Levelt in his 1961 thesis. In the arithmetic case,
where the monodromy has (Galois-stable) roots of unity as eigenvalues,
Katz gives an interpretation of the l-adic behaviour explicitly in
terms of Gauss sums, and Rodriguez-Villegas conjectures the existence
of a family of pure motives that realises this (at the level of Euler
factors of the L-function). We give some examples of this jargon, discuss
computations of Cohen, and describe the associated Magma package.