Type: Seminar

Distribution: World

Expiry: 25 Oct 2012

Auth: billu@daumier.maths.usyd.edu.au

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.