SMS scnews item created by Bill Unger at Mon 22 Oct 2012 1635
Type: Seminar
Distribution: World
Expiry: 25 Oct 2012
Calendar1: 25 Oct 2012 1505-1600
CalLoc1: Carslaw 535A
Auth: billu@daumier.maths.usyd.edu.au

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.


If you are registered you may mark the scnews item as read.
School members may try to .