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Coxeter-James Prize

VINAYAK VATSAL, University of British Columbia, Vancouver
Special values of L-functions modulo p

I will give a survey of old and new results on the non-vanishing of families of L-functions modulo a prime p. The emphasis will be on showing how all these results ultimately rely on some kind of rigidity principle that seems to dictate the the Zariski closure of a various group orbits tends to be rather big in comparison to the group.