Venkataramana (Tata Institute of Fundamental Research, Mumbai)

"Monodromy and arithmetic groups"

A natural class of subgroups of SL(N,Z) are monodromy groups, especially those arising from hypergeometric functions. This talk, which presents some recent work with Sandip Singh, is about those monodromy groups which are arithmetic subgroups of certain symplectic groups. We show that there are at least 60 examples of four by four symplectic hypergeometric groups which are arithmetic. The method also shows that certain families of Calabi-Yau threefolds parametrised by the thrice punctured projective line, have arithmetic groups as monodromy groups.