Speaker:  Frank Calegari (University of Chicago)

Title:  The arithmetic of power series

Abstract:  A function of a complex variable which is holomorphic around  = 0 has a power series expansion .  Suppose that the  are all integers: what restrictions does that place on the function ?  We explore the relationship between this problem to questions in complex analysis, number theory, and to Klein’s famous observation that not all finite index subgroups of SL₂(Z) are determined by congruence conditions. This talk is based on joint work with Vesselin Dimitrov and Yunqing Tang.

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