Joint IAS/Princeton University Number Theory Seminar

I have been developing a new bridge between number theory and symplectic geometry. The special program at the IAS and a workshop this week in Wolfensohn Hall are devoted to mirror symmetry. I will describe this bridge, explain that there are travel lanes in both directions, and discuss what the benefits are for us number theorists. I will focus in this talk on the generalized Kloosterman sums studied by Deligne, Dwork, Katz, Gross and Heinloth-Ngo-Yun, and which we relate to the Dubrovin-Givental quantum connection of flag varieties. Work with Thomas Lam.