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Dualities have proven useful in many areas of mathematics and physics. A famous example is the duality between elliptic curves and modular forms that led to the proof of Fermat’s last theorem. This is an example of an arithmetic global Langlands duality. More recently, Kapustin and Witten have used the S-duality in quantum field theory to clarify aspects of a geometric version of a global Langlands duality. In this talk I will explain how one can go the other direction and use number theoretic ideas to clarify aspects of the T-duality of two-dimensional quantum gravity.

There will be a reception after the talk.