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Intro to the theta correspondence I

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NC2W01 - Making the bridge: Exploring new connections between number theory and physics

In this series of talks, I will provide a brief introduction to the theta correspondence for non-specialists. The classical theory of theta functions is one of the most basic parts of the theory of modular forms. Its reformulation in terms of representation theory reveals a lot of not previously evident structure and, for example, allows one to transfer automorphic representations between groups in a dual pair. I will describe this theta correspondence and the (regularized) Siegel-Weil formula and Rallis inner product formula which link the non-vanishing of the correspondence to poles and values of Langlands L-functions.

This talk is part of the Isaac Newton Institute Seminar Series series.

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