For over 50 years, one of the most vibrant areas of mathematical research has been the Langlands Progam, which posits a remarkable connection between the study of algebraic equations and the study of symmetries of certain non-Euclidean spaces. Breakthrough Prize winner Richard Taylor will give a flavor of the Langlands Program in relatively concrete terms: namely, predictions about the number of solutions to polynomial congruences. Taylor will motivate and illustrate the talk with applications to Diophantine equations.
About the speaker:
A leader in the field of number theory and in particular Galois representations, automorphic forms, and Shimura varieties, Richard Taylor, with his collaborators, has developed powerful new techniques for use in solving longstanding problems, including the Shimura-Taniyama conjecture, the local Langlands conjecture, and the Sato-Tate conjecture. Currently, Taylor is interested in the relationship between l-adic representations for automorphic forms — how to construct l-adic representations for automorphic forms and how to prove given l-adic representations that arise in this way. Taylor is one of the winners of the first Breakthrough Prize in Mathematics, as well as many other awards including the Fermat Prize, the Clay Research Award, and the Shaw Prize in Mathematics.
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