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Explore a comprehensive colloquium talk by Tasho Kaletha from the University of Michigan, titled "Representations of Reductive Groups Over Local and Global Fields." Delve into the pioneering work of Langlands and its impact on modern number theory, focusing on the theory of reductive algebraic groups and their representations. Survey classical and modern results in representation theory over various fields, including rational, real, complex, p-adic numbers, and rational functions or Laurent series over finite fields. Examine how these results connect to Langlands' ideas and the fundamental concept of symmetry in arithmetic and geometry. Gain insights into this key area of mathematics through this hour-long presentation, part of the University of Chicago Department of Mathematics' colloquia series.
