Local systems, exponential sums, and simple groups

Abstract: We study the possible structure of monodromy groups of Airy, Kloosterman, and hypergeometric $\ell$-adic sheaves in characteristic $p$. We also discuss explicit constructions of local systems and their related exponential sums on $\mathbb{G}_m$ or $\mathbb{A}^1$ that realize various (close to be) simple groups.

This will be a 2-part talk, with Katz giving part 1 starting at 4:35pm Eastern (via zoom, projected on the screen in 2-449), and Tiep giving part 2 starting at around 5:20pm in person in 2-449.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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