Absolute Galois groups of 2-adic fields, AI, and formalization

Abstract: In 1982, Jannsen and Wingberg gave an explicit presentation for the absolute group of any $p$-adic field, as long as $p \ne 2$. I will describe the journey to completing this result by giving presentations for $2$-adic fields. Along the way I will discuss my experiences with AI-generated solutions, different methods for verification of proposed solutions, auto-formalization in Lean and the Tau Ceti project, which is rapidly expanding into a formal library spanning all of mathematics.

machine learningcombinatoricsnumber theory

Audience: researchers in the topic

AI, Combinatorics and Number Theory Seminar

Series comments: This seminar is devoted to the responsible and constructive use of AI in number theory and combinatorics. It is a space to think carefully about what these tools can and cannot do, and where the limits actually lie. Enthusiasm and skepticism are both welcome here, and we ask only that they be voiced with generosity. Questions from students and from people new to these areas are especially encouraged.

The seminar meets Online via Zoom from 2:00 PM – 3:00 PM Eastern Time.

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