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New results on prime polynomials

Algebra & Discrete Mathematics

Speaker: Will Sawin, Columbia U
Location: Zoom lecture
Start time: Thu, Nov 12 2020, 10:00AM

Many conjectures in number theory have analogues for polynomials in one variable over a finite field. In recent work with Mark Shusterman, we proved analogues of two conjectures about prime numbers - the twin primes conjecture and the conjecture that there are infinitely many primes of the form $n^2+1$. The proofs combine elementary, classical identities about the primes with elementary, non-classical manipulations of polynomials and geometric methods. I will give an introduction to these ideas.

All meetings this quarter will be by Zoom. Please see announcements or contact organizers for the passcode. Slides for the talk are also available.

Stay afterwards for a brief, informal reception. Refreshments will be self-provided.