Sums in progressions over F_q[T], the symmetric group, and geometry
Sums in progressions over F_q[T], the symmetric group, and geometry
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Will Sawin, Columbia University
In-Person and Online Talk听
Zoom link:听听
Passcode: The three digit integer that is the cube of the sum of its digits
I will discuss some recent progress in analytic number听 theory for polynomials over finite fields, giving strong new estimates听for the number of primes in arithmetic progressions, as well as for听sums of some arithmetic functions in arithmetic progressions. The听strategy of proof is fundamentally geometric, and I will explain some听of the geometric ideas in the proof, including how we can use the听representation of the symmetric group to handle many different arithmetic functions in a uniform way.