Sums in Progressions to Squarefree Moduli Among Polynomials Over a Finite Field

Explore a mathematical lecture on sums in progressions to squarefree moduli among polynomials over finite fields. Delve into topics such as primes in progressions, Fourier analysis approaches, and bounds on sums in progressions. Examine the polynomial analogue and the anatomy of polynomials, including an introduction, theorem, and methods for counting polynomials with large values. Investigate the Poisson Dirichlet distribution control and progress towards the main theorem by studying arithmetic functions and the trivial character. Conclude with a general formulation of the main theorem and its applications in this 58-minute presentation from the Hausdorff Center for Mathematics.

Primes in progressions
Approach by Fourier analysis
Bounds on sums in progressions
The analogue with polynomials
Anatomy of polynomials: Intro
Anatomy of polynomials: Theorem
Anatomy of polynomials: Counting polynomials with large
Anatomy of polynomials: Controlling the Poisson Dirichlet
Towards the main theorem: Arithmetic functions
The trivial character
Main theorem (general formulation)
Applications