New Avenues for the Circle Method - Lecture I

Explore new avenues for the circle method in this lecture by Jayce Getz. Delve into an adelic version of the delta-method developed by Duke, Friedlander, Iwaniec, and Heath-Brown, and examine a proposed nonabelian analogue that merits further investigation. Discover Poisson summation formulae and Fourier transforms for special families of varieties, including the zero locus of a quadratic form. Learn how these techniques may allow for broad generalizations of standard analytic number theory methods that rely on Fourier theory in vector spaces. This 59-minute lecture, presented at the Hausdorff Center for Mathematics, is motivated by research arising from automorphic representation theory and aims to open up new research possibilities in the field.

Jayce Getz: New avenues for the circle method, Lecture I