Alexandru Pascadi

The dispersion method and beyond: from primes to exceptional Maass forms

The dispersion method has found an impressive range of applications in analytic number theory, from bounded gaps between primes to the greatest prime factors of quadratic polynomials. The method requires bounding certain sums of Kloosterman sums, using deep inputs from algebraic geometry and the spectral theory of GL2 automorphic forms. We'll give a broad outline of this process and, time permitting, discuss the key new ideas in the recent work at arxiv.org/abs/2404.04239.