Pure Maths Colloquium: Jonathan Hickman

In the first half of the 20th century great advances were made in understanding convergence of Fourier series and integrals in one dimension. Many natural convergence problems in higher dimensions are still poorly understood, however, despite great attention by many prominent mathematicians over the last four decades. In this talk I will introduce the basic questions, describe their rich underlying geometry, and explain some recent developments in joint works with L. Guth (MIT) and M. Iliopoulou (UC Berkeley) and K. Rogers (ICMAT) which have applied tools from incidence and algebraic geometry to these problems.