Jens Marklof - Random lattices and their applications: from statistical mechanics to number theory

Lattices are fundamental objects in physics, mathematics and computer science. Starting from a cubic lattice, say, we can perturb the structure by linear transformations (shearing, stretching, rotating) to obtain new lattices. I will discuss the resulting "space of lattices", the dynamics of group actions on this space, natural probability measures, as well as some powerful applications to long-standing problems in various areas of mathematics and mathematical physics. King's Mathematical Colloquium on January 10th, 2023