Time: March 17, 2026, 10:15
S2 416-1

Titel: Globally optimal point sets in the torus

Abstract: The problem of distributing a given number of points as uniformly as possible throughout a given space has been studied for a long time by now. Common motivations for looking at such problems come from geometry via discrepancy theory or numerical analysis via the performance of the quasi-Monte Carlo method. A particularly popular setting in this context is the torus, where optimal point sets in an asymptotic sense are well-established by now. However, the question of determining the globally optimal point configuration has remained in the background until now. This talk will give an overview of techniques and known results for such problems, in particular emphasizing the role of Fibonacci lattices in the two-dimensional torus. This is based on joint work with Dmitriy Bilyk, Ian Ruohoniemi and Melia Haase.