On October 14 Reynold Fregoli defended his PhD thesis, written under the guidance of Prof. Martin Widmer.
Reynold’s PhD thesis addresses various problems in the area of Multiplicative Diophantine Approximation.
This branch of Number Theory studies products of approximations of real numbers by rational numbers as occurring in the famous Littlewood conjecture. Reynold significantly advanced our understanding of sums of reciprocals of fractional parts and thereby shed light on a question of Lê and Vaaler.He established new examples of affine subspaces of Khintchine type (for convergence) extending work of Huang and Liu. Both of these applications rely on his new powerful lattice point counting result for weakly admissible lattices which generalises previous work of Widmer.
He also generalised work of Moshchevitin on the existence of multiplicatively badly approximable vectors from two to arbitrary dimensions but using an entirely different method. And finally, he proved a conjecture of L. A’Campo about certain exponential sums, presented 2018 at a conference in Luminy.
Reynold was also involved in organising the first ERLASS meeting and in several outreach activities. In particular he was one of the students who run the first of our successful mathematical puzzles rooms which got much better because of several changes suggested by the group.
Congratulations to Reynold Fregoli and Martin Widmer!