Stieltjes Prize Award 2022-2023

Day 2 (Wednesday 3 April) @ 11:15–12:45

The jury for the Stieltjes Prize met on 13 December 2023 to award the prize for the best mathematical dissertation published in the academic year 2022-2023. A total of 76 dissertations were assessed. The jury therefore decided to award the Stieltjes Prize to Lucas Slot (CWI and Tilburg University) for the Stieltjesprijs 2022-2023 for his thesis entitled “Asymptotic Analysis of Semidefinite Bounds for Polynomial Optimization and Independent Sets in Geometric Hypergraphs”.

The dissertation of Lucas Slot consists of three parts. The first two parts deal with the performance analysis of hierarchies of semidefinite approximations for polynomial optimization problems. These nonlinear nonconvex optimization problems are hard to analyze and are used in many applications. These Lasserre hierarchies provide upper bounds (Part 1) and lower bounds (Part 2) for the global optimum. For the upper bounds the thesis offers an essentially optimal analysis for polynomial optimization problems over convex bodies and general compact semi-algebraic sets and a tight analysis for special sets including the box, the simplex, the ball and general convex bodies with a nice boundary. These results represent the state-of-the-art. They show an explicit performance analysis with quadratic dependence in the degree, which gives a strong improvement on the best known results in literature. The third part of the thesis is devoted to bounding the size of simplex-avoiding sets in geometric hypergraphs via a recursive theta-number, extending in a very nice way ideas that are classical in the case of graphs.

The thesis is based on 7 papers most of them already published in high ranked journals. Finally the jury noted that the thesis was written in only 3,5 years

Lucas Slot will give a presentation about the research performed during his PhD during the NMC 2024.