Lucas Slot
ETH Zürich
address: Universitätsstrasse 6, 8092 Zürich
office: F79
email: lucas.slot@inf.ethz.ch
About me
From November 2022, I am a postdoc in the group of David Steurer at ETH Zürich.
Previously, I was a PhD student at Centrum Wiskunde & Informatica (CWI) in the research group Networks & Optimization, under the supervision of
Monique Laurent. I defended my thesis cum laude at Tilburg University on 30 September 2022.
Research interests
My main interest is in polynomial optimization and semidefinite programming approaches to hard optimization problems. Some topics I have worked on are:
Asymptotic error analysis of sum-of-squares hierarchies.
Extensions of the Lovász theta-number to (geometric) hypergraphs.
Applications of reproducing (Christoffel-Darboux) kernels to topological data analysis.
Publications and preprints
2022
The Christoffel-Darboux kernel for topological data analysis
with Pepijn Roos Hoefgeest. preprint (2022). [arXiv]A recursive theta body for hypergraphs.
with Davi Castro-Silva, Fernando Mário de Oliveira Filho and Frank Vallentin. preprint (2022). [arXiv]Sum-of-squares hierarchies for polynomial optimization and the Christoffel-Darboux kernel.
in SIAM J. Optim. (2022). [arXiv] [journal]An effective version of Schmüdgen's Positivstellensatz for the hypercube.
with Monique Laurent. Optim. Lett. (2022). [arXiv] [journal]
2021
A recursive Lovász theta number for simplex-avoiding sets.
with Davi Castro-Silva, Fernando Mário de Oliveira Filho and Frank Vallentin. Proc. Am. Math. Soc. (2021). [arXiv] [journal]Sum-of-squares hierarchies for binary polynomial optimization.
with Monique Laurent. IPCO 2021. Extended version in Math. Program. (2022). [arXiv] [conference] [journal]
2020
Near-optimal analysis of Lasserre’s univariate measure-based bounds for multivariate polynomial optimization.
with Monique Laurent. Math. Program. (2020). [arXiv] [journal]Improved convergence analysis of Lasserre’s measure-based upper bounds for polynomial minimization on compact sets.
with Monique Laurent. Math. Program. (2020). [arXiv] [journal]
Education and theses
PhD Mathematics (cum laude) at Centrum Wiskunde & Informatica (CWI), Amsterdam and Tilburg University (2018-2022)
Thesis: Asymptotic Analysis of Semidefinite Bounds for Polynomial Optimization and Independent Sets in Geometric Hypergraphs
promotors: prof. dr. Monique Laurent and prof. dr. Etienne de Klerk.Msc. Mathematics at the University of Bonn (2016-2018)
Thesis: Global Gate Sizing and Buffering, under the supervision of prof. dr. Stephan HeldBsc. Mathematics and Bsc. Computer Science at the University of Amsterdam (2013-2016)
Thesis: Ultrametric Simplices, under the supervision of dr. Jan Brandts and dr. Leen Torenvliet