Lucas Slot

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 special polynomials to topological data analysis.

Publications and preprints

  • 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]

  • 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]

  • 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 Held

  • Bsc. 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