Lucas Slot

address: Centrum Wiskunde & Informatica (CWI), Science Park 123, Amsterdam

office: M240

email: lucas dot slot at cwi dot nl

About me

I am a PhD student at Centrum Wiskunde & Informatica (CWI) in the research group Networks & Optimization, under the supervision of Monique Laurent. You can view my resume here.

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.

Publications and preprints

  • Sum-of-squares hierarchies for polynomial optimization and the Christoffel-Darboux kernel.
    To appear in SIAM J. Optim. (2022). [arXiv]

  • An effective version of Schmüdgen's Positivstellensatz for the hypercube.
    with Monique Laurent. preprint (2021). [arXiv]

  • A recursive Lovász theta number for simplex-avoiding sets.
    with Davi Castro-Silva, Fernando Mário de Oliveira Filho and Frank Vallentin. To appear in Proc. Am. Math. Soc. (2021). [arXiv]

  • 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

  • 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