Group Theoretic Polynomial Bases for Global Optimization

Tobias Metzlaff
  Early Stage Researcher





INRIA Sophia Antipolis Méditerranée 
Project Team AROMATH

 
2004 Route des Lucioles 
06902 Sophia Antipolis, France 
Mail firstname.lastname@inria.fr
Phone +33 4 92 38 77 38 
Office Y 109 

Reflection Groups     -     Multiplicative Actions     -     Representation Theory     -     Cubatures     -     Gröbner Bases     -     Non-Commutative Algebras

Welcome! My name is Tobias Metzlaff. I am a Mathematics PhD student at Université Côte d'Azur and work with Evelyne Hubert in the AROMATH team of INRIA Sophia Antipolis Méditerranée as a doctoral researcher.

This project is supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Actions POEMA.



Research

My thesis is on group theoretic methods in global optimization. The goal is the generalization of monomial-based methods in terms of polynomial bases given by invariants of reflection groups. Applications involve polynomial optimization, discretizations such as cubatures, dynamical systems and many other fields of modern mathematics. Specific topics are representations of finite groups, multiplicative actions and generalized Cheyshev polynomials.

Furthermore, I am interested in effective methods for computations over non-commutative algebras and their application to control theory.


Publications and Talks

   With Evelyne Hubert, Philippe Moustrou and Cordian Riener at ISSAC 2022:  T-Orbit Spaces of Multiplicative Actions and Applications (poster available soon)

   With Evelyne Hubert and Cordian Riener:  Polynomial description for the T-Orbit Spaces of Multiplicative Actions (preprint submitted)

   With Evelyne Hubert and Cordian Riener at JNCF 2022:  Polynomial description for the T-Orbit Spaces of Multiplicative Actions (talk)

   With Evelyne Hubert and Cordian Riener at Modern Analysis Related to Root Systems with Applications:  Regions of orthogonality of generalized Chebyshev polynomials as semi-algebraic set (talk)

   With Evelyne Hubert, Philippe Moustrou and Cordian Riener at AROMATH Seminars:  The Chromatic Number of R^n via optimization of multivariate Chebyshev polynomials (talk)

   With Viktor Levandovskyy and Karim Abou Zeid:  Computing free non-commutative Gröbner Bases over ℤ with Singular:Letterplace (preprint submitted)

   With Viktor Levandovskyy, Hans Schönemann and Karim Abou Zeid at ICMS 2020:  Gröbner bases over 𝕂⟨X⟩ and ℤ⟨X⟩ in theory and practice (talk)

   With Viktor Levandovskyy and Karim Abou Zeid at ISSAC 2020:  Computation of free non-commutative Gröbner Bases over ℤ with Singular:Letterplace (conference paper)




Software

    Maple:GeneralizedChebyshev, a Maple package for root systems and generalized Chebyshev polynomials (click here to download).

    Singular:Letterplace, a Singular extension for finitely presented modules over finitely presented associative non-commutative algebras (click here for more information).




Short CV

October 2014 - March 2018:  Mathematics Bachelor of Science at RWTH Aachen University with Eva Zerz    October 2016 - March 2018:  Student Assistant at RWTH Chair C for Mathematics    April 2018 - October 2019:  Mathematics Master of Science at RWTH Aachen University with Viktor Levandovskyy    October 2018 - September 2019:  Student Assistant at RWTH Chair II for Mathematics    December 2019 - Present:  Doctoral Researcher at INRIA Méditerranée    January 2020: POEMA 1st Workshop    March 2020: JNCF 2020    May - September, 2020: POEMA Online Learning Weeks    June - July, 2020: SFO     July 2020: ICMS    July 2020: ISSAC    October 2020: POEMA 2nd Workshop    November 2020 - January 2021:  POEMA Secondment at UiT Tromso with Cordian Riener    January 2021: Mørketidens Mattemøte    January - February 2021: POEMA 3rd Workshop    April 2021: General online Julia training    July 2021: Workshop: Algebraic Combinatorics of the Symmetric Groups and Coxeter Groups    September 2021: POEMA Learning Week 2    October - December 2021:  Internship at NAG with Shuanghua Bai    October 2021:  Modern Analysis Related to Root Systems with Applications    December 2021: POEMA Industrial Workshop    January 2022: Mørketidens Mattemøte    February 2022: POEMA Workshop 4    March 2022: JNCF    June 2022: Nordfjordeid Summer School    July 2022: ISSAC 2022    September 2022: POEMA Final Workshop   




Find me on

   POEMA-Network.eu

   Blogger.com

   LinkedIn.com