"Be extraordinary!" - E.H.

Tobias Metzlaff

RPTU Kaiserslautern-Landau 
Department of Mathematics
Algebra, Geometry and Computer Algebra

Gottlieb-Daimler-Straße 47 
67663 Kaiserslautern, Germany 
Office 48-424 

Reflection Groups     -     Multiplicative Invariants     -     Chebyshev Polynomials     -     Optimization     -     Gröbner Bases

Welcome! My name is Tobias Metzlaff. This webpage is dedicated to my postdoctoral studies of mathematics at RPTU Kaiserslautern-Landau and my research work with Ulrich Thiel.

The project is supported by the transregional collaborative research centre of Deutsche Forschungsgemeinschaft (SFB-TRR) 195 Symbolic Tools in Mathematics and their Application.


My research revolves around crystallographic symmetries related to root systems, representations of Lie algebras and multiplicative invariant theory. Moreover, I am interested in computations over non-commutative algebras as well as exploiting algebraic structures in optimization.

My doctoral thesis entitled "Groupes Cristallographiques et Polynômes de Chebyshev en Optimisation Globale" ("Crystallographic Groups and Chebyshev Polynomials in Global Optimization") was defended on December 15, 2022 at Inria d'Université Côte d'Azur. The jury consisted of Christine Bachoc, Laurent Baratchart (président du jury), Evelyne Hubert (directrice de thèse), Victor Magron, Gabriele Nebe and Frédéric Patras. The thesis is accessible in the library of the university and online.

Currently, I am working on this problem.

Our research group organizes a seminar on representation theory and beyond every fortnight.


   With Evelyne Hubert, Philippe Moustrou and Cordian Riener:  Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs

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

   With Viktor Levandovskyy and Karim Abou Zeid:  Computing free non-commutative Gröbner Bases over with Singular:Letterplace

Conference Papers and Posters

   To be presented at ISSAC 2023:  Symmetry Adapted Bases for Trigonometric Optimization

Evelyne Hubert, Philippe Moustrou and Cordian Riener at ISSAC 2022:  𝕋-Orbit Spaces of Multiplicative Actions and Applications

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


    Maple:GeneralizedChebyshev: a Maple package for the irreducible reduced root systems and their associated generalized Chebyshev polynomials of the first kind.

    Singular:Letterplace: a Singular extension for finitely presented modules over finitely presented associative non-commutative algebras.


   JNCF 2023:  Trigonometric Optimization with Symmetry

   Paris POEMA Workshop:  Optimization of trigonometric polynomials with crystallographic symmetry and applications

   JNCF 2022:  Polynomial description for the 𝕋-Orbit Spaces of Multiplicative Actions

   Sophia Antipolis Industrial Workshop:  Orbit Spaces for exponential Weyl Group Actions and the Chromatic Number of n

   Modern Analysis Related to Root Systems with Applications:  Regions of orthogonality of generalized Chebyshev polynomials as semi-algebraic set

   AROMATH Seminars:  The Chromatic Number of n via optimization of multivariate Chebyshev polynomials

   ICMS 2020:  Gröbner bases over 𝕂 and in theory and practice

Short CV

June 2014:  Abitur at Gymnasium Würselen    October 2016 - March 2018:  Student Assistant at RWTH Chair C for Mathematics    March 2018:  Mathematics Bachelor of Science at RWTH Aachen University with Eva Zerz    October 2018 - September 2019:  Student Assistant at RWTH Chair II for Mathematics    October 2019:  Mathematics Master of Science at RWTH Aachen University with Viktor Levandovskyy    December 2019 - December 2022:  Doctoral Researcher at Inria d'Université Côte d'Azur    November 2020 - January 2021:  Secondment at UiT The Arctic University of Norway with Cordian Riener    October - December 2021:  Secondment at Numerical Algorithm Group with Shuanghua Bai    December 2022:  Docteur en Mathématiques d'Université Côte d'Azur with Evelyne Hubert    since January 2023:  wissenschaftlicher Mitarbeiter at RPTU Kaiserslautern-Landau   

Participation in Scientific Events

January 2020: Florence POEMA Workshop    March 2020: JNCF    May - September, 2020: POEMA Learning Weeks (online)    June - July 2020: SFO     July 2020: ICMS    July 2020: ISSAC    October 2020: POEMA Workshop (online)    January 2021: Mørketidens Mattemøte    January - February 2021: POEMA Workshop (online)    April 2021: General Julia Training    July 2021: Cetraro Workshop on Algebraic Combinatorics of the Symmetric Groups and Coxeter Groups    September 2021: Toulouse Workshop    October 2021:  Luminy Workshop on Modern Analysis Related to Root Systems with Applications    December 2021: Sophia Antipolis Industrial Workshop    January 2022: Mørketidens Mattemøte    February 2022: POEMA Workshop (online)    March 2022: JNCF    June 2022: Nordfjordeid Summer School on Real and Tropical Algebraic Geometry     July 2022: ISSAC    September 2022: Paris POEMA Workshop    November 2022: Kaiserslautern Winter School on Computational Algebraic Geometry    March 2023: JNCF    June 2023: Angers Summer School on Processes and Heat Kernels with Symmetries    July 2023: SIAM AG    July 2023: ISSAC    August 2023: Nordfjordeid Summer School on Higher Structures in Algebra and Geometry   

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