Tobias Metzlaff

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

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

Reflection Groups     -     Invariant Theory     -     Orthogonal Polynomials     -     Gröbner Bases     -     Optimization


(MSC 13 14 17 20 33 90)

I am a mathematics postdoc at the University of Kaiserslautern-Landau, working with Ulrich Thiel on this problem. The project is supported by the transregional collaborative research centre of the Deutsche Forschungsgemeinschaft (SFB-TRR) 195 Symbolic Tools in Mathematics and their Application.

My field of research lies at the intersection of algebraic geometry, commutative algebra and representation theory with a focus on computations. Specifically, I study crystallographic symmetries and special functions related to root systems, which give rise to generalized Chebyshev polynomials, as well as the invariant theoretic properties of rational, real, complex and symplectic reflection groups. Moreover, I am interested in computations over non-commutative rings and 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 supervised by Evelyne Hubert and defended on December 15, 2022 at Inria d'Université Côte d'Azur. The jury consisted of Christine Bachoc, Laurent Baratchart (président du jury), Victor Magron, Gabriele Nebe and Frédéric Patras. The thesis is accessible in the library of Université Côte d'Azur and online.

Our research group organizes a seminar on representation theory and beyond every fortnight. We are happy to invite new speekers from related fields of research so that our scientific networks can grow and connect. If you are interested in giving a talk and visiting the beautiful Pfalz, feel free to send me a mail.

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:  Postdoctoral Researcher at RPTU Kaiserslautern-Landau   


   On symmetry adapted bases in trigonometric optimization (arxiv, hal, to appear in JSC)

   Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs with Evelyne Hubert, Philippe Moustrou and Cordian Riener (arxiv, hal, to appear in MAPRA)

   Orbit spaces of Weyl groups acting on compact tori: a unified and explicit polynomial description with Evelyne Hubert and Cordian Riener (arxiv, hal, to appear in SIAGA)

   Computing free non-commutative Gröbner Bases over with Singular:Letterplace with Viktor Levandovskyy and Karim Abou Zeid (arxiv, hal, published in JSC)

Short Communications

   Fundamental invariants of improper symplectic reflection groups with Ulrich Thiel at Saarbrücken SFB-TRR 195 Annual Meeting (poster)

   Symmetry Adapted Bases for Trigonometric Optimization at ISSAC 2023 (poster, published in ACM)

   𝕋-Orbit Spaces of Multiplicative Actions and Applications with Evelyne Hubert, Philippe Moustrou and Cordian Riener at ISSAC 2022 (poster, published in ACM)

   Computation of free non-commutative Gröbner Bases over with Singular:Letterplace with Viktor Levandovskyy and Karim Abou Zeid at ISSAC 2020 (hal, published in ACM)


    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.


   MoPAT 2024:  Chebyshev Moments

   JNCF 2024:  Singularités symplectiques et invariants diagonaux

   AROMATH Seminars 2023:  Symplectic singularities and diagonal invariants

   AG 2023:  Crystallographic Symmetries in Trigonometric Optimization

   JNCF 2023:  Optimisation Trigonométrique avec Symétrie

   Paris POEMA Workshop 2022:  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 2021:  Orbit Spaces for exponential Weyl Group Actions and the Chromatic Number of n

   Modern Analysis Related to Root Systems with Applications 2021:  Regions of orthogonality of generalized Chebyshev polynomials as semi-algebraic set

   AROMATH Seminars 2021:  The Chromatic Number of n via optimization of multivariate Chebyshev polynomials

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


I am/was an assistant for the following lectures at the University of Kaiserslautern-Landau:

   Quadratic Number Fields with Ulrich Thiel (SS 23)

   Representation Theory with Gunter Malle (WS 23/24)

   Character Theory with Ulrich Thiel (SS 24)

Scientific Events

January 2020: Florence POEMA Workshop    March 2020: Luminy JNCF    May - September, 2020: POEMA Learning Weeks (online)    June - July 2020: SFO (online)     July 2020: Braunschweig ICMS    July 2020: Kalamata ISSAC    October 2020: POEMA Workshop (online)    January 2021: Mørketidens Mattemøte (online)    January - February 2021: POEMA Workshop (online)    April 2021: General Julia Training (online)    July 2021: Cetraro Workshop on Algebraic Combinatorics of the Symmetric Groups and Coxeter Groups    September 2021: Toulouse POEMA Workshop    October 2021:  Luminy Workshop on Modern Analysis Related to Root Systems with Applications    December 2021: Sophia Antipolis POEMA Industrial Workshop    January 2022: Mørketidens Mattemøte (online)    February 2022: POEMA Workshop (online)    March 2022: Luminy JNCF    June 2022: Nordfjordeid Summer School on Real and Tropical Algebraic Geometry     July 2022: Lille ISSAC    September 2022: Paris POEMA Workshop    November 2022: Kaiserslautern Winter School on Computational Algebraic Geometry    March 2023: Luminy JNCF    June 2023: Angers Summer School on Processes and Heat Kernels with Symmetries    July 2023: Eindhoven SIAM AG    July 2023: Tromso ISSAC    August 2023: Nordfjordeid Summer School on Higher Structures in Algebra and Geometry    September 2023: Postdoc Appreciation Week Germany (online)    September 2023: Saarbrücken SFB-TRR 195 Annual Meeting    October 2023: Kaiserslautern SingAlg    November 2023: Luminy Workshop on Symmetry, Stability, and interactions with Computation    March 2024: Luminy JNCF    March 2024: Konstanz MoPAT    June 2024: Arctic MSCA Symposium   

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last update: June 2024