
Tobias Metzlaff 
University of KaiserslauternLandau Department of Mathematics Algebra, Geometry and Computer Algebra GottliebDaimlerStraße 47 67663 Kaiserslautern, Germany firstname"dot"lastname"at"rptu"dot"de Office 48424 
Reflection Groups 
Invariant Theory 
Orthogonal Polynomials 
Gröbner Bases 
Optimization

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 symplectic, complex and rational reflection groups. Moreover, I am interested in computations over noncommutative rings and algebras that are motivated by group actions 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. Currently, I am working on this problem. Our research group organizes a seminar on representation theory and beyond every fortnight. 
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 KaiserslauternLandau
On symmetry adapted bases in trigonometric optimization (preprint)
Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs with Evelyne Hubert, Philippe Moustrou and Cordian Riener (submitted)
Orbit spaces of Weyl groups acting on compact tori: a unified and explicit polynomial description with Evelyne Hubert and Cordian Riener (submitted)
Computing free noncommutative Gröbner Bases over ℤ with Singular:Letterplace with Viktor Levandovskyy and Karim Abou Zeid (journal)
Symmetry Adapted Bases for Trigonometric Optimization at ISSAC 2023
𝕋Orbit Spaces of Multiplicative Actions and Applications with Evelyne Hubert, Philippe Moustrou and Cordian Riener at ISSAC 2022 (journal)
Computation of free noncommutative Gröbner Bases over ℤ with Singular:Letterplace with Viktor Levandovskyy and Karim Abou Zeid at ISSAC 2020 (journal)
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 noncommutative algebras.
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 𝕋Orbit Spaces of Multiplicative Actions
Sophia Antipolis Industrial Workshop 2021: Orbit Spaces for exponential Weyl Group Actions and the Chromatic Number of ℝ^{n}
Modern Analysis Related to Root Systems with Applications 2021: Regions of orthogonality of generalized Chebyshev polynomials as semialgebraic set
AROMATH Seminars 2021: The Chromatic Number of ℝ^{n} via optimization of multivariate Chebyshev polynomials
ICMS 2020: Gröbner bases over 𝕂 and ℤ in theory and practice
I am/was an assistant for the following lectures at the University of KaiserslauternLandau:

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 SFBTRR 195 Annual Meeting October 2023: Kaiserslautern SingAlg November 2023: Luminy Workshop on Symmetry, Stability, and interactions with Computation
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