"Be extraordinary!" - E.H.
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Reflection Groups - Multiplicative Invariants - Chebyshev Polynomials - Optimization - Gröbner Bases
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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.
Research
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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.
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Articles
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 ℤ with Singular:Letterplace
Conference Papers and Posters
To be presented at ISSAC 2023: Symmetry Adapted Bases for Trigonometric Optimization
With 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 ℤ with Singular:Letterplace
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Software
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.
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Talks
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 ℝn
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 ℝn via optimization of multivariate Chebyshev polynomials
ICMS 2020: Gröbner bases over 𝕂 and ℤ in theory and practice
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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
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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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Find me on
POEMA-Network.eu
Blogger.com
LinkedIn.com
Inria.fr
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