Crystallographic Groups and Chebyshev Polynomials in Global Optimization
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Tobias Metzlaff
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Inria d'Université Côte d'Azur
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
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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 doctoral studies of mathematics at Université Côte d'Azur and my research work with Evelyne Hubert in the AROMATH team of Inria d'Université Côte d'Azur.
The project is supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Actions POEMA.
Research
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My main interests in mathematics are crystallographic symmetries related to root systems, representations of Lie algebras and invariant theory of multiplicative group actions. Furthermore, my research revolves around computations over non-commutative algebras as well as applications in optimization, integration and differential equations (click here to read my full research statement).
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.
In January 2023, I joined the Algebra, Geometry and Computer Algebra Group of Technische Universität Kaiserslautern to work with Ulrich Thiel as a postdoctoral researcher.
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Scientific Works
With Evelyne Hubert, Philippe Moustrou and Cordian Riener: Optimization of trigonometric polynomials with crystallographic symmetry and applications
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
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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 (download as .zip).
Singular:Letterplace, a Singular extension for finitely presented modules over finitely presented associative non-commutative algebras (more information).
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Other Contributions
With Evelyne Hubert, Philippe Moustrou and Cordian Riener at ISSAC 2022: T-Orbit Spaces of Multiplicative Actions and Applications (conference poster)
With Evelyne Hubert and Cordian Riener at JNCF 2022: Polynomial description for the T-Orbit Spaces of Multiplicative Actions (conference 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 (conference talk)
With Evelyne Hubert, Philippe Moustrou and Cordian Riener at AROMATH Seminars: The Chromatic Number of R^n via optimization of multivariate Chebyshev polynomials (seminar talk)
With Viktor Levandovskyy, Hans Schönemann and Karim Abou Zeid at ICMS 2020: Gröbner bases over 𝕂⟨X⟩ and ℤ⟨X⟩ in theory and practice (conference 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)
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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
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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
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Find me on
POEMA-Network.eu
Blogger.com
LinkedIn.com
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