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Tobias Metzlaff |
University of Kaiserslautern-Landau Department of Mathematics Algebra, Geometry and Computer Algebra Gottlieb-Daimler-Straße 47 67663 Kaiserslautern, Germany math"at"tobiasmetzlaff"dot"com Office 48-424 |
Reflection Groups -
Invariant Theory -
Orthogonal Polynomials -
Gröbner Bases -
Optimization
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(Click here for my Research Statement.)
(Math Subject Classification 13 14 17 20 33 90) 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 (click the figures on the right), 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. To access the thesis, please click here or visit the library of Université Côte d'Azur. The doctorate was part of the POEMA network, supported by European Union's Horizon 2020 research and innovation programme under the Marie Sk\l odowska-Curie Actions. Currently, I am a mathematics postdoc at the University of Kaiserslautern-Landau, working with Ulrich Thiel on this problem. The project is supported by the Rheinland Pfalz research initiative (SymbTools) and German Research Foundation's transregional collaborative research centre (SFB-TRR 195). 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. |
June 2014: High School Diploma (Abitur) awarded by Gymnasium Würselen October 2014 - March 2018: Bachelor Student at RWTH Aachen University October 2016 - March 2018: Student Assistant at RWTH Chair C for Mathematics March 2018: Mathematics BSc awarded by RWTH Aachen University with Eva Zerz April 2018 - November 2019: Master Student at RWTH Aachen University October 2018 - September 2019: Student Assistant at RWTH Chair II for Mathematics October 2019: Mathematics MSc awarded by 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: Mathematics PhD (Docteur en Mathématiques) awarded by Université Côte d'Azur with Evelyne Hubert since January 2023: Postdoctoral Researcher at University of Kaiserslautern-Landau
On symmetry adapted bases in trigonometric optimization (arxiv, hal, published 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, published 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, published in SIAGA)
Computing free non-commutative Gröbner Bases over ℤ with Singular:Letterplace with Viktor Levandovskyy and Karim Abou Zeid (arxiv, hal, published in JSC)
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 ℤ 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.
EURO 2024: Spectral bounds for set avoiding graphs via polynomial optimization
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 ℝn
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 ℝn 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 Kaiserslautern-Landau:
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January 2020: Florence POEMA Workshop March 2020: Luminy JNCF May, 2020: POEMA Learning Weeks (online) July 2020: SFO (online) July 2020: Braunschweig ICMS July 2020: Kalamata ISSAC October 2020: POEMA Workshop (online) January 2021: Mørketidens Mattemøte (online) 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: Tromso Arctic MSCA Symposium July 2024: Copenhagen EURO
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