Crystallographic Groups and Chebyshev Polynomials in Global Optimization

Tobias Metzlaff






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 

Reflection Groups     -     Multiplicative Invariants     -     Chebyshev Polynomials     -     Optimization     -     Gröbner Bases

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

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.


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



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).



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)



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   



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   



Find me on

   POEMA-Network.eu

   Blogger.com

   LinkedIn.com