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Tobias Metzlaff |
LAAS-CNRS Équipe POP Office E53 7 Avenue du Colonel Roche 31400 Toulouse, France Mail: math"at"tobiasmetzlaff"dot"com Phone: (+33) 05 61 33 64 80 |
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November: New Preprint on arXiv |
February: SPP Workshop Announcement |
March: Talk at JNCF
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My research statement is available here.
I am a Mathematics postdoc in the
POP team
of
LAAS-CNRS
with
Victor Magron
and
Igor Klep
supported by
COMPUTE.
We develop and improve algorithms to solve computational problems through the exploitation of algebraic structures.
In particular, I am interested in crystallographic symmetries related to Weyl groups and weight lattices of Lie algebras, multiplicative invariants, generalized Chebyshev polynomials as well as applications in polynomial optimization and combinatorics. My favorite research project hides behind the images to the right. |
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Exploiting Term Sparsity in Symmetry-Adapted Basis for Polynomial Optimization
with
Igor Klep,
Victor Magron and
Jie Wang,
2025
(arxiv,
hal,
preprint submitted)
Additive and Multiplicative Coinvariant Spaces of Weyl Groups in the Light of Harmonics and Graded Transfer
with
Sebastian Debus,
2024
(arxiv,
hal,
published in
J. Algebra)
On symmetry adapted bases in trigonometric optimization,
2023
(arxiv,
hal,
published in
J. Symb. Comput.)
Symmetry Adapted Bases for Trigonometric Optimization,
2023
(published in
ACM Commun. Comput. Algebra)
Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs
with
Evelyne Hubert,
Philippe Moustrou and
Cordian Riener,
2022
(arxiv,
hal,
published in
Math. Program.)
Orbit Spaces of Weyl Groups Acting on Compact Tori: A Unified and Explicit Polynomial Description
with
Evelyne Hubert and
Cordian Riener,
2022
(arxiv,
hal,
published in
SIAM J. Appl. Algebra Geom.)
𝕋-Orbit Spaces of Multiplicative Actions and Applications
with
Evelyne Hubert,
Philippe Moustrou and
Cordian Riener,
2022
(published in ACM Commun. Comput. Algebra)
Computing free non-commutative Gröbner Bases over ℤ with Singular:Letterplace
with
Viktor Levandovskyy and
Karim Abou Zeid,
2020
(arxiv,
hal,
published in
J. Symb. Comput.)
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 Commun. Comput. Algebra)
TSSOS
a Julia package for polynomial optimization with term and chordal sparsity
(Contribution: symmetry reduction, benchmarks)
GeneralizedChebyshev
a Maple package for the irreducible reduced root systems and their associated generalized Chebyshev polynomials of the first kind
(Contribution: 100%)
Singular:Letterplace
a Singular extension for finitely presented modules over finitely presented associative non-commutative algebras
(Contribution: Gröbner Bases for noncommutative polynomials with coefficients in rings, benchmarks)
Saarbrücken SFB-TRR 195 Annual Meeting 2023:
Fundamental invariants of improper symplectic reflection groups
with
Ulrich Thiel
ISSAC 2023:
Symmetry Adapted Bases for Trigonometric Optimization
ISSAC 2022:
𝕋-Orbit Spaces of Multiplicative Actions and Applications
with
Evelyne Hubert,
Philippe Moustrou and
Cordian Riener
Crystallographic Groups and Chebyshev Polynomials in Global Optimization
(PhD thesis with
Evelyne Hubert
at
Université Côte d'Azur)
Computational Improvements for Non-Commutative Gröbner Bases over ℤ/mℤ
(MSc thesis with
Viktor Levandovskyy
at
RWTH Aachen University)
Periodic Linear Discrete Systems and their Canonical Form
(BSc thesis with
Eva Zerz
at
RWTH Aachen University)
JNCF 2026: Exploiting Term Sparsity in Symmetry-Adapted Basis for Polynomial Optimization
EUCCO 2025: A Symmetric TSSOS Hierarchy for Polynomial Optimization
ACA 2025: Combining Sparsity and Symmetry for SOS-Certificates
SPOT 96: Symmetry in Trigonometric Optimization
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
My CV in tabular form is available here. I have studied Mathematics at RWTH Aachen University and conducted my doctorate at Centre Inria d'Université Côte d'Azur with Evelyne Hubert. As a member of the Marie Skłodowska-Curie Innovative Training Network POEMA, I have been elected representative of the network's fifteen early stage researchers together with Corbinian Schlosser. My doctoral thesis on Crystallographic Groups and Chebyshev Polynomials in Global Optimization was defended on 15 December 2022 in front of the jury consisting of Christine Bachoc, Laurent Baratchart, Victor Magron, Gabriele Nebe and Frédéric Patras. Afterwards, I joined the Algebra Group of University of Kaiserslautern-Landau as a postdoc with Ulrich Thiel and contributed to the DFG project SFB-TRR 195 and the research program SymbTools. Next to research and advanced algebra studies, I have participated in various teaching and dissemination activities. Following my interest in applying algebra to problems in optimization and combinatorics, I did a second postdoc within the POP team of LAAS-CNRS with Victor Magron and Igor Klep supported by COMPUTE. At LAAS, I have specialized on optimization algorithms and algebraic structure exploitation.
2026:
JNCF
(Luminy, FR)
2025:
TENORS Learning Week
(Sophia Antipolis, FR)
SPOT Seminar
(Toulouse, FR)
COMPUTE Kickoff Meeting
(Saclay, FR)
ACA
(Heraklion, GR)
EUCCO
(Klagenfurt, AT)
2024:
JNCF
(Luminy, FR)
MoPAT
(Konstanz, DE)
Arctic MSCA Symposium
(Tromsø, NO)
EURO
(Copenhagen, DK)
With
Vu Trung Hieu,
Ettore Turatti
and Arne Lien
(7 June 2024, Tromsø, NO, picture taken by
Cordian Riener)
With
Ulrich Thiel,
Erec Thorn,
Liam Rogel,
Tam Linke and Fabian Mäurer
(28 Novembre 2024, Kaiserslautern, DE)
2023:
JNCF
(Luminy, FR)
Summer School on Processes and Heat Kernels with Symmetries
(Angers, FR)
SIAM AG
(Eindhoven, NL)
ISSAC
(Tromsø, NO)
Summer School on Higher Structures in Algebra and Geometry
(Nordfjordeid, NO)
Postdoc Appreciation Week Germany
(online)
SFB-TRR 195 Annual Meeting
(Saarbrücken, DE)
SingAlg
(Kaiserslautern, DE)
Workshop on Symmetry, Stability, and interactions with Computation
(Luminy, FR)
With
Sven Polak
and Arne Lien
(18 November 2023, Parc National des Calanques, FR, picture taken by
Sebastian Debus)
2022:
Mørketidens Mattemøte
(Tromsø)
POEMA Workshop
(online)
JNCF
(Luminy, FR)
Summer School on Real and Tropical Algebraic Geometry
(Nordfjordeid, FR)
ISSAC
(Lille, FR)
POEMA Workshop
(Paris, FR)
Winter School on Computational Algebraic Geometry
(Kaiserslautern, DE)
2021:
Mørketidens Mattemøte
(Tromsø, NO)
POEMA Workshop
(online)
General Julia Training
(online)
Workshop on Algebraic Combinatorics of the Symmetric Groups and Coxeter Groups
(Cetraro, IT)
POEMA Workshop
(Toulouse, FR)
Workshop on Modern Analysis Related to Root Systems with Applications
(Luminy, FR)
POEMA Industrial Workshop
(Sophia Antipolis, FR)
2020:
POEMA Workshop
(Florence, IT)
JNCF
(Luminy, FR)
POEMA Learning Weeks
(online)
SFO
(online)
ICMS
(Braunschweig, DE)
ISSAC
(Kalamata, GR)
POEMA Workshop
(online)
2026:
Mont Ventoux
(Provence, FR)
Tom Simpson Memorial (10 April 2026, Provence, FR)
2025:
Tourmalet (Pyrénées, FR)
Aubisque/Soulor (Pyrénées, FR)
200k (Landes de Gascogne, FR)
Port de Balès/Peyresoudre/Aspin (Pyrénées, FR)
Tourmalet 2 (Pyrénées, FR)
Octave Lapize: "Le Géant du Tourmalet" (4 July 2025, Pyrénées, FR)
2024:
Kahler Asten (Rothaargebirge, DE)
200k
(Nordpfälzer Bergland, DE)
Limburger Dom (29 July 2024, Hessen, DE)