Mateusz Skomra

CNRS Researcher

About Me

I am a CNRS researcher working in Laboratoire d'analyse et d'architecture des systèmes, within the POP research team.

Until September 2020 I was a postdoctoral researcher at École normale supérieure de Lyon, CNRS, Laboratoire de l'Informatique du Parallélisme, within the research team MC2.

From 2015 to 2018 I was a doctoral researcher at Centre de Mathématiques Appliquées, École polytechnique, CNRS, Université Paris-Saclay, within INRIA research team Tropical, where I worked under the supervision of Xavier Allamigeon and Stéphane Gaubert.

My research is focused on the interplay between tropical geometry, convex optimization, and algorithmic game theory. I am also working on problems related to algebraic complexity.

Postdoctoral position

Together with Georg Loho we offer a 12 month postdoctoral fellowship on the topic Neural networks and tropical geometry. The position will be funded through the POPML4PS chair of the ANITI AI cluster. Click here for more details and contact us by e-mail if you are interested!

Master internship

I offer an internship for a Master student on the topic Analyzing Mean Payoff Games Using Sums-of-Squares. Click here for more details and contact me by e-mail if you are interested!

Book chapter

Stochastic Games

Nathalie Bertrand, Patricia Bouyer-Decitre, Nathanaël Fijalkow, and Mateusz Skomra

I am one of the authors of the chapter Stochastic Games in the book Games on Graphs coordinated by Nathanaël Fijalkow. A printed version will be published in 2026 by Cambridge University Press.

arXiv version

Publications

Finite convergence of the Moment-SOS hierarchy on the product of spheres

Sami Halaseh, Victor Magron, and Mateusz Skomra

arXiv version

Reducing stochastic games to semidefinite programming

Manuel Bodirsky, Georg Loho, and Mateusz Skomra

Proceedings of the 52nd International Colloquium on Automata, Languages, and Programming (ICALP), 2025, pp. 145:1–145:15

arXiv version DOI (conference)

Cycle patterns and mean payoff games

Georg Loho, Matthew Maat, and Mateusz Skomra

arXiv version

Universal complexity bounds based on value iteration and application to entropy games

Xavier Allamigeon, Stéphane Gaubert, Ricardo D. Katz, and Mateusz Skomra

Information and Computation, 302 (2025), pp. 105236:1–105236:31

A preliminary version of this paper was published in the Proceedings of the 49th International Colloquium on Automata, Languages, and Programming (ICALP), 2022, pp. 110:1–110:20

arXiv version DOI (conference) DOI (journal)

Smoothed analysis of deterministic discounted and mean-payoff games

Bruno Loff and Mateusz Skomra

Proceedings of the 51st International Colloquium on Automata, Languages, and Programming (ICALP), 2024, pp. 147:1–147:16

arXiv version DOI (conference)

Signed tropicalizations of convex semialgebraic sets

Mateusz Skomra

Extended Abstracts presented at the 25th International Symposium on Mathematical Theory of Networks and Systems (MTNS), 2022, pp. 697–700

HAL version DOI (conference)

Signed tropical halfspaces and convexity

Georg Loho and Mateusz Skomra

arXiv version

Optimal bounds for bit-sizes of stationary distributions in finite Markov chains

Mateusz Skomra

arXiv version

Derandomization and absolute reconstruction for sums of powers of linear forms

Pascal Koiran and Mateusz Skomra

Theoretical Computer Science, 887 (2021), pp. 63–84

arXiv version DOI

Convexly independent subsets of Minkowski sums of convex polygons

Mateusz Skomra and Stéphan Thomassé

Discrete Mathematics, 344 (2021), article 112472

arXiv version DOI

Intersection multiplicity of a sparse curve and a low-degree curve

Pascal Koiran and Mateusz Skomra

Journal of Pure and Applied Algebra, 224 (2020), article 106279

arXiv version DOI

Tropical spectrahedra

Xavier Allamigeon, Stéphane Gaubert, and Mateusz Skomra

Discrete & Computational Geometry, 63 (2020), pp. 507–548

arXiv version DOI

The tropical analogue of the Helton–Nie conjecture is true

Xavier Allamigeon, Stéphane Gaubert, and Mateusz Skomra

Journal of Symbolic Computation, 91 (2019), pp. 129–148

A preliminary version of this paper was presented at the International Conference on Effective Methods in Algebraic Geometry (MEGA), 2017

arXiv version DOI (journal)

Individual security and network design with malicious nodes

Tomasz Janus, Mateusz Skomra, and Marcin Dziubiński

Extended abstract published in the Proceedings of the 17th International Conference on Autonomous Agents and Multiagent Systems (AAMAS), 2018, pp. 1968–1970

arXiv version conference version

Condition numbers of stochastic mean payoff games and what they say about nonarchimedean semidefinite programming

Xavier Allamigeon, Stéphane Gaubert, Ricardo D. Katz, and Mateusz Skomra

Proceedings of the 23rd International Symposium on Mathematical Theory of Networks and Systems (MTNS), 2018, pp. 160–167

arXiv version conference version

Solving generic nonarchimedean semidefinite programs using stochastic game algorithms

Xavier Allamigeon, Stéphane Gaubert, and Mateusz Skomra

Journal of Symbolic Computation, 85 (2018), pp. 25–54

A preliminary version of this paper was published in the Proceedings of the 41st International Symposium on Symbolic and Algebraic Computation (ISSAC), ACM, 2016, pp. 31–38

arXiv version DOI (conference) DOI (journal)

PhD thesis

Tropical spectrahedra: Application to semidefinite programming and mean payoff games

Defended at École polytechnique on the 5th of December 2018

PASTEL link local file

Past and Upcoming Events

Teaching

  • Initiation aux Equations aux Dérivées Partielles, tutorial classes, September – December 2025, INSA Toulouse
  • Analyse Fonctionnelle, tutorial classes, October 2025, ISAE-SUPAERO
  • Initiation aux Equations aux Dérivées Partielles, tutorial classes, September – December 2024, INSA Toulouse
  • Analyse Fonctionnelle, tutorial classes, October 2024, ISAE-SUPAERO
  • Initiation aux Equations aux Dérivées Partielles, tutorial classes, September – December 2023, INSA Toulouse
  • Analyse Fonctionnelle, tutorial classes, November 2023, ISAE-SUPAERO
  • Analyse Numérique, tutorial classes, October – December 2022, INSA Toulouse
  • Analyse Numérique, tutorial classes, October – December 2021, INSA Toulouse
  • C++ language and object-oriented programming, lecture and tutorial classes, February – April 2020, IUT Lyon 1
  • Computational Complexity, tutorial classes, January – April 2020, ENS de Lyon
  • Cryptography and Security, tutorial classes, January – April 2020, ENS de Lyon
  • Architecture, système, réseau 1, tutorial classes, September – December 2019, ENS de Lyon
  • Information theory, tutorial classes, September – December 2019, ENS de Lyon
  • Introduction to concepts of Computer Science, tutorial classes, September – October 2019, ENS de Lyon
  • Algorithmique avancée, tutorial classes, February – May 2019, ENS de Lyon
  • Optimisation linéaire et convexité, tutorial classes, February – May 2018, Sorbonne Université
  • Programmation Python, tutorial classes, September – December 2017, Sorbonne Université
  • Optimisation linéaire et convexité, tutorial classes, January – May 2017, Sorbonne Université
  • Suites, Intégrales, Introduction à l'algèbre linéaire, tutorial classes, January – May 2017, Sorbonne Université
  • Introduction à l'optimisation, tutorial classes, September – October 2016, École des Ponts ParisTech

Contact

  • Location:LAAS–CNRS, équipe POP
    7, avenue du Colonel Roche
    31031 Toulouse cedex 4
    France

  • Email: