Mathieu Vallée

Ph.D. Student

I am a Ph.D. student in Computer Science and Mathematics in the LIPN (Laboratoire d'Informatique de Paris Nord), at the University of Sorbonne Paris Nord in France, supervised by Roland Grappe and Bruno Vallette. My Ph.D. subject is "Cones, fans, and wedges: combinatorial and geometrical perpectives". It gathers combinatorial optimization, polyhedral geometry, toric geometry and operad theory. The tentative date for my defense is September 8th 2025.

I teach at the IUT Villetaneuse.

Research

Toric topology

During my Master degree, I took a year off to focus on research with Suyoung Choi, with whom I undertook my bachelor degree internship. Our research is mainly focused on the study of toric manifolds, and the combinatorics that appear from them. The tools used here range from (binary) matroid theory to PL-spheres together with algebraic geometry and Groebner bases.

Box-integrality and the integer decomposition property

Box-integrality is a property of some integer polyhedron to remain integer after a truncation with any integer box. Integer decomposition properties is the study of integer points in convex polyhedra and, more precisely, of how to find "minimal" generators of these integer points. I study integer decomposition properties of polyhedra satisfying box-integrality. For this subject, I use plenty of discrete geometry such as triangulation of polyhedron, box-total dual integrality, and a class of matrices that generalizes totally unimodular matrices: totally equimodular matrices.

Preprints

Complete non-singular toric varieties with Picard number 4: joint work with Suyoung Choi and Hyeontae Jang (2025)
ArXiv:2504.18134

Totally equimodular matrices: decomposition and triangulation: joint work with Patrick Chervet and Roland Grappe (2025)
ArXiv:2504.05930

Toric wedge induction and toric lifting property for piecewise linear spheres with a few vertices: joint work with Suyoung Choi and Hyeontae Jang (2024)
ArXiv:2404.15600
(To appear in Journal of the London Mathematical Society)

Publications

The characterization of (n−1)-spheres with n+4 vertices having maximal Buchstaber number: joint work with Suyoung Choi and Hyeontae Jang (2024)
Journal für die reine und angewandte Mathematik (Crelles Journal)
Vol. 2024, no. 811, 2024, pages 267-292

An algorithmic strategy for finding characteristic maps over wedged simplicial complexes: joint work with Suyoung Choi (2022)
Pacific Journal of Mathematics
Vol. 320-1, pages 13–43

Cohomological rigidity of the connected sum of three real projective spaces: joint work with Suyoung Choi (2022)
Proceedings of the Steklov Institute of Mathematics
Vol. 317, pages 178–188

Conferences

GPU Algorithm for Enumerating PL Spheres of Picard Number 4: Application to Toric Topology: joint work with Suyoung Choi and Hyeontae Jang (2024)
40th International Symposium on Computational Geometry (SoCG 2024).
Leibniz International Proceedings in Informatics (LIPIcs),
Volume 293, pp. 41:1-41:15

Teaching

IUT de Villetaneuse

BUT Informatique.

Chargé de Cours/TD de première année de formation initiale: Introduction Base de Données.
Responsable du cours de passerelle: Développement efficace.

Photography

I have been an amateur photographer starting from 2020 when I went to Korea for an exchange year. Since then I took this hobby seriously and always carry a camera with me.