I am currently an associate professor in Université Toulouse Jean Jaures, attached to the Institut de Mathématiques de Toulouse.
Before, I was a PostDoc in the Algebra group led by Cordian Riener in the department of Mathematics and Statistics in Tromsø.
I defended my PhD in December 2017, I was in the number theory team of the Institut de Mathématiques de Bordeaux and the "graph and optimization" team of the LaBRI, under the supervision of Christine Bachoc and Arnaud Pêcher.
In 2018, I was a PostDoc at ICERM, Brown University for the semester program Point Configurations in Geometry, Physics and Computer Science.
Before, I was a PostDoc in the Algebra group led by Cordian Riener in the department of Mathematics and Statistics in Tromsø.
I defended my PhD in December 2017, I was in the number theory team of the Institut de Mathématiques de Bordeaux and the "graph and optimization" team of the LaBRI, under the supervision of Christine Bachoc and Arnaud Pêcher.
In 2018, I was a PostDoc at ICERM, Brown University for the semester program Point Configurations in Geometry, Physics and Computer Science.
Research
My research concerns both theoretical and computational questions in several topics, ranging from number theory to polynomial optimization, going through discrete geometry, coding theory and real algebraic geometry. I am particularly excited by questions involving lattices and sphere packings.Preprints & Publications
- Polarization of lattices: Stable cold spots and spherical designs, with C. Bachoc, F. Vallentin and M. Zimmermann, (2025), submitted.
- Constructively describing orbit spaces of finite groups by few inequalities, with C. Riener and R. Schabert, (2024), submitted.
- Symmetric SAGE and SONC forms, exactness and quantitative gaps, with C. Riener, T. Theobald and H. Verdure, Journal of Symbolic Computation, Special issue Computational Algebra and Geometry: A special issue in memory and honor of Agnes Szanto 107 , (2025) 102374
- Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs, with É. Hubert, T. Metzlaff and C. Riener, to appear in Mathematical Programming (2024).
- The poset of Specht ideals for hyperoctahedral groups, with S. Debus, C. Riener and H. Verdure, Algebraic Combinatorics, 6 (6) (2024), 1593-1619.
- Symmetries in polynomial optimization, with C. Riener, and H. Verdure (2023), chapter for the book Polynomial Optimisation, Moments, and Applications presenting research activies conducted in the Marie Skłodowska-Curie Innovative Training Network POEMA.
- Least distortion Euclidean embeddings of flat tori, with F. Vallentin, ISSAC 2023: International Symposium on Symbolic and Algebraic Computation 2023, ACM (2023) 13-23.
- Symmetry reduction in AM/GM-based optimization, with H. Naumann, C. Riener, T. Theobald and H. Verdure, SIAM Journal on Optimization 32 (2022) 765-785.
- Exact semidefinite programming bounds for packing problems, with M. Dostert and D. de Laat, SIAM Journal on Optimization 31(2) (2021), 1433-1458.
- Symmetric ideals, Specht polynomials and solutions to symmetric systems of equations, with C. Riener and H. Verdure, Journal of Symbolic Computation, 107, (2021) 106-121.
- Coloring the Voronoi tessellation of lattices, with M. Dutour Sikirić, D. Madore, and F. Vallentin, Journal of the London Mathematical Society (2) 104 (2021) 1135-1171.
- On the Density of Sets Avoiding Parallelohedron Distance 1, with C. Bachoc, T. Bellitto, and A. Pêcher, Discrete & Computational Geometry, 62(3), (2019) 497–524.
- On the Density of Cyclotomic Lattices Constructed from Codes, International Journal of Number Theory, Vol. 13, No. 5 (2017) 1261–1274
- Geometric Distance Graphs, Lattices and Polytopes, Ph.D. thesis.
Activities
Recent and upcoming talks
- PolSys Seminar, Paris, April 2025: Polarization of lattices: Stable cold spots and spherical designs
- CANARI Seminar, Bordeaux, March 2025: Polarization of lattices: Stable cold spots and spherical designs
- ANR Barracuda, Bayeux, January 2025: Oesterlé/Weil bounds for the number of points of a curve over a finite field and refinements
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- Together with Sabine Mercier, we organize popularization talks about math at UT2J, more information on Sabine's page.
Teaching
Since 2021, I am teaching Méthodologie Mathématique, Cryptographie et Codes correcteurs d'erreurs, and Calcul formel in the MIASHS program at UT2J. If ever you are a student looking for the course documents, as you know, they are all on IRIS...Contact
- Mail: philippe(dot)moustrou(at)math(dot)univ-toulouse(dot)fr