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
- 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.
- Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs, with É. Hubert, T. Metzlaff and C. Riener, (2023), submitted.
- The poset of Specht ideals for hyperoctahedral groups, with S. Debus, C. Riener and H. Verdure, (2022), to appear in Algebraic Combinatorics.
- 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
- SIAM AG 2023, Eindhoven, July 2023: Symmetry reduction in AM/GM- optimization
- Summer school on harmonic analysis and PDEs: Sphere packing, Bilbao, June 2023: Optimization methods for sphere packing problems.
- Oberwolfach workshop New Directions in Real Algebraic Geometry, Oberwolfach, March 2023: Sn and Bn- Specht Ideals.
- Workshop Three days of computational methods for extremal discrete geometry, Cologne, November 2022: Computing spectral bounds for geometric graphs via polynomial optimization.
- Oberwolfach workshop Conic Linear Optimization for Computer-Assisted Proofs, Oberwolfach, April 2022: Symmetry reduction in AM/GM-based optimization.
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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