Damien Galant

News and upcoming events

I am delighted to announce that I have received a Research Fellowship from the Belgian American Educational Foundation! An article (in French) about this is available on UMONS' website.

This will allow me to spend one year at Brown University starting from October 2025 to work as a postdoc under the supervision of Prof. Javier Gómez-Serrano.

Current research interests

• Nonlinear elliptic partial differential equations (PDEs), in particular the nonlinear Schrödinger equation;
• Role played by the domain geometry in PDEs;
• Unidimensional aspects of PDEs: metric graphs, ODE techniques;
• Critical point theory;
• Variational problems with lack of compactness;
• Normalized solutions to nonlinear problems, including in the L²-supercritical case;
• Interface between nonlinear elliptic PDEs and fluid mechanics;
• Control theory of PDEs;
• Computer-assisted mathematics in the broad sense, including computer-assisted proofs in analysis (using interval arithmetic).

Publications and preprints

1. An action approach to nodal and least energy normalized solutions for nonlinear Schrödinger equations: Colette De Coster, Simone Dovetta, Damien Galant, Enrico Serra, 2024 (Preprint available on arXiv).
2. Infinitely many normalized solutions of L²-supercritical NLS equations on noncompact metric graphs with localized nonlinearities: Pablo Carrillo, Damien Galant, Louis Jeanjean, Christophe Troestler, 2024 (Preprint available on arXiv).
3. Constant sign and sign changing NLS ground states on noncompact metric graphs: Colette De Coster, Simone Dovetta, Damien Galant, Enrico Serra, Christophe Troestler, 2023, accepted for publication in Analysis & PDE (Preprint available on arXiv).
4. On the notion of ground state for nonlinear Schrödinger equations on metric graphs: Colette De Coster, Simone Dovetta, Damien Galant, Enrico Serra, Calculus of Variations and Partial Differential Equations, Vol. 62, No. 159, 2023 (Available on the publisher website).
5. A note on optimal degree-three spanners of the square lattice: Cédric Pilatte, Damien Galant, Discrete Mathematics, Algorithms and Applications. Vol. 14, No. 03, 2150124, 2022 (Available on the publisher website).
6. Geography of bilinearized Legendrian contact homology: Frédéric Bourgeois, Damien Galant, Algebraic & Geometric Topology, Vol. 24, No. 7, 2024 (Available on the publisher website).

Dissertations

1. The nonlinear Schrödinger equation on metric graphs: PhD Thesis (directors: Prof. Colette De Coster and Prof. Christophe Troestler): defended publicly on December 9th 2024, available here.
2. Ondes solitaires pour une équation de Schrödinger non-linéaire: Master's Thesis (in French, director: Prof. Christophe Troestler), UMONS, 2021, available here.

Talks

1. Seminar in the department of basic and applied sciences for engineering, Sapienza Università di Roma (Rome, Italy), Qualitative properties of solutions of the nonlinear Schrödinger equation on metric graphs: computer-assisted study of sign-changing solutions on the tetrahedron graph, 19 February 2025 (slides).
2. Séminaire doctorant du LAMFA (LAMFA, Université de Picardie Jules Verne, Amiens, France), Introduction to computer-assisted proofs in nonlinear analysis, 5 February 2025 (slides).
3. Séminaire "Doctorants et postdoctorants" du laboratoire Paul Painlevé (Université de Lille, Lille, France), Introduction to computer-assisted proofs in nonlinear analysis, 6 November 2024 (slides).
4. 18ème Journée des Doctorants en Mathématiques de la région Hauts-de-France (JDM 2024, Université de Lille, Lille, France), The nonlinear Schrödinger Equation on metric graphs, 20 September 2024 (slides).
5. Brussels Summer School of Mathematics (ULB, Brussels, Belgium), The nonlinear Schrödinger Equation on metric graphs, 30 August 2024 (slides).
6. Séminaire de l’équipe EMA du Laboratoire de Mathématiques Pures et Appliquées de l’Université du Littoral Côte d’Opale (LMPA, ULCO, Calais, France), Constant sign and sign changing NLS ground states on noncompact metric graphs, 30 May 2024.
7. Junior Colloquium de l’Institut de Recherche en Mathématiques et Physique (IRMP, UCLouvain, Belgium), The nonlinear Schrödinger equation on noncompact graphs: what is a solution?, 22 January 2024 (slides).
8. Nonlinear Quantum Graphs (Institut de Mathématiques de Toulouse, UPS, Toulouse, France), Qualitative properties of solutions of NLS on graphs, 16 January 2024 (slides).
9. Séminaire doctorant du laboratoire LAMFA (LAMFA, UPJV, Amiens, France), An introduction to variational methods, 6 December 2023 (slides).
10. Annual meeting of the COMPLEX doctoral School, edition 2023 (ULB, Brussels, Belgium), Study of the effect of parameters on the decay rate of a fourth order problem, 13 November 2023 (slides).
11. Control of Partial Differential Equations in Hauts-De-France 2023 (UPHF, Valenciennes, France), Study of the effect of parameters on the decay rate of a fourth order problem, 8 November 2023 (slides).
12. Young researchers in PDEs (ICMAT and UAM, Madrid, Spain), On the notion of “ground state” for the nonlinear Schrödinger equation on metric graphs, 2 October 2023 (slides).
13. Séminaire de mathématiques discrètes de l’ULiège (ULiège, Liège, Belgium), Optimal bounds for geometric dilation and computer-assisted proofs, 3 May 2023 (slides).
14. « Séminaire jeunes » des départements de mathématique et d'informatique (UMONS, Mons, Belgium), Équation de Schrödinger non-linéaire sur les graphes métriques (in French), 28 April 2023 (slides).
15. Séminaire EDP du Laboratoire de Mathématiques de Besançon (LMB, UBFC, Besançon, France), On the notion of ground state for the nonlinear Schrödinger equation on metric graphs, 16 March 2023 (slides).
16. Séminaire d’analyse appliquée A³ (LAMFA, UPJV, Amiens, France), On the notion of ground state for the nonlinear Schrödinger equation on metric graphs, 16 January 2023 (slides).
17. Séminaire de Mathématiques de Valenciennes (CERAMATHS/DMATHS, UPHF, Valenciennes, France), On the notion of ground state for the nonlinear Schrödinger equation on metric graphs, 15 December 2022 (slides).
18. COMPLEX Doctoral School (UMONS, Mons, Belgium), Nonlinear Schrödinger equation on metric graphs, 15 November 2022 (slides).
19. 18e Journées Montoises d’Informatique Théorique (Czech Technical University in Prague, Prague, Czech Republic), Optimal bounds for geometric dilation and computer-assisted proofs, 7 September 2022 (slides).
20. DEMAV Seminar (UPHF, Valenciennes, France), Blow-up phenomena for a Nonlinear Schrödinger Equation, 25 November 2021 (slides).
21. Séminaire d'Algèbre et Logique (UMONS, Mons, Belgium), Interactions entre l'apprentissage statistique et la théorie des modèles (part 2, in French), 5 February 2021 (slides).
22. Séminaire d'Algèbre et Logique (UMONS, Mons, Belgium), Interactions entre l'apprentissage statistique et la théorie des modèles (part 1, in French), 18 December 2020 (slides).
23. Symplectix Seminar (Institut Henri Poincaré, Paris, France), Effective computation of the bilinearized Legendrian contact homology, 8 November 2019 ( lecture notes).
24. « Séminaire sandwiches » (UMONS, Mons, Belgium), Dilation of regular polygons - Algorithmic aspects (in French), 24 October 2019 (slides).
25. Young Mathematicians Symposium of the Greater Region (ULiège, Liège, Belgium), The Minimum Dilation Triangulation Problem, 24 September 2019 (slides).

Posters

1. Fluids@PoliMi (Politecnico di Milano, Milano, Italy), An action approach to nodal and least energy normalized solutions for nonlinear Schrödinger equations, 9 January 2025 (poster).
2. "Nonlinear Quantum Graphs" Summer school (UPHF Campus Mont Houy, Valenciennes, France), The Nonlinear Schrödinger Equation on Metric Graphs, 18 June 2024 (poster).
3. Mardi des Chercheurs 2024 (UMONS, Mons, Belgium), The Nonlinear Schrödinger Equation on Metric Graphs, 26 March 2024 (poster).

Attended events

• January 15-16 2025: Participation to the Scientific Machine Learning: error control and analysis (at Laboratoire de Mathématiques de Besançon, Université Marie & Louis Pasteur, France).
• 2024-present: Regular attendance at the Analysis and PDE seminar (at ULB, Brussels, Belgium).
• 2022-present: Regular attendance at the DMATHS Seminar (at CERAMATHS, UPHF, Valenciennes, France).
• 27-30 June 2022: Participation to the conference Nonlinear Elliptic PDE in Hauts-de-France (3rd edition).
• 2021:
  • Regular participation to the DEMAV (ex-LAMAV) seminar at UPHF.
  • 2-5 November: participation to the conference PDE, Analysis and Applications — Conference in honor of the 60th birthday of Serge Nicaise.
• 2019: After my third year of bachelor, I participated to the "On the crossroads of topology, geometry and algebra" summer school organized at Eötvös Loránd University in Budapest.
• 2018: After my second year of bachelor, I was selected to the "Mathematical Summer in Paris" organized at ENS Ulm in Paris. The participants followed several lectures and problem sessions with leading mathematicians. I really enjoyed the lectures on combinatorics by Timothy Gowers.
• 2017: After my first year of bachelor, I was selected to participate in the Modern Mathematics Summer School organized at Jacobs University in Bremen where I met a lot of passionate students and professors. I had the great honor to meet John Horton Conway at this occasion, this encounter was very inspiring to me.

Organisation of events

1. "Nonlinear Quantum Graphs" Summer school, (UPHF Campus Mont Houy, Valenciennes, France), organizing committee.

Supervision

"Bourses d'initiation à la recherche" (grants given for student researcher position during the summer, available (after application) for the students of UMONS willing to pursue their career in research)

1. Summer 2022, Naomi Desobry (currently doing research in AI)

Teaching

Popularization of mathematics

• Talks:
  1. « Star Graph Academy : découvrez les équations différentielles sur les réseaux ! » 6èmes Rencontres mathématiques Valenciennoises, Valenciennes, 20 March 2025 (slides).
  2. « Modélisation de quelques systèmes biologiques », presentation of mathematical biology models to high school students from Lycée Kastler in Denain (France), 7 April 2022.
  3. « Modélisation de quelques systèmes biologiques », presentation of mathematical biology models to high school students from Lycée Professionnel François Mansart in Marly (France), 27 April 2022.
• Supervision of students:

  1. In June 2022, 2023 and 2024, I supervised high school students (aged around 15/16) participating to the camp “Faire des maths autrement” (“Doing math differently”), see here for more details (in French).

     I was one of the people responsible for the research workshops in which students work in groups (of 2–5, usually) on some small research projects and present their results in front of their relatives and teachers at the end of the week.

  2. In the academic year 2021–2022, I proposed a research subject to high school students (aged around 14/15) as part of the MATh.en.JEANS programme. I created the subject and did some follow-up during the year.
• Miscellaneous:
  1. Here is a short video (in French) of myself presenting the content of my thesis and the work of a PhD student in mathematics. This was part of a promotion of doctoral studies organized by INSA Hauts-de-France.

Olympiads and contests

• Mathematics, as a contestant:
  • I participated in the Belgian Mathematical Olympiad, I was qualified to the final every year and won the first prize in 2012 (MINI category), 2014 (MIDI category) and 2016 (MAXI category).
  • I participated in the Belgian Olympiad training camps for the International Mathematical Olympiad organized in Wépion in 2014, 2015 and 2016.
  • I also participated in the French Mathematical Olympiad training camps in Montpellier in 2014 and Valbonne in 2015.
  • I was selected to the Belgian team for the Benelux Mathematical Olympiad in Soest (Netherlands) in 2016 where I ended first and received a gold medal.
  • I was selected to the Belgian team for the International Mathematical Olympiad in Hong Kong in 2016 where I received a bronze medal.
  • In 2016, I was selected in the French team for the Romanian Masters in Mathematics 2016 (since Belgium does not participate in this contest, I was a member of the French team).
• Mathematics, as a trainer:
  • Since 2018, I am a trainer for the Belgian Mathematical Olympiad training camps organized in Wépion. I give a lecture on the scalar product, the Cauchy-Schwarz inequality, convexity and the Jensen inequality.
• Informatics, as a contestant:
  • I participated in the Belgian Informatics Olympiad since I was in third grade in secondary school, I was qualified to the final every year and won the first prize in 2016.
  • I was a member of the beCP Belgian training pools for the International Olympiad in Informatics (IOI). I participated in the IOI at Taipei (Taiwan) in 2014, at Almaty (Kazakhstan) in 2015 and at Kazan (Russia) in 2016. I won bronze medals in 2015 and 2016.
• Informatics, as a trainer:
  • Since 2017, I am a trainer for beCP. I gave several lectures and problem sessions to contestants training for IOI.
  • I was a "deputy leader" of a team of 4 Belgian contestants for the European Junior Olympiad in Informatics which took place in Sofia (Bulgaria) in 2017.
  • In 2020 I was a "deputy leader" of a team of 4 Belgian contestants for IOI 2020 that I helped to organize at UMONS due to the sanitary conditions.
• Informatics, team contests:
  • During my first year of bachelor at UMONS, I launched the group CPUMONS to participate in college-level programming contests.
  • I participated with my team CPUMONS in the Benelux Programming Contest. We scored 3/51 in 2016, 5/40 in 2017, 3/44 in 2018 and 2/78 in 2020. I was not able to participate in 2019 since I was in Orsay.
  • We also participated in the Northwestern Europe Regional Contest, a step of the ACM-ICPC contest. We ended 12/114 in 2016, 55/118 in 2017, 32/118 in 2018.
  • The CPUMONS organization is very active and involved in many activities surrounding programming at UMONS.