Clément Dupont – IMAG

Conference Topology and arithmetic of moduli spaces of curves, Montpellier, May 13-17, 2024.

I am a maître de conférences at the Université de Montpellier, France.

I am interested in the following subjects:
- motives, periods, regulators;
- amplitudes in quantum field theory and string theory;
- multiple zeta values and multiple polylogarithms;
- mixed Hodge theory;
- arrangements and matroids from the point of view of combinatorics, topology and geometry;
- combinatorial Hopf algebras;
- operads and operadic structures, especially in connection with algebraic geometry.

Research articles

Logarithmic morphisms, tangential basepoints, and little disks (with Erik Panzer and Brent Pym).
arXiv.
Regularized integrals and manifolds with log corners (with Erik Panzer and Brent Pym).
arXiv.
A construction of the polylogarithm motive (with Javier Fresán).
Épijournal Géom. Algébrique, to appear. arXiv.
The localization spectral sequence in the motivic setting (with Daniel Juteau).
Algebr. Geom. Topol. 24-3 (2024), 1431–1466. journal. arXiv.
Lauricella hypergeometric functions, unipotent fundamental groups of the punctured Riemann sphere, and their motivic coactions (with Francis Brown).
Nagoya Math. J. 249 (2023), 148–220. journal. arXiv.
Single-valued integration and superstring amplitudes in genus zero (with Francis Brown).
Comm. Math. Phys. 382 (2021), 815–874. journal. arXiv.
Single-valued integration and double copy (with Francis Brown).
J. reine angew. Math. (Crelle's Journal) 775 (2021), 145–196. journal. arXiv.
Universal Tutte characters via combinatorial coalgebras (with Alex Fink and Luca Moci).
Algebr. Comb. 1 (2018), no. 5, 603–651. journal. arXiv.
On two chain models for the gravity operad (with Geoffroy Horel).
Proc. Amer. Math. Soc. 146 (2018), no. 5, 1895–1910. journal. arXiv.
Odd zeta motive and linear forms in odd zeta values (with a joint appendix with Don Zagier).
Compos. Math. 154 (2018), no. 2, 342–379. journal. arXiv.
Relative cohomology of bi-arrangements.
Trans. Amer. Math. Soc. 369 (2017), no. 11, 8105–8160. journal. arXiv.
Brown's moduli spaces of curves and the gravity operad (with Bruno Vallette).
Geom. Topol. 21 (2017), no. 5, 2811–2850. journal. arXiv.
Purity, formality, and arrangement complements.
Int. Math. Res. Not. IMRN 2016, no. 13, 4132–4144. journal. arXiv.
The Orlik-Solomon model for hypersurface arrangements.
Ann. Inst. Fourier (Grenoble) 65 (2015), no. 6, 2507–2545. journal. arXiv.
The combinatorial Hopf algebra of motivic dissection polylogarithms.
Adv. Math. 264 (2014), 646–699. journal. arXiv.

Survey articles

An introduction to mixed Tate motives.
Written for the proceedings of the IRMA Summer School on Motives and Arithmetic Groups. arXiv.
Motifs : un tour d'horizon.
La Gazette de la Société Mathématique de France 178 (octobre 2023). journal. arXiv.
Progrès récents sur la conjecture de Zagier et le programme de Goncharov [d'après Goncharov, Rudenko, Gangl, ...].
Séminaire Bourbaki, 72ème année, 2019-2021, no. 1176, 294–343. journal. arXiv.
Valeurs zêta multiples.
Périodes et transcendance, Journées mathématiques X-UPS 2019. Éditions de l'École polytechnique. book. arXiv. video 1, video 2.

Theses

Periods of hyperplane arrangements and motivic coproduct (Périodes des arrangements d'hyperplans et coproduit motivique), my PhD thesis (Université Paris 6 Pierre et Marie Curie). pdf.
Périodes, motifs, arrangements : quelques contributions, my habilitation (HDR) thesis (Université de Montpellier). pdf.