🇫🇷 Version française

Luis Paris

Université Bourgogne Europe
Institut de Mathématiques de Bourgogne (IMB)
UMR 5584 – CNRS
21000 Dijon – France

📧 lparis@u-bourgogne.fr

Overview

I completed my university studies at the University of Geneva (Switzerland) from 1983 to 1987. In June 1987, I obtained my "diplôme de mathématicien", equivalent to today's Master's degree. From 1987 to 1989, I completed a PhD in mathematics, also at the University of Geneva, under the co-supervision of Pierre de la Harpe and Michel Kervaire. I defended my dissertation after a little over two years, in November 1989. During the 1990–1991 academic year, I spent a year as a postdoctoral researcher at the University of Wisconsin (Madison, USA), under the direction of Peter Orlik, one of the founders of the theory of hyperplane arrangements. Although my PhD dissertation focused on Coxeter groups, I was also interested in hyperplane arrangements. This subject became my main field of research that year. I returned to Geneva during the 1991–1992 academic year. I was offered a position as Associate Assistant Professor (maître de conférences associé) at the University of Nantes in 1992–1993, where I worked with Michel Jambu. I returned to Geneva from September to December 1993, and from January to September 1994, I was an Associate Assistant Professor at the Université de Bourgogne. It was during this brief period that I defended my Habilitation (HDR).

From January 1994 to the present day, I have remained at the Université de Bourgogne. In September 1994, I was appointed Associate Professor (Maître de Conférences) at the Université de Bourgogne, and then, in September 1997, Full Professor (Professeur des Universités). My arrival in Dijon was also marked by a shift in my research toward braid groups, Artin groups, and mapping class groups. It was also between 1993 and 1997 that I collaborated with Dale Rolfsen on these topics. They remain my primary research interests today. Starting in 1996, driven by Patrick Dehornoy, a community formed in France around braid group theory. This community was formalized through the creation of a CNRS GDR (Research Network), for which I served as Deputy Director from 2004 to 2007 and Director from 2007 to 2011. In 1997, Patrick Dehornoy and I authored the founding paper on the theory of Garside groups.

Main Administrative Responsibilities

• Head of the Bachelor's Program in Mathematics at UBE [link]
• Referent Researcher for MATh.en.JEANS for the Bourgogne-Franche-Comté region [link]

Main Teaching Assignments

• Math1B (1st-year Bachelor's in Science and Technology)
• Topology of Metric Spaces (3rd-year Bachelor's in Mathematics)
• Algebra 2 (1st-year Master's PMG)

Research Interests

My field of research is group theory, and more specifically braid groups and Artin groups. It is a well-defined field with its own AMS classification (20F36). Braid groups were introduced by Artin in 1925 and play an important role in several branches of mathematics, including mathematical physics, singularities, low-dimensional topology, representation theory, and of course, group theory. Artin groups, on the other hand, were introduced by Tits in the late 1960s as extensions of Coxeter groups, but their systematic study began in the early 1970s with the work of Brieskorn, Saito, and Deligne on spherical type Artin groups in connection with discriminant varieties.

PhD Students

• Juan Gonzalez-Meneses [link]
• Nuno Franco [link]
• Loic Rabenda
• Christelle Holtzman
• Fabrice Castel
• Emmanuel Toinet
• Bruno Aron Cisneros de la Cruz [link]
• Olivier Geneste [link]
• Diego Arcis [link]
• Mireille Soergel [link]
• Federica Gavazzi [link]
• Hugo Forget

Preprints

• J. Galvez Mateos, L. Paris. A cube complex for virtual Artin groups. arXiv:2607.24840. [link]
• B. Baumeister, L. Paris, S. Rees. The braid group Bn is not a quotient of a quasi-Coxeter interval group of type Dn. arXiv:2607.14369. [link]
• L. Paris, I. Soroko. Automorphisms of the Artin group of type D5. arXiv:2606.26082. [link]
• B. A. Cisneros de la Cruz, M. Cumplido, I. Foniqi, L. Paris. Classification of Artin groups admitting retractions onto their parabolic subgroups. arXiv:2603.15314. [link]
• J. Gálvez Mateos, F. Gavazzi, L. Paris. Parabolic subgroups and word problem in virtual Artin groups. arXiv:2602.23819. [link]
• E. Heng, L. Paris. Representations of Coxeter groups over fusion rings and hyperplane complements. arXiv:2511.04836. [link]
• P. Bellingeri, E. Godelle, L. Paris. Trickle groups. arXiv:2412.04932. [link]

Recent Publications

• F. Castel, L. Paris. Endomorphisms of Artin groups of type D. Algebr. Geom. Topol. 25 (2025), no. 7, 3975-4008. [link]
• Y. Antolín, M. Blufstein, L. Paris. When is a TRAAG orderable? Comm. Algebra 53 (2025), no. 8, 3550-3554. [link]
• L. Paris, I. Soroko. Endomorphisms of Artin groups of type Bn. J. Algebra 678 (2025), 831-861. [link]
• L. Paris, I. Soroko. Endomorphisms of Artin groups of type Ã. J. Algebra 678 (2025), 809-830. [link]
• M. Cumplido, F. Gavazzi, L. Paris. Intersection of parabolic subgroups in Euclidean braid groups: a short proof. C. R. Math. Acad. Sci. Paris 362 (2024), 1445-1448. [link]
• P. Möller, L. Paris, O. Varghese. On parabolic subgroups of Artin groups. Israel J. Math. 261 (2024), no. 2, 809-840. [link]
• L. Paris, O. Varghese. The spherical growth series of Dyer groups. Proc. Edinb. Math. Soc. (2) 67 (2024), no. 1, 168-187. [link]
• L. Paris, O. Varghese. Narrow normal subgroups of Coxeter groups and of automorphism groups of Coxeter groups. J. Group Theory 27 (2024), no. 2, 255-274. [link]
• P. Bellingeri, L. Paris, A.-L. Thiel. Virtual Artin groups. Proc. Lond. Math. Soc. (3) 126 (2023), no. 1, 192-215. [link]
• L. Paris, M. Soergel. Word problem and parabolic subgroups in Dyer groups. Bull. Lond. Math. Soc. 55 (2023), no. 6, 2928-2947. [link]
• M. A. Blufstein, L. Paris. Parabolic subgroups inside parabolic subgroups of Artin groups. Proc. Amer. Math. Soc. 151 (2023), no. 4, 1519-1526. [link]
• L. Paris. Birth of Garside groups in memory of Patrick Dehornoy. J. Knot Theory Ramifications 31 (2022), no. 8, Paper No. 2240004, 15 pp. [link]
• R. Blasco-García, L. Paris. On the isomorphism problem for even Artin groups. J. Algebra 607 (2022), part B, 35-52. [link]
• F. Digne, E. Godelle, S. Hermiller, L. Paris. Special issue in memory of Patrick Dehornoy [Introduction]. J. Algebra 607 (2022), part B, 1-4. [link]
• M. Cumplido, L. Paris. Commensurability in Artin groups of spherical type. Rev. Mat. Iberoam. 38 (2022), no. 2, 503--526.[link]
• L. Paris, L. Rabenda; Virtual and arrow Temperley-Lieb algebras, Markov traces, and virtual link invariants. J. Knot Theory Ramifications 30 (2021), no. 6, Paper No. 2150041, 36 pp. [link]
• Y. Antolín, L. Paris. Transverse properties of parabolic subgroups of Garside groups. Israel J. Math. 241 (2021), no. 2, 501-526. [link]
• P. Bellingeri, L. Paris. Virtual braids and permutations. Ann. Inst. Fourier (Grenoble) 70 (2020), no. 3, 1341-1362. [link]
• E. Irmak, L. Paris. Superinjective simplicial maps of the two-sided curve complexes on nonorientable surfaces. Fund. Math. 249 (2020), no. 3, 211-260. [link]
• O. Geneste, J.-Y. Hée, L. Paris. Root systems, symmetries and linear representations of Artin groups. Ann. Math. Blaise Pascal 26 (2019), no. 1, 25-54. [link]

Contact

Université Bourgogne Europe
Institut de Mathématiques de Bourgogne
9 avenue Alain Savary
21000 Dijon
France

☎️ +33 380 39 58 19