Matthieu Faitg

Teaching and research assistant

Institut de Mathématiques de Toulouse
Université Toulouse III Paul Sabatier
118 route de Narbonne
F-31062 Toulouse Cedex 9, France

Office: 206 in Building 1R2 (2nd floor)

E-Mail:
first.last(at)math.univ-toulouse.fr
with first = matthieu and last = faitg

   

Since September 2024 I am an ATER (non-tenured teaching and research assistant) at the Université Toulouse III and the Institut de Mathématiques de Toulouse, in the "Geometry, Topology, Algebra" team.

From 2022 to 2024 I was a postdoc in this lab, funded by the LabEx CIMI and under the supervision of Francesco Costantino.

From 2019 to 2022, I was a postdoc at the mathematics department of the University of Hamburg (Germany) under the supervision of Christoph Schweigert, funded by the Cluster of Excellence Quantum Universe.

From 2016 to 2019, I prepared my PhD thesis at the University of Montpellier under the supervision of Stéphane Baseilhac and Philippe Roche.

Curriculum Vitae (.pdf)

Research interests

  • Quantum algebra: non-commutative rings and representation theory, Hopf algebras and in particular quantum groups.
  • Quantum topology, in particular quantum character varieties of surfaces (a.k.a. moduli algebras) and skein algebras.
  • Deformation theory of tensor categories: Davydov-Yetter cohomology and its relations with relative homological algebra.

(Pre)Publications

All my papers can be found on the arXiv with this link. My PhD thesis can be found here.

  • M. Faitg, Derived representations of quantum character varieties, 53 pages, 2025. (arXiv)
  • With A.M. Gainutdinov and C. Schweigert: An adjunction theorem for Davydov-Yetter cohomology and infinitesimal braidings, 71 pages, 2024. (arXiv)
  • With S. Baseilhac and P. Roche: Unrestricted quantum moduli algebras III: surfaces of aribitrary genus and skein algebras, 75 pages, 2023. (arXiv)
  • With A.M. Gainutdinov and C. Schweigert: Davydov-Yetter cohomology and relative homological algebra, Selecta Math. New Ser. 30, article no26, 2024, 80 pages. (journal, arXiv), (GAP programs)
  • Holonomy and (stated) skein algebras in combinatorial quantization, Quantum Topol. (published online first, DOI 10.4171/QT/176), 2024, 73 pages. (journal, arXiv)
  • Projective representations of mapping class groups in combinatorial quantization, Comm. Math. Phys 377(1), pp. 161-198, 2020. (journal, arXiv)
  • Modular group representations in combinatorial quantization with non-semisimple Hopf algebras, SIGMA 15 (2019), 077, 39 pages. (journal, arXiv)
  • A note on symmetric linear forms and traces on the restricted quantum group Uq(sl2), Osaka J. Math. 57, pp. 575-595, 2020. (journal, arXiv)

Lecture notes

Here are Notes on moduli algebras and projective representations of mapping class groups (in French), written to accompany my talks at the ‘‘Quantum workshop’’ in Montpellier, November 2023 and April 2024.

  • Lecture 1: construction of the projective representation.
  • Lecture 2: explicit formulas for the Lickorish generators.

Slides on knot theory and the Jones polynomial

Here are the slides (in French) of an online talk given in February 2025 for the math teachers of the Académie de Montpellier (high school teachers).