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)

Summary of research works (.pdf)    Warning: version from February 2024, has to be updated.

Research interests

  • Quantum algebra and low-dimensional topology, in particular quantum character varieties of surfaces (moduli algebras), skein algebras, mapping class groups.
  • Deformation theory and homological algebra, in particular deformation of monoidal structures in tensor categories (Davydov-Yetter cohomology).

Other relevant keywords: quantum groups, Hopf algebras, braidings and link invariants, representation theory, relative homological algebra, non-commutative rings.

(Pre)Publications

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

  • 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 group (in French), written to accompany my talk at the ‘‘Quantum workshop’’ in Montpellier, November 2023.