Dr. Louis-Clément Lefèvre
My field of research is the topology of complex algebraic varieties and the study of moduli spaces of representations of their fundamental groups. The methods that I use come from Hodge theory (mixed Hodge structures, variations of Hodge structure, Hodge modules) as well as formal deformation theory (functors of Artin rings, differential graded Lie algebras) and homotopy theory (rational homotopy, algebraic structures up to homotopy).
Title: Théorie de Hodge mixte et variétés des représentations des groupes fondamentaux des variétés algébriques complexes (Mixed Hodge theory and representation varieties of fundamental groups of complex algebraic varieties).
Publications and prepublications
-  Deformations of representations of fundamental groups of non-compact complex varieties. arXiv:1912.04787, hal-02399676.
-  Mixed Hodge structures and representations of fundamental groups of algebraic varieties. Advances in Mathematics, 349 (2019), 869–910. DOI:10.1016/j.aim.2019.04.028, arXiv:1806.02688, hal-01809625.
-  A criterion for quadraticity of a representation of the fundamental group of an algebraic variety. Manuscripta Mathematica, 152 (2017), no. 3-4, 381–397. DOI:10.1007/s00229-016-0866-7, arXiv:1509.02871, hal-01196355.
- Tutorial, linear algebra, first year. Language: German. 1 semester. Professor: Ingo JANISZCZAK.
- Seminar, Polynomials, Geometry, Algorithms, Bachelor and Master Lehramt (teaching). 1 semester. Language: German. Professor: Jochen HEINLOTH.
- Seminar on stacks (Summer Semester 2020)
- Seminar on stacks (Winter Semester)