Photo: Talk at the seminar, November 2nd 2015

Louis-Clément LEFÈVRE

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I'm a postdoctoral researcher in Mathematics at the Universität Duisburg-Essen in Germany in the group of Prof. Dr. Jochen HEINLOTH. I defended my Ph.D. thesis on June 25th 2018 at the Institut Fourier in Grenoble under the supervision of Philippe EYSSIDIEUX.

Last update: June 2019.

Photo: At the office, back from Pisa, March 2015

Short CV

Born on March 15th 1990 in Saint-Cloud (France, 92). French nationality.

Employment

Studies and diplomas

Stokes formla (click for more information)

Research

My main interests are complex geometry and Hodge theory with interactions to formal deformation theory and homotopy theory.

Ph.D. thesis

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).

Abstract: The mixed Hodge theory of Deligne provides additional structures on the cohomology groups of complex algebraic varieties. Since then, mixed Hodge structures have been constructed on the rational homotopy groups of such varieties by Morgan and Hain.

In this vein, we construct mixed Hodge structures on invariants associated to linear representations of fundamental groups of smooth complex algebraic varieties. The starting point is the theory of Goldman and Millson that relates the deformation theory of such representations to the deformation theory via differential graded Lie algebras. This was reviewed by P. Eyssidieux and C. Simpson in the case of compact Kähler manifolds. In the non-compact case, and for representations with finite image, Kapovich and Millson constructed only non-canonical gradings.

In order to construct mixed Hodge structures in the non-compact case and unify it with the compact case treated by Eyssidieux-Simpson, we re-write the classical Goldman-Millson theory using more modern ideas from derived deformation theory and a construction of L-infinity algebras due to Fiorenza and Manetti. Our mixed Hodge structure comes then directly from the H^0 of and explicit mixed Hodge complex, in a similar way as the method of Hain for the fundamental group, and whose functoriality appears clearly.

Publications and prepublications

Memoirs and internships

Photo: Surf lesson, Portugal, Summer 2013

Teaching

At the Universität Duisburg-Essen

At the Université Grenoble Alpes

I taught for the UFR Informatique, Mathématiques et Mathématiques Appliquées at the Département Licence Sciences et Technologies

Previous experience

Talks and travels

Talks in seminars

Visitor

Conferences, meetings, schools

Photo: The Mont Blanc

Activities at the Institut Fourier in Grenoble

Ph.D. seminar

With Alejandro RIVERA we organized in 2016–2018 the Ph.D. seminar of the Institut Fourier. Every week a speaker, from the Institut Fourier or from the outside, is invited to talk about a subject of his choice (not necessarily related to his research) in an understandable way for our Ph.D. students.

Working groups

With Pedro MONTERO we organized every year our own working group for PhD students. The goal is to read a book together with one talk a week, on a quite large topic around complex algebraic geometry.

Popularization of Sciences

In 2014, 2015 and 2016 I animated a stand at the Fête de la science (national annual event of popularization of Science). Photo.

Institute board

In 2016–2018 I was elected to represents Ph.D. students at the institute board.

Other skills

Languages

My native language is French. I speak English, German and Italian.

My friends

Who have a personal page!

Photo: Surf, summer 2014

Personal

On Summer I go surfing waves. For this I traveled to Portugal (Peniche, Summer 2013, Summer 2014, Spring 2018, photos of colored rocks on Almagreira beach, Baleal and the bay, the city of Nazaré, famous for its very big wave, I was there), to Morocco (Imessouane, Summer 2015, photo of the bay during a memorable longboard session), to Indonesia (Bali, Summer 2016, I surfed Kuta Beach, Kedungu, Balangan, the mythical spot Uluwatu, other photos of my back, the board, a big wave in Medewi, coconut tree, rice fields, jungle, traditional dance Legong) and I'm used to going to the French South-West coast (Vieux-Boucau is my home spot, weather forecast, daily photo). During the winter season in Grenoble I went to the mountains to ride snowboard. Here are my videos taken with a GoPro camera, HD quality, on musics I enjoy.

I like dancing. I'm learning Bachata (latin couple dance, see for example this video clip, this demonstration). In Lyon I participated for two years to a choregraphy presented at the InterENS (meetings between the different ENS).