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: October 2020.

Short CV

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

Employment

• 2018–2021: Postdoctoral researcher (wissenschaftlicher Mitarbeiter). Universität Duisburg-Essen.
• 2017–2018: Attaché Temporaire d'Enseignement et de Recherche (temporary teaching and research assistant). Université Grenoble Alpes.
• 2014–2017: Ph.D. student. Université Grenoble Alpes.
• 2010–2014: Élève fonctionnaire (student with a status of State employee). École Normale Supérieure de Lyon.

Studies and diplomas

• 2014–2018: Ph.D. Université Grenoble Alpes.
• 2013–2014: Second year of Master. Université Grenoble Alpes.
• 2012–2013: Agrégation de mathématiques (rank: 20) (French national examination for teaching in high school and undergraduate). École Normale Supérieure de Lyon.
• 2010–2012: Licence 3 (equiv. Bachelor), first year of Master. École Normale Supérieure de Lyon.
• 2008–2010: Classes préparatoires MPSI, MP* (equiv. first two years of Licence for preparing selective entrance examinations, with major in Mathematics and Physics). Lycée Saint-Louis, Paris.
• 2008: Baccalauréat Scientifique (equiv. high school diploma, with major in Science). Lycée Jeanne d'Albret, Saint-Germain en Laye (78).

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Research

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).

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).

• Manuscript, tel-01908625, theses.fr/2018GREAM029.

Publications and prepublications

• [3] Deformations of representations of fundamental groups of non-compact complex varieties. arXiv:1912.04787, hal-02399676.
• [2] 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.
• [1] 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.

Memoirs and internships

• Master's thesis: Variété des représentations du groupe fondamental d'une variété algébrique complexe lisse. Supervisor: Philippe EYSSIDIEUX. Institut Fourier, Grenoble, January–June 2014.
• First year Master's thesis: Courbure des espaces hermitiens symétriques et rigidité des variétés hermitiennes localement symétriques. Supervisor: Benoît CLAUDON. Institut Élie Cartan, Nancy, May–June 2012.
• Bachelor's thesis: Homologie simpliciale de quelques sous-variétés de R^n. Supervisor: François-Xavier DEHON. Laboratoire J. A. Dieudonné, Nice, May–June 2011.

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Teaching

At the Universität Duisburg-Essen

• 2020–2021:
  • Tutorial (online), Intersection Cohomology, Master. Language: English. 1 semester. Professor: Jochen HEINLOTH.
  • Tutorial (online), linear algebra 2, Bachelor. Language: German. 1 semester. Professor: Ingo JANISZCZAK.
• 2019–2020:
  • Tutorial (online), linear algebra 1, Bachelor. Language: German. 1 semester. Professor: Ingo JANISZCZAK.
  • Seminar, Polynomials, Geometry, Algorithms, Lehramt (teaching formation). Language: German. 1 semester. Professor: Jochen HEINLOTH.
• 2018–2019: Tutorial, Geometric Invariant Theory, Master. Language: English. 1 semester. Professor: Daniel GREB.

At the Université Grenoble Alpes

• 2017–2018:
  • Lecture and tutorial, logics, algebra, geometry and vector spaces, first year Mathematics / Computer Science. 76.5 hours. Professor: Emmanuel PEYRE.
  • Tutorial and practical work on computers, parametrized curves, differential equations, symbolic computation, second year Physics / Mechanics. 19.5 hours. Professor: Bernard PARISSE.
• 2016–2017: Lecture and tutorial, elementary analysis, population dynamics, first year Biology. 64 hours. Professor: Hervé PAJOT.
• 2015–2016: Lecture and tutorial, elementary analysis, first year Biology. 64 hours. Professor: Hervé PAJOT.
• 2014–2015: Lecture and tutorial, elementary analysis, first year Biology. 64 hours. Professor: Hervé PAJOT.

Previous experience

• 2012–2013: Colles en classes préparatoires (oral interrogations for preparing entrance examinations), filière PSI (equiv. second year of Licence). Lycée Jean Perrin, Lyon.
• 2010–2011: Tutoring in a high school. Association Trait d'Union ENS Lyon.

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Talks and travels

Talks in seminars

• Séminaire HORUS. Institut de Recherche Mathématique Avancée, Strasbourg, March 9, 2020.
• Séminaire algèbre, géométrie algébrique, topologie algébrique. Institut Montpelliérain Alexander Grothendieck, Montpellier, October 3, 2019.
• Seminar Number Theory and Algebraic Geometry. KU Leuven, Belgium, November 21, 2018.
• Forschungsseminar Arithmetische Geometrie. Universität Duisburg-Essen, November 8, 2018.
• Séminaire géométrie complexe. Institut de Mathématiques de Marseille, May 29, 2018.
• Séminaire d'homotopie en géométrie algébrique. Institut de Mathématiques de Toulouse, May 22, 2018.
• Séminaire algèbre et géométries. Institut Fourier, Grenoble, February 5, 2018.
• Séminaire de géométrie complexe. Institut Élie Cartan, Nancy, June 6, 2016.
• Séminaire algèbre et géométries. Institut Fourier, Grenoble, November 2, 2015.

Visitor

• Cohomology in Algebraic Geometry and Representation Theory. Freiburg Institute for Advanced Studies, Freiburg, Germany, May 1–18 , 2018.
  • Talk. May 18, 2018.

Conferences, meetings, schools

• Rencontre du groupement de recherche Géométrie Algébrique et Géométrie Complexe. CIRM, Marseille, November 1–29 , 2019.
  • Talk. November 28, 2019. Video.
• School on Motives and Stacks. Essen, Germany, September 1–27 , 2019.
• o-Minimal Structures in Algebraic Geometry. Freiburg, Germany, September 1–13 , 2019.
• Mixed Hodge Modules: Applications. Île de Tatihou, Normandie, July 1–26 , 2019.
• Women in Homotopy Theory and Algebraic Geometry II. Freie Universität Berlin, Germany, March 1–22 , 2019.
• Birational Geometry and Hodge Theory. CIRM, Marseille, February 1–15 , 2019.
• Higher Structures. CIRM, Marseille, January 1–25 , 2019.
• Rencontre du projet ANR Hodgefun (Groupes fondamentaux, théorie de Hodge et motifs). Bordeaux, November 1–16 , 2018.
• Mixed Hodge Modules in Birational Geometry. Mainz, Germany, July 1–13 , 2018.
• French-German Meeting on Complex Algebraic Geometry. CIRM, Marseille, April 1–13 , 2018.
• Rencontre du projet ANR Hodgefun (Groupes fondamentaux, théorie de Hodge et motifs). Villa Finaly, Florence, Italy, February 1 – March 2, 2018.
  • Talk. March 1, 2018.
• Workshop in Deformation Theory III. Bari, Italy, February 1–23 , 2018.
  • Talk. February 22, 2018.
• Rencontre du groupement de recherche Géométrie Algébrique et Géométrie Complexe. CIRM, Marseille, December 1–15 , 2017.
• Rencontre du projet ANR Hodgefun (Groupes fondamentaux, théorie de Hodge et motifs). Nancy, October 1–27 , 2017.
• États de la Recherche: Derived Algebraic Geometry and Interactions. Toulouse, June 1–15 , 2017.
• Complex Analytic and Differential Geometry. A conference in honor of Jean-Pierre Demailly. Grenoble, June 1–9 , 2017.
• School: Limits and Flows in Kähler Geometry. Nantes, April 1–22 , 2017.
• Rencontre du groupement de recherche Géométrie Algébrique et Géométrie Complexe. CIRM, Marseille, January 1–27 , 2017.
• Rencontre du projet ANR GRACK (Équations de Monge-Ampère complexes et géométrie kählérienne). Pisa, Italy, October 1–27 , 2016.
• School on Higgs Bundles and Fundamental Groups of Algebraic Varieties. Essen, Germany, September 1–30 , 2016.
• Recent Advances in Complex Differential Geometry. Toulouse, June 1–22 , 2016.
• Topology of Complex Algebraic Varieties. CIRM, Marseille, May 1 – June 3, 2016.
• School: Varieties of Calabi-Yau type. Banach Center, Warsaw, Poland, April 1–22 , 2016.
• Komplex Analysis Winter School and Workshop (KAWA 7). Toulouse and Albi, March 1–12 , 2016.
• Rencontre du projet ANR GRACK (Équations de Monge-Ampère complexes et géométrie kählérienne). Institut Mathématiques de Jussieu, Paris, January 1–29 , 2016.
• Rencontre du groupement de recherche Géométrie Algébrique et Géométrie Complexe. CIRM, Marseille, November 1–27 , 2015.
  • Short talk. November 24, 2015.
• Journées Complexes Lorraines. Nancy, September 1 – October 2, 2015.
• II Latin American School of Algebraic Geometry and Applications (II ELGA). Cabo Frio, Rio de Janeiro, Brazil, June 1–12 , 2015.
• Komplex Analysis Winter School and Workshop (KAWA 6). Pisa, Italy, March 1–28 , 2015.
• Rencontre du groupement de recherche Géométrie Algébrique et Géométrie Complexe. CIRM, Marseille, November 1–28 , 2014.
• Atelier franco-chinois sur la stabilité en géométrie et arithmétique. Grenoble, June 1–6 , 2014.
• Spring School: Classical and p-adic Hodge Theory. Rennes, May 1–23 , 2014.
• Master Class: Around Torelli's Theorem for K3 Surfaces. Strasbourg, October 1 – November 1, 2013.

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Other activities at the Universität Duisburg-Essen

Working groups

• Seminar on stacks (Summer Semester 2020)
• Seminar on stacks (Winter Semester 2019–2020)
• Seminar on stacks (Summer Semester 2019)
• Seminar on stacks (Winter Semester 2018–2019)

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Other activities at the Université Grenoble Alpes

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.

• Séminaire compréhensible (Ph.D. seminar)

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.

• Working group 2016–2017 on algebraic stacks (séminaire champêtre)
• Working group 2015–2016 on complex algebraic surfaces
• Working group 2014–2015 on deformations and moduli spaces

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).

Institute board

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

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Other skills

Languages

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

Computer

GNU/Linux, Emacs, clavier BÉPO.

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My friends

Who have a personal page!

• Who work in the same fields and that I often meet: Yohan BRUNEBARBE, Nero BUDUR, Benoît CADOREL, Joana CIRICI, Benoît CLAUDON, Jérémy DANIEL, Lionel DARONDEAU, Clément DUPONT, Louis IOOS, Lucas KAUFMAN, Julien KELLER, Damien MÉGY, Ronan TERPEREAU, Caroline VERNIER.
• In Duisburg-Essen: Chirantan CHOWDHURY, Nicolas DUPRÉ, Antonio MEJÍAS GIL, Martin SCHWALD, Tariq SYED, Xu-Cheng ZHANG.
• From Grenoble: Rodolfo AGUILAR, Amina AZZOUZ, Thibaut DELCROIX, Ya DENG, Zhizhong HUANG, Julien KORINMAN, David LETURCQ, Pedro MONTERO, Lucas PASTOR, Giuseppe PIPOLI, Juan VIU-SOS, Binbin XU, Florent YGOUF.
• From the ENS Lyon: Arnaud DEMARAIS, Loïc DEVILLIERS, Quentin FORTIER, Nicolas MARTIN, Álvaro MATEOS GONZÁLEZ.
• Exterior: Claudia DRAWE, Bettina HERMANN, Hichem NAAR.

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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 giant 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). I also traveled to Chile (Summer 2019, photos of Valparaíso, view from the harbour, view from the hills, Viña del Mar, at the sunset, the surf spot Concón, Valle de la Luna in the Atacama desert, lamas, geysers, laguna, paragliding flight in Iquique, Santiago).

I'm learning and practicing regularly latin couple dances: Salsa and mainly Bachata. I participated to dance festivals in Düsseldorf (March 2019, February 202O), Lyon (April 2019, photo of a course, demonstration), Cologne (October 2019), Amsterdam (November 2019), Prague (February 2020, photo of a course, the Dancing House).

Finally, some photos of the region Rhine-Ruhr where I currently live: Essen (Grugapark, Villa Hügel, skyline, carnival, Stadtgarten, in the Zollverein mine, coking plant), Düsseldorf (city, view from the Rheinturm, view from the harbour), Duisburg (Landschaftpark, view from the top), Bochum (city, mining museum), Oberhausen (gasometer), Dortmund (Zollern mine).