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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: March 2020.
Born on March 15th 1990 in Saint-Cloud (France, 92). French nationality.
- 2018–2020: 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).
My main interests are complex geometry and Hodge theory with interactions to formal deformation theory and homotopy theory.
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).
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
- Deformations of representations of fundamental groups of non-compact complex varieties.
- Mixed Hodge structures and representations of fundamental groups of algebraic varieties.
Advances in Mathematics, 349 (2019), 869–910.
- A criterion for quadraticity of a representation of the fundamental group of an algebraic variety.
Manuscripta Mathematica, 152 (2017), no. 3-4, 381–397.
Memoirs and internships
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
- Lecture and tutorial, logics, algebra, geometry and vector spaces, for first year Mathematics / Computer Science. 76.5 hours. Professor: Emmanuel PEYRE.
- Tutorial and practical work on computers, parametrized curves, differential equations, symbolic computation, for second year Physics / Mechanics. 19.5 hours. Professor: Bernard PARISSE.
- 2016–2017: Lecture and tutorial, elementary analysis, population dynamics, for first year Biology. 64 hours. Professor: Hervé PAJOT.
- 2015–2016: Lecture and tutorial, elementary analysis, for first year Biology. 64 hours. Professor: Hervé PAJOT.
- 2014–2015: Lecture and tutorial, elementary analysis, for first year Biology. 64 hours. Professor: Hervé PAJOT.
- 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.
Talks and travels
Talks in seminars
- Séminaire HORUS. Institut de Recherche Mathématique Avancée, Strasbourg, March 9th 2020.
- Séminaire algèbre, géométrie algébrique, topologie algébrique. Institut Montpelliérain Alexander Grothendieck, Montpellier, October 3rd 2019.
- Seminar Number Theory and Algebraic Geometry. KU Leuven, November 21st 2018.
- Forschungsseminar Arithmetische Geometrie. Universität Duisburg-Essen, November 8th 2018.
- Séminaire géométrie complexe. Institut de Mathématiques de Marseille, May 29th 2018.
- Séminaire d'homotopie en géométrie algébrique. Institut de Mathématiques de Toulouse, May 22nd 2018.
- Séminaire algèbre et géométries. Institut Fourier, Grenoble, February 5th 2018.
- Séminaire de géométrie complexe. Institut Élie Cartan, Nancy, June 6th 2016.
- Séminaire algèbre et géométries. Institut Fourier, Grenoble, November 2nd 2015.
Conferences, meetings, schools
- (upcoming) School on Hodge Theory and Shimura Varieties. Essen, Germany, August 10th to 14th 2020.
- (upcoming) Summer school: Non-Abelian Hodge Theory. Grenoble, June 15th to July 3rd 2020.
- Rencontre du groupement de recherche Géométrie Algébrique et Géométrie Complexe. CIRM, Marseille, November 25th to 29th 2019.
- Talk. November 28th 2019.
- School on Motives and Stacks. Essen, Germany, September 23rd to 27th 2019.
- o-Minimal Structures in Algebraic Geometry. Freiburg, Germany, September 9th to 13th 2019.
- Mixed Hodge Modules: Applications. Île de Tatihou, Normandie, July 22nd to 26th 2019.
- Women in Homotopy Theory and Algebraic Geometry II. Freie Universität Berlin, Berlin, Germany, March 20th to 22nd 2019.
- Birational Geometry and Hodge Theory. CIRM, Marseille, February 11th to 15th 2019.
- Higher Structures. CIRM, Marseille, January 21st to 25th 2019.
- Rencontre du projet ANR Hodgefun (Groupes fondamentaux, théorie de Hodge et motifs). Bordeaux, November 14th to 16th 2018.
- Mixed Hodge Modules in Birational Geometry. Mainz, Germany, July 9th to 13th 2018.
- French-German Meeting on Complex Algebraic Geometry. CIRM, Marseille, April 9th to 13th 2018.
- Rencontre du projet ANR Hodgefun (Groupes fondamentaux, théorie de Hodge et motifs). Villa Finaly, Florence, Italy, February 26th to March 2nd 2018.
- Workshop in Deformation Theory III. Bari, Italy, February 19th to 23rd 2018.
- Talk. February 22nd 2018.
- Rencontre du groupement de recherche Géométrie Algébrique et Géométrie Complexe. CIRM, Marseille, December 11th to 15th 2017.
- Rencontre du projet ANR Hodgefun (Groupes fondamentaux, théorie de Hodge et motifs). Nancy, October 25th to 27th 2017.
- États de la Recherche: Derived Algebraic Geometry and Interactions. Toulouse, June 12th to 15th 2017.
- Complex Analytic and Differential Geometry. A conference in honor of Jean-Pierre Demailly. Grenoble, June 6th to 9th 2017.
- School: Limits and Flows in Kähler Geometry. Nantes, April 18th to 22nd 2017.
- Rencontre du groupement de recherche Géométrie Algébrique et Géométrie Complexe. CIRM, Marseille, January 23rd to 27th 2017.
- Rencontre du projet ANR GRACK (Équations de Monge-Ampère complexes et géométrie kählérienne). Pisa, Italy, October 24th to 27th 2016.
- School on Higgs Bundles and Fundamental Groups of Algebraic Varieties. Essen, Germany, September 27th to 30th 2016.
- Recent Advances in Complex Differential Geometry. Toulouse, June 13th to 22nd 2016.
- Topology of Complex Algebraic Varieties. CIRM, Marseille, May 30th to June 3rd 2016.
- School: Varieties of Calabi-Yau type. Banach Center, Warsaw, Poland, April 18th to 22nd 2016.
- Komplex Analysis Winter School and Workshop (KAWA 7). Toulouse and Albi, March 7th to 12th 2016.
- Rencontre du projet ANR GRACK (Équations de Monge-Ampère complexes et géométrie kählérienne). Institut Mathématiques de Jussieu, Paris, January 27th to 29th 2016.
- Rencontre du groupement de recherche Géométrie Algébrique et Géométrie Complexe. CIRM, Marseille, November 23rd to 27th 2015.
- Short talk. November 24th 2015.
- Journées Complexes Lorraines. Nancy, September 28th to October 2nd 2015.
- II Latin American School of Algebraic Geometry and Applications (II ELGA). Cabo Frio, Rio de Janeiro, Brazil, June 1st to 12th 2015.
- Komplex Analysis Winter School and Workshop (KAWA 6). Pisa, Italy, March 23rd to 28th 2015.
- Rencontre du groupement de recherche Géométrie Algébrique et Géométrie Complexe. CIRM, Marseille, November 24th to 28th 2014.
- Atelier franco-chinois sur la stabilité en géométrie et arithmétique. Grenoble, June 2nd to 6th 2014.
- Spring School: Classical and p-adic Hodge Theory. Rennes, May 12th to 23rd 2014.
- Master Class: Around Torelli's Theorem for K3 Surfaces. Strasbourg, October 25th to November 1st 2013.
Other activities at the Universität Duisburg-Essen
Other activities at the Université Grenoble Alpes
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.
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).
In 2016–2018 I was elected to represents Ph.D. students at the institute board.
My native language is French. I speak English, German and Italian.
Who have a personal page!
- Who work in the same fields and that I often meet:
- In Duisburg-Essen:
Antonio MEJÍAS GIL,
- From Grenoble:
- From the ENS Lyon:
Álvaro MATEOS GONZÁLEZ.
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
I was there),
to Morocco (Imessouane, Summer 2015, photo of
the bay during a memorable longboard session),
to Indonesia (Bali, Summer 2016, I surfed
the mythical spot
other photos of
a big wave in Medewi,
traditional dance Legong)
and I'm used to going to the French South-West coast (Vieux-Boucau is my home spot,
I also traveled to Chile (Summer 2019, photos of
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,
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
Cologne (October 2019),
Amsterdam (November 2019),
Prague (February 2020, photo of a
the Dancing House).
Finally, some photos of the region Rhine-Ruhr where I currently live:
in the Zollverein mine,
view from the Rheinturm,
view from the harbour),
view from the top),