Vincent Pecastaing Laboratoire J.A. Dieudonné UMR CNRS 7351 Université Côte d'Azur, Parc Valrose 06108 Nice, Cedex 2, France Email: first name (dot) last name (at) unice.fr Office: 811 (4th floor) Phone: (+33) 489150643

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Welcome to my personal homepage

I am maître de conférences in the math department of Université Côte d'Azur (Nice) since September 2020. Previously, I was postdoc in the research group of Jean-Marc Schlenker at the University of Luxembourg (2017-2020), and I visited University of Maryland (Fall 2016) and Hümboldt University of Berlin (Fall 2015). I completed my PhD at the Université Paris-Sud in 2014. For more information, here is a CV.

Thematic trimester at IHP, Spring 2024

With A. Brown, D. Fisher, K. Mann and R. Spatzier, I coorganize a thematric trimester: Group Actions and Rigidity: Around the Zimmer Program held at IHP from April 15 to July 5 2024. The program is the following:

• Pre-school: Rigidity, Dynamics and Geometric Structures, CIRM, April 15 - 19.
• Conference: Low Dimensional Actions, IHP, April 29 - May 4.
• Conference: Group Actions with Hyperbolicity and Measure Rigidity, IHP, May 27 - 31.
• Conference: Actions of Large Groups, Geometric Structures, and the Zimmer Program, IHP, June 10 - 14.

Poster of the program.

Registration to the trimester and conferences are now opened at Indico.

Deadline for financial support: November 1st, 2023.

Research interests

• Pseudo-Riemannian Geometry, Conformal Geometry, Parabolic Geometries
• Dynamical Systems, Zimmer program, Actions of Lie groups
• Rigidity of Geometric Structures, Cartan Geometries

Publications/Preprints

Preprints

• Conformal actions of solvable Lie groups on closed Lorentzian manifolds
  pdf
, arxiv.
• Projective and conformal closed manifolds with a higher-rank lattice action
  Accepted at Mathematische Annalen. Preprint arXiv:1910.06199.

Published articles

• The conformal group of a compact simply-connected Lorentzian manifold, with Karin Melnick.
  J. Amer. Math. Society, 35(2022), pp. 81-122. pdf, arxiv.
• Conformal actions of higher-rank lattices on pseudo-Riemannian manifolds.
  Geom. Funct. Anal., 30(2020), pp. 955-987. pdf, arxiv.
• Conformal actions of real-rank 1 simple Lie groups on pseudo-Riemannian manifolds.
  Transf. Groups, 24(2019), no. 4, pp. 1213-1239. pdf, arxiv.
• Lorentzian manifolds with a conformal action of SL(2,R).
  Comment. Math. Helvetici. 93(2018), no. 2, pp. 401-439. pdf, arxiv.
• Essential conformal actions of PSL(2,R) on real-analytic compact Lorentz manifolds.
  Geom. Dedicata 188(2017), no. 1, pp. 171-194. pdf, arxiv.
• On two theorems about local automorphisms of geometric structures.
  Ann. Inst. Fourier, 66(2016), no. 1, pp. 175-208. pdf, arxiv.

Other preprints

• Semi-simple Lie groups acting conformally on compact Lorentz manifolds.
  
  Finalized in June 2015, this preprint is extracted from my thesis and improves some of the results. Its main result is now incorporated in the paper "Conformal actions of real-rank 1 simple Lie groups on pseudo-Riemannian manifolds".

Thesis

Here is the manuscript of my PhD thesis (in French). It had been prepared in the Mathematics department of Université Paris-Sud (Orsay), under the supervision of Charles Frances, who is now in Strasbourg.

Recent and upcoming talks

• Colloquium of pure Mathematics, University of Hamburg (online) May 2021.
• Workshop : Global rigidity of actions by higher-rank groups, AIM San Jose (postponed).
• Conference: Geometric structures, compactifications and group actions, Goethe University Frankfurt (postponed)
• Séminaire d'algèbre, topologie et géométrie, Université Nice Côte d'Azur, April 2020.
• Séminaires Géométrie, Algèbre, Dynamique et Topologie, Université de Bourgogne, Dijon, April 2020.
• Séminaire TSG, Université Grenoble Alpes, March 2020.
• Séminaire de Géométrie, Université de Bordeaux, February 2020.
• Seminar of differential geometry, Masaryk University, Brno, December 2019.
• Séminaire de théorie ergodique et systèmes dynamiques, Université Paris-Nord, November 2019
• Séminaire de Géométrie Topologie et Dynamique, Université Paris-Sud, November 2019
• Arbeitsgemeinschaft: Zimmer's Conjecture, Oberwolfach, October 2019
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Webpage created in 2020
Last modification : 12/2021
Vincent Pecastaing