I am an Associate Professor at the University of Maryland in College Park, partially supported by the National Science Foundation. Here is my curriculum vitae as of October 2018.

Research Interests

• differential-geometric aspects of rigidity
• Lorentzian geometry
• conformal pseudo-Riemannian geometry and parabolic Cartan geometries in general
• smooth dynamics

  Papers:
  

• C¹ deformations of almost-Grassmannian structures with strongly essential symmetry, with Andreas Čap
  pdf also posted at http://arxiv.org/abs/1902.01801
  

• Topology of automorphism groups of parabolic geometries, with Charles Frances
  pdf
  Geometry & Topology 23 no. 1 (2019) 135--169.
  

• Nonstationary smooth geometric structures for contracting measurable cocycles
  pdf
  Ergodic Theory and Dynamical Systems 39 no. 2 (2019) 392--424
  (published online in 2017 here)
  

• Strongly essential flows on irreducible parabolic geometries, with Katharina Neusser
  pdf
  Transactions of the American Mathematical Society 368 no. 11 (2016) 8079--8110
  

• Quasihomogeneous three-dimensional real analytic Lorentz metrics do not exist, with Sorin Dumitrescu
  pdf
  Geometriae Dedicata 179 no. 1 (2015) 229-253

• Essential Killing fields of parabolic geometries: projective and conformal structures, with Andreas Čap
  pdf or in the ESI Preprint Series (number 2393)
  Central European Journal of Mathematics 11 no. 12 (2013) 2053-2061

• Essential Killing fields of parabolic geometries, with Andreas Čap
  pdf or in the ESI Preprint Series (number 2388)
  Indiana University Mathematics Journal 62 no. 6 (2013) 1917-1953

• Formes normales pour les champs conformes pseudo-riemanniens [Normal forms for pseudo-Riemannian conformal vector fields], with Charles Frances
  dvi pdf ps
  Bulletin de la Société Mathématique de France 141 no. 3 (2013), 377-421

• A Frobenius theorem for Cartan geometries, with applications
  dvi pdf ps
  L'Enseignement Mathématique (Sér. II) 57 no. 1-2 (2011) 57-89
  
  Erratum: There is an error in the proof of Theorem 6.3, the Frobenius theorem for Killing fields around regular points in the smooth case. Pecastaing has an alternative proof of this result: On two theorems about local automorphisms of geometric structures, Ann. Inst. Fourier (Grenoble) 66 no. 1 (2016) 175-208, arxiv.org/abs/1402.5048. There are no known issues with the real-analtyic results that constitute the bulk of my paper.

• Conformal actions of nilpotent groups on pseudo-Riemannian manifolds, with Charles Frances
  dvi pdf ps
  Duke Mathematical Journal 153 no. 3 (2010) 511-550

• Dynamics on Lorentz manifolds, lecture notes in English from the École de Géométrie Différentielle et Systèmes Dynamiques, ENSET Oran, Algeria, November 4-9, 2006
  dvi pdf ps
  French version, translated by D. Smai, in Algèbre, analyse, et dynamique pour la géométrie: Actes des Écoles de Géométrie et Dynamique au Maghreb 2004-2007 (eds. T. Barbot, H. Belbachir, S. Mehdi, D. Smai, R. Souam) Paris: Ellipses (2010) 307-342

• An embedding theorem for automorphism groups of Cartan geometries, with Uri Bader and Charles Frances
  dvi pdf ps
  Geometric and Functional Analysis 19 no. 2 (2009) 333-355

• Compact Lorentz manifolds with local symmetry
  University of Chicago dissertation, 2006 dvi pdf ps
  article version dvi pdf ps
  Journal of Differential Geometry 81 no. 2 (2009) 355-390

• A primer on the (2+1) Einstein universe, with Thierry Barbot, Virginie Charette, Todd Drumm, and William Goldman
  dvi pdf ps
  in Recent developments in pseudo-Riemannian Geometry: Proceedings of the Special Semester "Geometry of pseudo-Riemannian manifolds with application to physics", Erwin Schrödinger Insitute, Vienna, Sept - Dec 2005 (eds. D. Alekseevsky and H. Baum) in ESI-Series on Mathematics and Physics

• Actions of noncompact semisimple groups on Lorentz manifolds, with Mohamed Deffaf and Abdelghani Zeghib
  dvi pdf ps
  Geometric and Functional Analysis 18 no. 2 (2008) 463-488

• Isometric actions of Heisenberg groups on compact Lorentz manifolds
  dvi pdf ps
  Geometriae Dedicata 126 no. 1 (2007) 131-154

Recent and upcoming talks and conferences

• Differentialgeometrie im Großen Mathematisches Forschungsinstitut Oberwolfach, June/July 2019
• Abel Symposium Ålesund, Norway, June 2019
• Leibniz Universität Hannover Oberseminar Differentialgeometrie, June 2019
• HORUS Seminar Université de Strasbourg, April 2019
• SPP Conference "Geometry at Infinity" WWU Münster, April 2019
• Groups, Geometries, and Spaces in honour of Alessandra Iozzi ETH Zürich, January 2019

• Workshop on Cartan Connections, Geometry of Homogeneous Spaces, and Dynamics (co-organizer) Erwin Schrödinger Institute, July 2011
      Abstracts for week 2, with some links to slides
      I am a guest editor for the ensuing special issue of the Central European Journal of Mathematics

Teaching

In Fall 2019, I am teaching Math 430: Euclidean and non-Euclidean Geometry. If you are registered for the course, you can access the Canvas web page. Math 742: Geometric Analysis. Here is the web page for the course. In 2015, I ran a module in the MAPS-REU on "Local isometries of 3-dimensional spacetimes." See below for a picture of our group.

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Some Pictures and Links

• Portrait of incoming graduate students, University of Chicago, September 1999
• A gathering of Chicago mathematicians, June 2010
• MAPS-REU Team Geometry, 2015