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 September 2016.

Research Interests

• differential-geometric aspects of rigidity
• Lorentz geometry
• conformal pseudo-Riemannian geometry
• parabolic Cartan geometries

  Papers:
  

• Nonstationary smooth geometric structures for contracting measurable cocycles
  pdf also posted at http://arxiv.org/abs/1604.04423
  

• 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
  
  Caution: There is an error, indicated to me by Vincent Pecastaing, in the proof of Theorem 6.3, the Frobenius theorem for Killing fields around regular points in the smooth case. I am working on fixing this proof; meanwhile, Pecastaing has an alternative proof of this result for Killing fields in the smooth case, which can be found at 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

• Workshop on Boundaries of Groups American Institute of Mathematics, October 2016
• Geometries, Surfaces, and Representations of Fundamental Groups (in honor of Bill Goldman's 60th birthday) University of Maryland, June 2016
• Universität Heidelberg Hauptseminar Geometrie, May 2016
• Université de Strasbourg Séminaire Géométrie et applications, May 2016
• Université du Luxembourg Geometry and Topology seminar, May 2016
• Université de Strasbourg Professeure Invitée, April-May 2016
• MPI/Universität Bonn Oberseminar Differentialgeometrie, January 2016
• Max Planck Institut für Mathematik Guest Program, January-March 2016
• Relativity and Geometry: In memory of A. Lichnerowicz Institut Henri Poincaré, December 2015
• University of Michigan Geometry Seminar, November 2015
• Indiana University Geometry Seminar, October 2015

• 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 2016, I am teaching Math 430: Euclidean and non-Euclidean Geometry. If you are registered for the course, you can access the Canvas web page on ELMS. Math 744: Lie Groups. 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