I am a Professor at the University of Maryland in College Park, partially supported by the National Science Foundation. Here is my curriculum vitae as of January 2022.

Research Interests

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

Recent papers:

• The Lorentzian Lichnerowicz Conjecture for real-analytic, three-dimensional manifolds, with Charles Frances
  pdf also posted at http://arxiv.org/abs/2108.07215
  
• The conformal group of a compact, simply connected Lorentzian manifold, with Vincent Pecastaing
  pdf
  Journal of the American Mathematical Society 35 no. 1 (2022) 81-122.
• Survey article on Rigidity of transformation groups in differential geometry
  pdf
  Notices of the American Mathematical Society 68 no. 5 (2021) 721--732.
• C¹ deformations of almost-Grassmannian structures with strongly essential symmetry, with Andreas Čap
  pdf also posted at http://arxiv.org/abs/1902.01801
  to appear in Transformation Groups
• 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)
  

All older papers:

Recent and upcoming talks and conferences

• Geometric Structures, Compactifications, and Group Actions (co-organizer), Université de Strasbourg, July 2022
• Differential Geometry and Applications, Hradec Králové, Czech Republic, July 2022.
• Pseudo-Riemannian geometry and invariants in General Relativity, Stavanger, Norway (Hybrid), May-June 2022
• Global rigidity of actions by higher-rank groups, American Institute for Mathematics, May 2022
• University of Maryland: Dynamics Seminar, December, 2021.
• University of Maryland: Geometry-Topology Seminar, November, 2021.
• Westfälische Wilhelms-Universität Münster: Oberseminar Differentialgeometrie (Online), June 2021.
• 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

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  Teaching

  In Spring 2022, I am teaching Math 310, Introduction to Mathematical Proof. If you are a member of this course, you can access the web page here. 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. In 2013, I read about the social psychology of evaluations of teaching effectiveness, and produced this short essay.

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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