Department of Mathematics
4176 Campus Dr
University of Maryland
College Park, MD 20742
karin at math.umd.edu
(301) 405-5148

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 November 2019.

Here is a link to the University of Maryland Geometry-Topology seminar.

differential-geometric aspects of rigidity
Lorentzian geometry
conformal pseudo-Riemannian geometry and parabolic Cartan geometries in general
smooth dynamics
Papers:
The conformal group of a compact, simply connected Lorentzian manifold, with Vincent Pecastaing
pdf also posted at http://arxiv.org/abs/1911.06251

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)

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

Geometric Structures, Compactifications, and Group Actions (co-organizer), Goethe-Universität Frankfurt, July 2020
University of Wisconsin Geometry & Topology Seminar, March 2020
George Mason University Colloquium, February 2020
University of Maryland Geometry-Topology Seminar, October 2019
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

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

In Spring 2020, I am teaching a graduate topics course on Exterior Differential Systems. 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.