4176 Campus Dr

University of Maryland

College Park, MD 20742

karin at math.umd.edu

(301) 405-5148

I am a Professor (effective 8/23/21) at the University of Maryland in College
Park, partially supported by the National Science Foundation.
Here is my |

- 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

- Survey article on
*Rigidity of transformation groups in differential geometry*

pdf

*Notices of the American Mathematical Society***68**no. 5 (2021) 721--732. *The conformal group of a compact, simply connected Lorentzian manifold*, with Vincent Pecastaing

pdf*also posted at*http://arxiv.org/abs/1911.06251

to appear in*Journal of the American Mathematical Society**C*, with Andreas Čap^{1}deformations of almost-Grassmannian structures with strongly essential symmetry

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:

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*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), Université de Strasbourg, July 2022
- Global rigidity of actions by higher-rank groups, American Institute for Mathematics, May 2022
- Flexibility and Rigidity in Dynamical Systems, Simons Institute for Geometry and Physics, March 2022.
- Virginia Topology Conference, Charlottesville, November 2021
- SCREAM Project Opening Workshop Ilawa, Poland/Online, August 2021
- Westfälische Wilhelms-Universität Münster: Oberseminar Differentialgeometrie (Online), June 2021.
- University of Maryland: RIT on Mathematical Concepts and Practices (Online), March 2021.
- Friedrich-Schiller-Universität Jena Analysis & Geometry/Dynamical Systems & Mathematical Physics Seminar (Online), November 2020
- 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 2021, I am teaching Math 730,

*Foundations of Topology*, and Math 430,*Euclidean and non-Euclidean Geometry*. If you are are a member of either 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.