Profile
Profile

Prof. Dr. Ursula Hamenstädt

E-mail: ursula(at)math.uni-bonn.de
Phone: +49 228 73 2914
Homepage: http://www.math.uni-bonn.de/people/ursula/
Room: 2.007
Location: Mathematics Center
Institute: Mathematical Institute
Research Areas: Former Research Area F (Leader)
Research Area A
Research Area F*
Research Area G (until 10/2012)
Former Research Area E
Birthdate: 15.Jan 1961
Mathscinet-Number: 243357

Academic Career

1986

PhD, University of Bonn

1986 - 1988

Miller Fellow for basic research in science, University of California, Berkeley, CA, USA

1988 - 1990

Assistant Professor, California Institute of Technology, CA, USA

1990 - 1991

Professor (C3), University of Bonn

Since 1992

Professor (C4), University of Bonn

Research Profile

Current research:

1) Geometric group theory: Investigation of the geometry of the mapping class group of a surface of finite type, the handle body group and the outer automorphism group of the free group as well as the structure of various hyperbolic graphs related to these groups. Contributions include large-scale geometric properties, identifying the large-scale structure of associated graphs and their boundaries, the investigation of interesting subgroups and questions geared at the Novikov conjecture.
2) Teichmüller dynamics: Investigation of statistical properties of the Teichmüller flow, symbolic codings, counting results, algebraic extensions of the flow and their properties, affine invariant manifolds, their structure, relations to the geometry of the moduli space of principally polarized abelian varieties, number theoretic properties.
3) Locally symmetric manifolds: Random hyperbolic 3-manifolds and their typical geometric and analytic properties, construction of surface subgroups in the fundamental group, equidistribution results for Weyl chamber flows in higher rank.


Future directions:

1) Understanding of torsion homology growth for hyperbolic 3-manifolds. The main goal is to express the volume of such a manifold in terms of growth of torsion homology of a tower of Galois covers whose fundamental groups have trivial intersection.
2) Investigation of pro finite completion of groups, in particular in view of the congruence subgroup property conjecture for mapping class groups and outer automorphisms groups of free groups.
3) Asymptotic properties of random walks on acylindrically hyperbolic groups in view of proper actions on Lp-spaces and understanding conditions for property (T).
4) Topological properties of strata of abelian differentials, in particular understanding their fundamental group and the relation to a geometric insight into the Schottky problem.
5) Spectral properties of closed hyperbolic 3-manifolds and a geometric understanding of covers using combinatorial methods and geometric flows.
6) Large scale geometric properties of Weil Petersson metrics on moduli spaces and dynamical properties of Weil-Petersson flows, also in the context of higher Teichmüller theory.

Contribution to Research Areas

Research Area A
Investigation of Reeb orbits on the boundary of compact convex domains using minimal discs.
Former Research Area E
Dynamical properties of the Teichmüller flow and the Weil Petersson flow.
Former Research Area F
Construction of second bounded cohomology classes with coefficients for groups acting on some hyperbolic space.
Investigation of geometric and topological properties of the mapping class group.
Research Area F*

Selected Publications

[1] Ursula Hamenstädt
Incompressible surfaces in rank one locally symmetric spaces
Geom. Funct. Anal. , 25: (3): 815--859
2015
ISSN: 1016-443X
DOI: 10.1007/s00039-015-0330-y
[2] Ursula Hamenstädt, Sebastian Hensel
Spheres and projections for {Out(F_n)}
J. Topol. , 8: (1): 65--92
2015
ISSN: 1753-8416
DOI: 10.1112/jtopol/jtu015
[3] Ursula Hamenstädt
Lines of minima in outer space
Duke Math. J. , 163: (4): 733--776
2014
ISSN: 0012-7094
DOI: 10.1215/00127094-2429807
[4] Ursula Hamenstädt
Bowen's construction for the Teichmüller flow
J. Mod. Dyn. , 7: (4): 489--526
2013
ISSN: 1930-5311
DOI: 10.3934/jmd.2013.7.489
[5] Ursula Hamenstädt, Sebastian Hensel
Isoperimetric inequalities for the handlebody groups
Trans. Amer. Math. Soc. , 365: (10): 5313--5327
2013
ISSN: 0002-9947
DOI: 10.1090/S0002-9947-2012-05808-9
[6] Ursula Hamenstädt
Isometry groups of proper CAT(0)-spaces of rank one
Groups Geom. Dyn. , 6: (3): 579--618
2012
ISSN: 1661-7207
DOI: 10.4171/GGD/166
[7] Ursula Hamenstädt
Isometry groups of proper hyperbolic spaces
Geom. Funct. Anal. , 19: (1): 170--205
2009
ISSN: 1016-443X
DOI: 10.1007/s00039-009-0719-6
[8] Ursula Hamenstädt
Invariant Radon measures on measured lamination space
Invent. Math. , 176: (2): 223--273
2009
ISSN: 0020-9910
DOI: 10.1007/s00222-008-0163-5
[9] Ursula Hamenstädt
Geometry of the mapping class groups. I. Boundary amenability
Invent. Math. , 175: (3): 545--609
2009
ISSN: 0020-9910
DOI: 10.1007/s00222-008-0158-2
[10] Ursula Hamenstädt
Bounded cohomology and isometry groups of hyperbolic spaces
J. Eur. Math. Soc. (JEMS) , 10: (2): 315--349
2008
ISSN: 1435-9855
DOI: 10.4171/JEMS/112

Publication List

Editorships

• Commentarii Math. Helvetici
• Journal de l'Ecole Polytechnique

Awards

2012

Advanced Grant of the European Research Council

2012

Member of the German National Academy of Sciences Leopoldina

2012

Fellow of the American Mathematical Society

Selected Invited Lectures

2010

ICM, Hyderabad, India

Offers

1991

University of Zürich, Switzerland

1991

University of Göttingen

2004

University of Bern, Switzerland

2007

University of Pennsylvania, USA

2010

Yale University, CT, USA

Selected PhD students

Juan Souto (2001): “Geometric Structures on 3-Manifolds and their Deformations”,
now Researcher, CNRS, University of Rennes 1, France

Supervised Theses

  • Master theses: 5, currently 3
  • Diplom theses: 42
  • PhD theses: 15, currently 1
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