Prof. Dr. Anna Wienhard

 
Research Interests
Discrete subgroups of Lie groups
Deformation spaces of geometric structures
Representation varieties, Anosov representations, higher Teichmüller theory
Positivity in Lie groups
Applications of geometry and topology in other sciences

 
 
Short CV
since 2020 Scientific Director Research Station Geometry and Dynamics
since 2019 CoSpokesperson Excellence Cluster STRUCTURES
since 2015 Group Leader Heidelberger Institut für Theoretische Studien HITS
since 2012 Professor, Mathematisches Institut, RuprechtKarlsUniversität Heidelberg
Scientific Chair Heidelberg Laureate Forum Foundation
Fellow of the American Mathematical Society
Advisory Board Springer Lecture Notes in Mathematics
Scientific Committee Wissenschaftskommunikation.de
Member Heidelberg Academy of Sciences
Member BerlinBrandenburg Academy of Sciences and Humanities
Editor Annales Henri Lebesgue
Editor Annales scientifiques de l'Ecole Normale Superieure
Editor Geometric and Functional Analysis
Editor Geometry & Topology
Editor Proceedings of the London Mathematical Society
Editor Geometriae Dedicata (2011  2020)
Editor Forum Mathematicum (2016  2020)
20122014 Sloan Research Fellowship, Sloan Foundation
20092013 Member, Junge Akademie der BBAW und der Leopoldina
20072012 Assistant Professor, Department of Mathematics, Princeton University
20072010 Director of Graduate Studies, Department of Mathematics, Princeton University
20092012 Visitor, School of Mathematics, Institute for Advanced Study, Princeton
20052007 Dickson Instructor, Department of Mathematics, University of Chicago
20052006 Member, School of Mathematics, Institute for Advanced Study, Princeton
20042005 Postdoc, Mathematisches Institut, Universität Basel
2004 PhD, Mathematisches Institut, Rheinische Friedrich WilhelmsUniversität Bonn

Publications and Preprints

Hessian of Hausdorff dimension on purely imaginary directions (with B. Pozzetti,
A. Sambarino and M. Bridgeman ), Preprint.

Noncommutative coordinates for symplectic representations (with D. Alessandrini, O. Guichard and E. Rogozinnikov), Preprint.

Finding universal structures in quantum manybody dynamics via persistent homology,
( with D. Spitz, J. Berges, M. Oberthaler ), Preprint.

Conformality for a robust class of nonconformal attractors (with B. Pozzetti and
A. Sambarino ), Preprint, to appear in Journal für die reine und angewandte Mathematik (Crelle)

Flows on the PSL(V)Hitchin component (with Z. Sun and
T. Zhang ), Geometric and Functional Analysis 30 (2020), 588692

Horofunction Compactifications of Symmetric Spaces (with T.Haettel,
A. Schilling and C. Walsh ), Preprint.
 Tameness of Riemannian locally symmetric spaces arising from Anosov representations
(with O. Guichard,
F. Kassel), Preprint under revision.

An invitation to higher Teichmüller theory, Proceedings of the ICM 2018.

Representations and geometric structures, appeared in: What's Next?: The Mathematical Legacy of William P. Thurston.

Deforming convex real projective structures (with
T. Zhang ), Geometriae Dedicata (2017), 134.

Positivity and higher Teichmüller theory (with (with O. Guichard), European Congress of Mathematics, 289?310, Eur. Math. Soc., Zürich, 2018.

On order preserving representations (with G. Ben Simon ;
M. Burger; T. Hartnick; A. Iozzi), J. Lond. Math. Soc. (2) 94 (2016), no. 2, 525544.

Compactification of certain CliffordKlein forms of reductive
homogeneous spaces
(with F.Gueritaud, O. Guichard, F. Kassel),Michigan Mathematical Journal, Volume 66 (2017), Issue 1, 4984.

Anosov representations and proper actions
(with F. Gueritaud , O. Guichard,
F. Kassel), Geometry & Topology 211 (2017) 485584.

Limits of geometries (with D. Cooper; J. Danciger), Transactions of the AMS 370 (2018), 65856627.

On weakly maximal representations of surface groups (with G. Ben Simon ; M. Burger; T. Hartnick;
A. Iozzi), Journal of Differential Geometry 105 (2017) 375404.

Weakly maximal representations of surface groups (with G. Ben Simon ; M. Burger; T. Hartnick;
A. Iozzi),
Research Announcement.

Anosov representations: Domains of
discontinuity and applications,
(with O. Guichard),
Inventiones Mathematicae, Volume 190, Issue 2 (2012), Page 357438.

Higher Teichmüller spaces: From SL(2,R) to other Lie groups
,
(with M. Burger;
A. Iozzi),
Handbook of
Teichmüller Theory IV, 2014.

Topological Invariants of Anosov Representations,
(with O. Guichard),
Journal of Topology 3, 2010 578642.

Domains of discontinuity for surface groups, (with O. Guichard),
C. R. Math. Acad. Sci. Paris I 347 (2009), 10571060.

Surface group representations with maximal Toledo invariant , (with M. Burger;
A. Iozzi),
Annals of Mathematics 172 (2010), no.1, 517566.

Tight homomorphisms and Hermitian symmetric spaces,
(with M. Burger;
A. Iozzi),
GAFA 19 (2009), no. 3, 678721.

Remarks on and around bounded differential forms,
Pure and Applied Mathematics Quaterly 8 (2012), no. 2, (Special Issue: In honor of F. Thomas Farrell and Lowell E. Jones part 2 of 2), 481  498.

Convex foliated projective structures and the Hitchin component of SL(4,R), (with O. Guichard),
Duke Mathematical Journal 144 (2008) no.3, 381445.

Hermitian symmetric spaces and Kähler rigidity,
(with M. Burger;
A. Iozzi),
Transformation Groups 12 (2007), no. 1, 532. electronic article .

The action of the mapping class group on maximal representations,
Geom. Dedicata 120 (2006), 179191, electronic article .

Maximal representations of surface groups: Symplectic Anosov structures
(with M. Burger;
A. Iozzi; F. Labourie),
Pure and Applied Mathematics Quaterly, 1 (2005), no. 2, (Special Issue: In Memory of Armand Borel), 555601.

Surface group representations with maximal Toledo invariant
(with M. Burger;
A. Iozzi),
C. R. Math. Acad. Sci. Paris 336 (2003), no. 5, 387390.

Bounded cohomology and geometry,
PhDthesis,
Bonner Mathematische Schriften Nr. 368, Bonn 2004.

A generalisation of Teichmüller space in the Hermitian context,
Seminaire de Theorie Spectrale et Geometrie Grenoble, Vol.22 (2004), 103123.

Bounded cohomology and representations of surface groups,
Vortrag auf der Mathematischen Arbeitstagung 2007, MPIM Bonn.

Bounds for cohomology classes, (with M. Burger;
A. Iozzi; N. Monod),
in Guido's book of conjectures, 3839, L'Enseignement Mathematique 54 (2008), 3189.

Foliated projective structures and the Hitchin component of PSL(4,R),
Oberwolfach Reports, 32 (2007), 3841.

Surface Groups and Hermitian Symmetric Spaces,
Oberwolfach Reports, 26 (2006), 15461548.

Flexibilität und Starrheit  Gruppenhomomorphismen und
geometrische Strukturen,
Mitteilungen der Deutschen Mathematiker Vereinigung, 13 (2005) no. 2, 8083.

Workshops and Conferences
For more recent workshops, see here.
Workshop on Higgs bundles in Geometry and Physics Feb 28  Mar 3, 2016,
IWH Heidelberg
Workshop on Surface Group Representations Mar 17  20, 2016,
Caltech
Research Program Dynamics on Moduli Spaces of Geometric Structures, MSRI
Sixth HeidelbergKarlsruheStrasbourg Geometry Day, Heidelberg, 30.10.2015.
Dynamics on Moduli Spaces , MSRI, April 13, 2015  April 17, 2015.
Connections for Women: Dynamics on Moduli Spaces of Geometric Structures, MSRI, January 15, 2015  January 16, 2015.
GEAR Junior Retreat, Ann Arbor, 27.05.01.06.2014.
GEAR Network Retreat, Maryland, 17.21.03.2014.
Geometry and Physics of Ftheory, Heidelberg, 24.27.02.3014.
New Trends in Teichmüller Theory and Mapping Class Groups, Feb 9  15, 2014, Oberwolfach.
Fourth HeidelbergKarlsruheStrasbourg Geoemtry Day, Heidelberg, 24.01.2014.
First HeidelbergKarlsruheStrasbourg Geometry Day, Heidelberg 18.01.2013.
Mathematics and Physics of Moduli Spaces,
Heidelberg, September 2428, 2012.
GEAR Network Retreat, UrbanaChampaign, August 6 10, 2012.
Trimester on Geometry and analysis of surface group representations, Institut Henri Poincare, Paris, January  March 2012.
Workshop on Ergodic Decompositions of Character Varieties, Princeton University, October 17  19, 2011.
Mathematical Research Community  The geometry of real projective structures, Snowbird Resort, Utah, June 12  18, 2011.
Mathematical Retreat on Integrable Systems, February 18  20, 2011.
Summer Workshop in Mathematics for High School Students, Women in Mathematics, SWIM Princeton, June 16 25, 2010.
Workshop on Flat Conformal Lorentzian Structures, February 18  20, 2010.
Mathematical Retreat on Lattices and NonLattices, February 12  14, 2010.
Summer Workshop in Mathematics for High School Students, Women in Mathematics, SWIM Princeton, June 10 19, 2009.
Mathematical Retreat on "Ratner's Theorem", February 27  March 1, 2009.
Representations of Surface Groups, March 19 to March 23, 2007,
American Institute of Mathematics, Palo Alto, California,
organized with Steven Bradlow,
Oscar GarciaPrada, William M. Goldman.
Here is some Background
Material.
The wiki maintained by G. WILKIN (user name is "surface" and password is "groups").
Conference on Bounded Cohomology, Harmonic Maps and Higgs Bundles, March 1319, 2005.
Workshop on hprinciples with Christian Becker and Hartmut Weiss, funded by Schwerpunktprogramm Differentialgeometrie
of DFG.
Workshop on Foliations with Christian Becker and Hartmut Weiss, funded by Schwerpunktprogramm Differentialgeometrie
of DFG.



Address:
Mathematisches Institut
Universität Heidelberg
Mathematikon
Im Neuenheimer Feld 205
69120 Heidelberg
Germany
Tel:  +49(0)622154 14206 
Fax:  +49(0)622154 14245 
email
Office: Room 3/309, Mathematikon, INF 205
Office hours:
by appointment
Secretariat:
Ms. Evelyne Bachmann
Room 3/412, INF 205
Tel: +4962215414237
sekrwienhard@mathi.uniheidelberg.de
