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

Research Activities

DFG Excellence Cluster 2181 "STRUCTURES: A unifying approach to emergent phenomena in the physical world, mathematics, and complex data"
DFG Graduiertenkolleg 2229 "Asymptotic Invariants and Limits of Groups and Spaces"
DFG SFB/TRR 191 "Symplectic Structures in Geometry, Algebra and Dynamics"
DFG Schwerpunktprogramm "Geometry at Infinity" (SPP 2026)
DFG Research Project Rigidity, deformations and limits of maximal representations
Research Network GEometric structures And Representation varieties (GEAR)

Exploratory Project Math and Data
Hyperbolic Geometry and Data Science

Former ERC-Consolidator Grant Deformation Spaces of Geometric Structures
Former DFG Research Project Higher Teichmüller theory
Former interdisciplinary seminar series Structures and Mathematics

Current Teaching

Lecture courses and seminars

Short CV

since 2020 Scientific Director Research Station Geometry and Dynamics
since 2019 Co-Spokesperson Excellence Cluster STRUCTURES
since 2015 Group Leader Heidelberger Institut für Theoretische Studien HITS
since 2012 Professor, Mathematisches Institut, Ruprecht-Karls-Universität 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 Berlin-Brandenburg 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)

2012-2014 Sloan Research Fellowship, Sloan Foundation
2009-2013 Member, Junge Akademie der BBAW und der Leopoldina
2007-2012 Assistant Professor, Department of Mathematics, Princeton University
2007-2010 Director of Graduate Studies, Department of Mathematics, Princeton University
2009-2012 Visitor, School of Mathematics, Institute for Advanced Study, Princeton
2005-2007 Dickson Instructor, Department of Mathematics, University of Chicago
2005-2006 Member, School of Mathematics, Institute for Advanced Study, Princeton
2004-2005 Postdoc, Mathematisches Institut, Universität Basel
2004 PhD, Mathematisches Institut, Rheinische Friedrich Wilhelms-Universität 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 many-body dynamics via persistent homology, ( with D. Spitz, J. Berges, M. Oberthaler ), Preprint.
Conformality for a robust class of non-conformal 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), 588-692
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), 1--34.
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, 525--544.
Compactification of certain Clifford-Klein forms of reductive homogeneous spaces (with F.Gueritaud, O. Guichard, F. Kassel),Michigan Mathematical Journal, Volume 66 (2017), Issue 1, 49-84.
Anosov representations and proper actions (with F. Gueritaud , O. Guichard, F. Kassel), Geometry & Topology 21-1 (2017) 485--584.
Limits of geometries (with D. Cooper; J. Danciger), Transactions of the AMS 370 (2018), 6585--6627.
On weakly maximal representations of surface groups (with G. Ben Simon ; M. Burger; T. Hartnick; A. Iozzi), Journal of Differential Geometry 105 (2017) 375--404.
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 357-438.
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 578--642.
Domains of discontinuity for surface groups, (with O. Guichard),
C. R. Math. Acad. Sci. Paris I 347 (2009), 1057--1060.
Surface group representations with maximal Toledo invariant , (with M. Burger; A. Iozzi),
Annals of Mathematics 172 (2010), no.1, 517--566.
Tight homomorphisms and Hermitian symmetric spaces, (with M. Burger; A. Iozzi),
GAFA 19 (2009), no. 3, 678--721.
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, 381--445.
Hermitian symmetric spaces and Kähler rigidity, (with M. Burger; A. Iozzi),
Transformation Groups 12 (2007), no. 1, 5--32. electronic article .
The action of the mapping class group on maximal representations,
Geom. Dedicata 120 (2006), 179--191, 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), 555--601.
Surface group representations with maximal Toledo invariant (with M. Burger; A. Iozzi),
C. R. Math. Acad. Sci. Paris 336 (2003), no. 5, 387--390.
Bounded cohomology and geometry,
PhD-thesis, 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), 103--123.
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, 38--39, L'Enseignement Mathematique 54 (2008), 3-189.
Foliated projective structures and the Hitchin component of PSL(4,R),
Oberwolfach Reports, 32 (2007), 38--41.
Surface Groups and Hermitian Symmetric Spaces,
Oberwolfach Reports, 26 (2006), 1546--1548.
Flexibilität und Starrheit -- Gruppenhomomorphismen und geometrische Strukturen,
Mitteilungen der Deutschen Mathematiker Vereinigung, 13 (2005) no. 2, 80--83.

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 Heidelberg-Karlsruhe-Strasbourg 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 F-theory, Heidelberg, 24.-27.02.3014.
New Trends in Teichmüller Theory and Mapping Class Groups, Feb 9 - 15, 2014, Oberwolfach.
Fourth Heidelberg-Karlsruhe-Strasbourg Geoemtry Day, Heidelberg, 24.01.2014.
First Heidelberg-Karlsruhe-Strasbourg Geometry Day, Heidelberg 18.01.2013.
Mathematics and Physics of Moduli Spaces, Heidelberg, September 24-28, 2012.
GEAR Network Retreat, Urbana-Champaign, 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 Non-Lattices, 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 Garcia-Prada, 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 13--19, 2005.
Workshop on h-principles 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)6221-54 14206
Fax:	+49-(0)6221-54 14245

email

Office:
Room 3/309, Mathematikon, INF 205

Office hours:
by appointment

Secretariat:
Ms. Evelyne Bachmann
Room 3/412, INF 205
Tel: +49-6221-54-14237
sekr-wienhard@mathi.uni-heidelberg.de