

1981  Diploma  1982  1985  Research Assistant, Mathematical Institute, University of Göttingen  1984  Dr. rer. nat., University of Göttingen  1985  1989  Assistant Professor, Mathematical Institute, University of Göttingen  1989  Habilitation, Department of Mathematics , University of Göttingen  1989  1990  Assistant Professor (C2Oberassistent), Department of Mathematics, University of Göttingen  1990  1991  Associate Professor (with tenure), University of Kentucky, Lexington, KY, USA  1991  1996  Professor (C3), University of Mainz  1996  2010  Professor (C4/W3), University of Münster  2011  2017  Director, Hausdorff Research Institute for Mathematics (HIM), Bonn  Since 2010  Professor (W3), University of Bonn 


One of my main project has been and will be the FarrellJones Conjecture for algebraic Ktheory and Ltheory. I made substantial contributions to its proof for hyperbolic, CAT(0), Sarithmetic groups, lattices in almost connected Lie groups, and fundamental groups of manifolds of dimension less or equal to three and to the proof of inheritance properties like passage to subgroups or directed colimits. The importance of this conjecture is illustrated by the facts that it implies other prominent conjectures such as the ones due to Bass, Borel and Novikov and has many significant applications to problems in topology, geometry, and group theory. We have also used the cycloctomic trace for topological cyclic homology to compute algebraic Kgroups of integral group rings. The second key topic of my research are invariants. These are invariants defined in terms of the heat kernel or the simplicial chain complex of the universal covering of a closed Riemannian manifold using the theory of von Neumann algebras. They generalize classical invariants such as Betti numbers and Reidemeister torsion. I have analyzed questions about approximating invariants by their finitedimensional analogues and given applications to group theory. A current and ongoing project is to link invariants from lowdimensional topology such as the Thurston norm and the Thurston polytope to generalized torsion invariants.
The FarrellJones Conjecture has only been formulated and investigated for discrete groups so far. We want to establish a version for totally disconnected groups and their Hecke algebras. The ultimate goal is to prove it for reductive padic groups. This would open a door to get new information about the representation theory of such groups. We also want to establish a version of the BaumConnes Conjecture for Frechet algebras and prove it for case for which the BaumConnes Conjecture is still open, for instance for CAT(0)groups and lattices in almost connected Lie groups. All these activities are linked to the general problem to establish equivariant homotopy theory for proper actions of not necessarily finite or compact groups. This concerns both the general structure of the equivariant stable homotopy category and explicite computations based on finding good models for classifying spaces of families via geometry and the construction of equivariant Chern characters. The latest proof of the FarrellJones Conjecture for Waldhausen's Atheory for a large class of groups will be the basis of getting new information about the automorphism groups of closed aspherical manifolds. There are a variety of prominent open conjectures about invariants such as the ones due to Atiyah, BergeronVenkatesh, and Singer which we want to attack. The proposed methods are either algebraic or analytic. The project about lowdimensional manifolds and generalized notions of torsion has just been started and will lead to further interactions and results. In particular we would like to study torsion twisted with non necessarily unitary finitedimensional representations and investigate the function it will give on the representation variety of a given group. Moreover, we will analyze further what these invariants such as the torsion or the polytope say about group automorphisms.


DFG Collaborative Research Center SFB 478 “Geometric structures in mathematics” in Münster
One of the two vicespeakers, 1997  2009
DFG Research Training Group GRK 627 “Analytic Topology and Metageometry” in Münster
Speaker, 2000  2009
DFG Collaborative Research Center SFB 878 “Groups, Geometry, and Actions” in Münster
Coordinator, July 1, 2010  September 30, 2010
ERC Advanced Investigator Grant “Ktheory, invariants, manifolds, groups and their interactions”
“Hausdorff Research Institute for Mathematics”
Director
DFG Cluster of Excellence “Hausdorff Center for Mathematics”
Principal Investigator


Research Area A We mainly focus on invariants. These are invariants obtained from the spectrum of the Laplace operators on the universal covering of a closed Riemannian manifold, and often have geometric or topological interpretations. Examples are Betti numbers and torsion. We will work on the Atiyah Conjecture, and on approximation problems for invariants for towers of coverings.  Research Area C We will work on questions around the BaumConnes Conjecture. In particular we will develop tools for and carry out computation of the topological Ktheory of group algebras using this conjecture. These are not only interesting in their own right but have applications to classification of algebras, classifications of manifolds, and to the (unstable) GromovLawsonRosenberg Conjecture about closed Riemannian manifolds with positive scalar curvature.  Research Area F* The FarrellJones Conjecture predicts the algebraic K and Ltheory of group rings. It implies other prominent conjectures due to Borel (topological rigidity of aspherical manifolds), Kaplansky (idempotents in group rings) and Novikov (homotopy invariance of higher signatures). We will extend the class of groups for which the conjecture is known and work on its analogue for Waldhausen's Atheory and for pseudoisotopy. 


[ 1] Wolfgang Lück, Holger Reich, John Rognes, Marco Varisco
Algebraic Ktheory of group rings and the cyclotomic trace map Adv. Math. , 304: : 9301020 2017[ 2] Holger Kammeyer, Wolfgang Lück, Henrik Rüping
The FarrellJones conjecture for arbitrary lattices in virtually connected Lie groups Geom. Topol. , 20: (3): 12751287 2016[ 3] Arthur Bartels, Wolfgang Lück, Holger Reich, Henrik Rüping
K and Ltheory of group rings over {GL_n(\bf Z)} Publ. Math. Inst. Hautes Études Sci. , 119: : 97125 2014[ 4] A. Bartels, F. T. Farrell, W. Lück
The FarrellJones conjecture for cocompact lattices in virtually connected Lie groups J. Amer. Math. Soc. , 27: (2): 339388 2014[ 5] W. Lück
Approximating L^{2}invariants and homology growth Geom. Funct. Anal. , 23: (2): 622663 2013[ 6] Arthur Bartels, Wolfgang Lück
The Borel conjecture for hyperbolic and {CAT(0)}groups Ann. of Math. (2) , 175: (2): 631689 2012[ 7] Arthur Bartels, Wolfgang Lück, Holger Reich
The Ktheoretic FarrellJones conjecture for hyperbolic groups Invent. Math. , 172: (1): 2970 2008[ 8] Wolfgang Lück
The relation between the BaumConnes conjecture and the trace conjecture Invent. Math. , 149: (1): 123152 2002[ 9] John Lott, Wolfgang Lück
L^{2}topological invariants of 3manifolds Invent. Math. , 120: (1): 1560 1995[ 10] W. Lück
Approximating L^{2}invariants by their finitedimensional analogues Geom. Funct. Anal. , 4: (4): 455481 1994




• Journal Mathematische Annalen, Springer (1997  2008)
• Proceedings “Tel Aviv Topology Conference: Rothenberg Festschrift”, Contemp. Mathematics 231 (1999)
• Proceedings of the School / Conference “Highdimensional manifold theory”, Trieste (May and June 2001)
• Topology, Elsevier (2002  2006)
• Commentarii Mathematici Helvetici, European Mathematical Society Publishing House (2003  2008)
• Mathematische Annalen (Managing Editor, 2004  2008)
• Geometry and Topology (2005  2008)
• Groups, Geometry and Dynamics, European Mathematical Society Publishing House (2006  2012)
• KTheory (Interim Editor, August  December 2007)
• Münster Journal of Mathematics (2007  2012)
• Journal of Topology, LMS (2007  2012)
• Proceedings of Fourth Arolla Conference on Algebraic Topology (2012)


2003  Max Planck Research Award  2008  Leibniz Prize  2010  Member of the German National Academy of Sciences Leopoldina  2012  Fellow of the American Mathematical Society  2012  Max Planck Fellow  2013  Member of the North RhineWestphalian Academy of Sciences, Humanities and the Arts  2015  ERC Advanced Investigator Grant for his project “Ktheory, $L^2$invariants, manifolds, groups and their interactions” 


2006  25th anniversary of Max Planck Institute for Mathematics, Bonn  2008  5th European Congress of Mathematics, invited lecture, Amsterdam, Netherlands  2010  International Congress of Mathematicians, Topology section, Hyderabad, India  2012  Homological growth and $L^2$invariants, Hirzebruch Lecture, Münster  2013  Survey on $L^2$invariants, 20th anniversary of ESI, Erwin Schrödinger Institute, Vienna, Austria  2014  Heat kernels and their applications in geometry, topology and group theory, Bethe Kolloquium of Institute for Physics, Bonn 


2001  University of Bonn  2003  ETH Zürich, Switzerland  2009  University of Göttingen  2010  University of Bonn 


Thomas Schick (2000), now Professor, University of Göttingen
Michael Joachim (2003), now Professor (Apl), University of Münster
Arthur Bartels (2005), now Professor, University of Münster
Holger Reich (2005), now Professor, FU Berlin
Tilman Bauer (2008), now Professor, KTH Royal Institute of Technology, Stockholm, Sweden
Roman Sauer (2009), now Professor, Karlsruhe Institute of Technology


Thomas Schick (1996): “Analysis on manifolds of bounded geometry, HodgedeRham isomorphism and L²index theorem”,
now Professor (W3), University of Göttingen
Holger Reich (1999): “Group von Neumann algebras and related algebras”,
now Professor (W3), FU Berlin
Roman Sauer (2003): “Invariance properties of L²Betti numbers and NovikovShubin invariants under orbit equivalence and quasiisometry”,
now Professor (W3), Karlsruhe Institute of Technology
Marco Varisco (2006): “Algebraic Ltheory and triangular Witt groups”,
now Associate Professor, University at Albany, NY, USA
Clara Löh (2007): “L²invariants, simplical volume and measure theory”,
now Professor (W2), University of Regensburg
Wolfgang Steimle (2010): “Obstructions to Stably Fibering Manifolds”,
now Professor (W2), University of Augsburg
Henrik Rüping (2011): “The FarrellJones conjecture for some general linear groups”,
now Postdoc, University of Bonn
Philipp Kühl (2014): “The hotel of algebraic surgery”
Markus Land (2016): “On the relation between K and Ltheory of complex algebras”,
now Postdoc, University of Regensburg


 Master theses: 13, currently 3
 Diplom theses: 30
 PhD theses: 20, currently 7


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