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| 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 (C2-Oberassistent), 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 | | Since 2019 | Spokesperson, Hausdorff Center for Mathematics (HCM), Bonn |
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One of my main project has been and will be the Farrell-Jones Conjecture for algebraic K-theory and L-theory. I made substantial contributions to its proof for hyperbolic, CAT(0), S-arithmetic 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 K-groups 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 finite-dimensional analogues and given applications to group theory. A current and ongoing project is to link invariants from low-dimensional topology such as the Thurston norm and the Thurston polytope to generalized -torsion invariants.
The Farrell-Jones 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 p-adic 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 Baum-Connes Conjecture for Frechet algebras and prove it for case for which the Baum-Connes 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 Farrell-Jones Conjecture for Waldhausen's A-theory 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, Bergeron-Venkatesh, and Singer which we want to attack. The proposed methods are either algebraic or analytic. The project about low-dimensional 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 finite-dimensional 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.
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DFG Collaborative Research Center SFB 478 “Geometric structures in mathematics” in Münster
One of the two vice-speakers, 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 “K-theory, -invariants, manifolds, groups and their interactions”
DFG Cluster of Excellence “Hausdorff Center for Mathematics”
Principal Investigator
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[ 1] Wolfgang Lück, Holger Reich, John Rognes, Marco Varisco
Algebraic K-theory of group rings and the cyclotomic trace map
Adv. Math. , 304: : 930--1020
2017
DOI: 10.1016/j.aim.2016.09.004[ 2] Holger Kammeyer, Wolfgang Lück, Henrik Rüping
The Farrell-Jones conjecture for arbitrary lattices in virtually connected Lie groups
Geom. Topol. , 20: (3): 1275--1287
2016
DOI: 10.2140/gt.2016.20.1275[ 3] Arthur Bartels, Wolfgang Lück, Holger Reich, Henrik Rüping
K- and L-theory of group rings over {GL_n(\bf Z)}
Publications mathématiques de l'IHÉS , 119: : 97--125
2014
DOI: 10.1007/s10240-013-0055-0[ 4] A. Bartels, F. T. Farrell, W. Lück
The Farrell-Jones conjecture for cocompact lattices in virtually connected Lie groups
J. Amer. Math. Soc. , 27: (2): 339--388
2014
DOI: 10.1090/S0894-0347-2014-00782-7[ 5] W. Lück
Approximating L2-invariants and homology growth
Geom. Funct. Anal. , 23: (2): 622--663
2013
DOI: 10.1007/s00039-013-0218-7[ 6] Arthur Bartels, Wolfgang Lück
The Borel conjecture for hyperbolic and $CAT(0)$-groups
Ann. of Math. (2) , 175: (2): 631--689
2012
DOI: 10.4007/annals.2012.175.2.5[ 7] Arthur Bartels, Wolfgang Lück, Holger Reich
The K-theoretic Farrell-Jones conjecture for hyperbolic groups
Invent. Math. , 172: (1): 29--70
2008
DOI: 10.1007/s00222-007-0093-7[ 8] Wolfgang Lück
The relation between the Baum-Connes conjecture and the trace conjecture
Invent. Math. , 149: (1): 123--152
2002
DOI: 10.1007/s002220200215[ 9] John Lott, Wolfgang Lück
L2-topological invariants of 3-manifolds
Invent. Math. , 120: (1): 15--60
1995
DOI: 10.1007/BF01241121[ 10] W. Lück
Approximating L2-invariants by their finite-dimensional analogues
Geom. Funct. Anal. , 4: (4): 455--481
1994
DOI: 10.1007/BF01896404 |
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• Journal Mathematische Annalen, Springer (1997 - 2008)
• Proceedings “Tel Aviv Topology Conference: Rothenberg Festschrift”, Contemp. Mathematics 231 (1999)
• Proceedings of the School / Conference “High-dimensional 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)
• K-Theory (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)
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| 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 Rhine-Westphalian Academy of Sciences, Humanities and the Arts | | 2015 | ERC Advanced Investigator Grant for his project “K-theory, $L^2$-invariants, manifolds, groups and their interactions” |
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| 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 | | 2018 | Inaugural Colloquium of the Thematic program \"L2-invariants and their analogues in positive characteristic\", Madrid | | 2019 | Distinguished Lecture series at Indiana University, Bloomington, U.S.A | | 2019 | Distinguished Lecture series at University of Notre Dame, Notre Dame, U.S.A. |
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| 2001 | University of Bonn | | 2003 | ETH Zürich, Switzerland | | 2009 | University of Göttingen | | 2010 | University of Bonn |
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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
Danile Kaspwrowski (2020), now at University of Bonn
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Thomas Schick (1996): “Analysis on manifolds of bounded geometry, Hodge-deRham isomorphism and L²-index 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 L²-Betti numbers and Novikov-Shubin invariants under orbit equivalence and quasi-isometry”,
now Professor (W3), Karlsruhe Institute of Technology
Marco Varisco (2006): “Algebraic L-theory and triangular Witt groups”,
now Associate Professor, University at Albany, NY, USA
Clara Löh (2007): “L²-invariants, 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 Farrell-Jones 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 L-theory of complex  -algebras”,
now postdoc in Copenhagen
Florian Funke (2018): “The L^2-Torsion Polytope of Groups and the Integral Polytope Groups”, now postdoc in Dresden
Julia Semikina (2018): “G-theory for finite groups”, now postdoc at Bonn
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- Master theses: 18, currently 1
- Diplom theses: 30
- PhD theses: 25, currently 2
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