For my research and publications please see my private homepage https://romansauer.net/.
Prof. Dr. Roman Sauer
- Head of RG Topology and geometric group theory
- Office Hours: nach Vereinbarung
- Room:
20.30 - Phone: +49 721 608-46325
- Fax: +49 721 608-42148
- roman sauer ∂does-not-exist.kit edu
- topology.math.kit.edu/english/index.php
- Englerstr. 2
76131 Karlsruhe
Publications
Book projects
- L2-Invariants – n years after (working title)
joint with Wolfgang Lück and Thomas Schick
[link]
- Metric topology of aspherical manifolds (MFO seminar series)
joint with Clara Löh
[link]
Preprints
- The cheap embedding principle: Dynamical upper bounds for homology growth
joint with Kevin Li, Clara Löh, Marco Moraschini and Matthias Uschold
[arXiv:2508.01347]
- The algebraic cheap rebuilding property
joint with Kevin Li, Clara Löh, Marco Moraschini and Matthias Uschold
[arXiv:2409.05774]
- Uniform waist inequalities in codimension two for manifolds with Kazhdan fundamental group
joint with Uri Bader
[arXiv:2407.19783]
- On homological properties of the Schlichting completion
joint with Laura Bonn
[arXiv:2406.12740]
- Higher Kazhdan property and unitary cohomology of arithmetic groups
joint with Uri Bader
[arXiv:2308.06517]
Research articles
- On homological properties of the Schlichting completion
joint with Laura Bonn
Mathematical Proceedings of the Cambridge Philosophical Society. Published online 2025:1-12. doi:10.1017/S0305004125101357
[Journal] [arXiv:2406.12740"] [MR4474178]
- Stability and instability of lattices in semisimple groups
joint with Uri Bader and Alex Lubotzky and Shmuel Weinberger
J. Anal. Math. 151 (2023), 1-23.
[Journal] [arXiv:2303.08943] [MR4474178]
- Amenable covers and integral foliated simplicial volume
joint with Clara Löh and Marco Moraschini
New York J. Math. 28 (2022), 1112–1136.
[Journal] [arXiv:2112.12223] [Journal] [arXiv:2012.08999] [MR4386411]
- Bounded cohomology of amenable covers via classifying spaces
joint with Clara Löh
Enseign. Math. 66 (2020), no. 1-2, 151–172.
[Journal] [arXiv:1910.11716] [MR4162286]
- Profinite invariants of arithmetic groups
joint with Holger Kammeyer, Steffen Kionke and Jean Raimbault
Forum Math. Sigma 8 (2020), Paper No. e54.
[Journal] [arXiv:1901.01227] [MR4176758]
- S-arithmetic spinor groups with the same finite quotients and distinct l²-cohomology
joint with Holger Kammeyer
Groups Geom. Dyn. 14 (2020), no. 3, 857–869.
[Journal] [arXiv:1804.10604] [MR4167024]
- Homology and homotopy complexity in negative curvature
joint with Uri Bader and Tsachik Gelander
J. Eur. Math. Soc. (JEMS) 22 (2020), no. 8, 2537–2571.
[Journal] [arXiv:1612.04871] [MR4118615]
- Lattice Envelopes
joint with Uri Bader and Alex Furman
Duke Math. J. 169 (2020), no. 2, 213–278.
[Journal] [arXiv:1711.08410] [MR4057144]
- Counting maximally broken Morse trajectories on aspherical manifolds
joint with Caterina Campagnolo
Geom. Dedicata 202 (2019), 387–399.
[Journal] [arXiv:1808.08737] [MR4001823]
- An adelic arithmeticity theorem for lattices in products
joint with Uri Bader and Alex Furman
Math. Z. 293 (2019), no. 3-4, 1181–1199.
[Journal] [arXiv:1705.08158] [MR4024582]
- Vanishing of l²-Betti numbers of locally compact groups as an invariant of coarse equivalence
joint with Michael Schrödl
Fund. Math. 243 (2018), no. 3, 301–311.
[arXiv:1702.01685] [Journal] [MR3863061]
- l²-Betti numbers of totally disconnected groups and their approximation by Betti numbers of lattices
joint with Henrik D. Petersen and Andreas Thom
J. Topol. 11 (2018), no. 1, 257–282.
[arXiv:1612.04559] [Journal] [MR3784232]
- Cantor systems and quasi-isometry of groups
joint with Kostya Medynets and Andreas Thom
Bulletin of the LMS 49 (2017), no. 4, 709–724.
[arXiv:1508.07578] [Journal] [MR3725491]
- Topological models of finite type for tree almost automorphism groups
joint with Werner Thumann
Int. Math. Res. Not. IMRN 2017, no. 23, 7292–7320.
[arXiv: 1510.05554] [Journal] [MR3801421]
- Integral foliated simplicial volume of aspherical manifolds
joint with Roberto Frigerio and Clara Löh and Cristina Pagliantini
Israel J. Math. 216 (2016), no. 2, 707–751.
[arXiv:1506.05567] [Journal] [MR3557463]
- Volume and homology growth of aspherical manifolds
Geom. Topol. 20 (2016), 1035-1059.
[arXiv: 1403.7319] [Journal] [MR3493098]
- On the structure and arithmeticity of lattice envelopes
joint with Uri Bader and Alex Furman
C. R. Math. Acad. Sci. Paris 353 (2015), no. 5, 409–413.
[arXiv:1411.7332] [Journal] [MR3334993]
- L²-invisibility and a class of local similarity groups
joint with Werner Thumann
Compositio Math.150 (2014), no. 10, 1742-1754
[arXiv:1304.6843] [Journal] [MR3269466]
- On the growth of Betti numbers in p-adic analytic towers
joint with Nicolas Bergeron and Peter Linnell and Wolfgang Lück
Groups Geom. Dyn. 8 (2014), no. 2, 311–329.
[arXiv:1204.3298] [Journal] [MR3231217]
- Weak notions of normality and vanishing up to rank in L²-cohomology
joint with Uri Bader and Alex Furman
Int. Math. Res. Not. IMRN 2014, no. 12, 3177–3189.
[arXiv:1206.4793] [Journal] [MR3217658]
- On the cohomology of weakly almost periodic group representations
joint with Uri Bader and Christian Rosendal
Journal of Topology and Analysis 6 (2014), no. 2, 153-165.
[arXiv:1302.1392] [Journal] [MR3191647]
- Integrable measure equivalence and rigidity of hyperbolic lattices
joint with Uri Bader and Alex Furman
Inventiones Math. 194 (2013), No. 2, 313–379.
[arXiv:1006.5193] [Journal] [MR3117525]
- Efficient subdivision in hyperbolic groups and applications
joint with Uri Bader and Alex Furman
Groups, Geometry, and Dynamics 7 (2013), 263-292.
[arXiv:1003.1562] [Journal] [MR3054570]
- Euler characteristics of categories and homotopy colimits
joint with Tom Fiore and Wolfgang Lück
Documenta Math. 16 (2011), 301-354.
[arXiv:1007.3868] [Journal] [MR2804514]
- Spectral distribution and L²-isoperimetric profile of Laplace operators on groups
joint with Alexander Bendikov and Christophe Pittet
Mathematische Annalen 354 (2012), 43-72.
[arXiv:0901.0271] [Journal] [MR2957618]
- Finiteness obstructions and Euler characteristics of categories
joint with Tom Fiore and Wolfgang Lück
Advances in Mathematics 226 (2011), no. 3, 2371–2469.
[arXiv:0908.3417] [Journal] [MR2739781]
- The limit of F_p-Betti numbers of a tower of finite covers with amenable fundamental groups
joint with Peter Linnell and Wolfgang Lück
Proc. Amer. Math. Soc. 139 (2011), 421-434.
[arXiv:1003.0434] [Journal] [MR2736326]
- L²-torsion, the measure-theoretic determinant conjecture, and uniform measure equivalence
joint with Wolfgang Lück and Christian Wegner
Journal of Topology and Analysis 2 (2010), no. 2, 145-171.
[arXiv:0903.2925] [Journal] [MR2652905]
- A spectral sequence to compute L²-Betti numbers of groups and groupoids
joint with Andreas Thom
Journal of the London Mathematical Society 81 (2010), no. 3, 747-773.
[arXiv:0707.0906] [Journal] [MR2650795]
- Degree theorems and Lipschitz simplicial volume for non-positively curved manifolds of finite volume
joint with Clara Löh
Journal of Topology 2 (2009), no. 1, 193-225.
[arXiv:0710.1635] [Journal] [MR2499443]
- Simplicial Volume of Hilbert modular varieties
joint with Clara Löh
Commentarii Mathematici Helvetici 84 (2009), no. 3, 457-470.
[arXiv:0706.3904] [Journal] [MR2507250]
- Amenable covers, volume and L²-Betti numbers of aspherical manifolds
J. Reine Angew. Math (Crelle's Journal) 636 (2009), 47-92.
[math.AT/0605627] [Journal] [MR2572246]
- Homological invariants and quasi-isometry
Geom. Funct. Anal. (GAFA) 16 (2006), no. 2, 476–515.
[math.AT/0312129] [Journal] [MR2231471]
- L²-Betti numbers of discrete measured groupoids
Internat. J. Algebra Comput. 15 (2005), no. 5-6, 1169–1188.
[math.AT/0312411] [Journal] [MR2197826]
- Power series over the group ring of a free group and applications to Novikov-Shubin invariants
Proceedings of the School High-Dimensional Manifold Topology, Trieste, 2003.
[pdf] [MR2048733]
Expository articles
- l²-Betti numbers of discrete and non-discrete groups
in: London Mathematical Society Lecture Note Series 447, Cambridge University Press 2018
[arXiv:1509.05234] [Journal] [MR3793289]
- Homotopy invariance of almost flat Betti numbers
joint with Thomas Schick
Enseign. Math. (2) 54 (2008), no. 1-2 (Guido's book of conjectures).
[pdf] [MR2454697]
- Volume and L²-Betti numbers of aspherical manifolds
Proceedings of the Courant Colloquium Göttingen 2007 (ISBN 3-978-3-940344-56-4).
[Online edition] [pdf] [MR2906042]
Miscellaneous
- The asymptotic growth of twisted torsion
joint with Nicolas Bergeron and Wolfgang Lück
[pdf]
Conferences
-
Thematic Semester on Analytic Group Theory
July 1 - December 18, 2026, Lodha Mathematical Sciences Institute, Mumbai
Other organizers:
Indira Chatterji, Srivatsav Kunnawalkam Elayavalli, David Fisher, Mikolaj Fraczyk, Mehrdad Kalantar, Nicolas Monod
-
The ergodic method in group theory
May 26 - May 30, 2025, Northwestern University, Chicago
Other organizers:
Nir Avni, Uri Bader, Tsachik Gelander
-
Arithmetic (and Non-Arithmetic) Groups – Algebraic, Geometric and Analytic Aspects
July 13 - July 17, 2026, Brin Mathematics Research Center, Maryland
Other organizers:
Uri Bader
-
Oberwolfach Seminar: Metric Topology of Aspherical Spaces
October 20 - 25, 2024, MFO
Weitere Organisatoren:
Clara Löh (Regensburg)
Roman Sauer (Karlsruhe)
-
Conference on "Homology growth in topology and group theory"
May 13 - 17, 2024, MPI f. Mathematik, Bonn
Other organizers:
Grigori Avramidi (MPIM Bonn)
Dawid Kielak (University of Oxford)
Roman Sauer (KIT)
-
Workshop: Geometry, Topology and Computation
Workshop
June 12th - 14th, 2019
Universität Heidelberg
Other organizers: Peter Albers, Anna Wienhard
-
Workshop: Riemannian and Simplicial Volume
Workshop
April 8th - 11th, 2019
Karlsruher Institut für Technologie
Other organizers: Caterina Campagnolo, Clara Löh
-
Heidelberg-Karlsruhe-Strasbourg Geometry Day XII
Workshop
November 30th, 2018
Universität Heidelberg
Other organizers: Olivier Guichard, Enrico Leuzinger, Anna Wienhard
-
Heidelberg-Karlsruhe-Strasbourg Geometry Day XI
Workshop
June 22nd, 2018
Karlsruher Institut für Technologie
Other organizers: Olivier Guichard, Enrico Leuzinger, Anna Wienhard
-
Heidelberg-Karlsruhe-Strasbourg Geometry Day VIII
Workshop
December 1st, 2017
University Heidelberg
Other organizers: Olivier Guichard, Enrico Leuzinger, Anna Wienhard
-
Growth in Geometry and Topology
Summer School
August 21st - 25th, 2017
Les Diablerets
Other organizers: Vincent Emery, Ruth Kellerhals, Stefan Wenger
-
Asymptotic geometry of groups and spaces
Conference
February 20th - 23rd, 2017
University Heidelberg
Other organizers: Daniele Alessandrini, Beatrice Pozzetti, Petra Schwer, Anna Wienhard
-
Heidelberg-Karlsruhe-Strasbourg Geometry Day VII
Workshop
April 22nd, 2016
University Strasbourg
Other organizers: Olivier Guichard, Enrico Leuzinger, Anna Wienhard
-
Heidelberg-Karlsruhe-Strasbourg Geometry Day VI
Workshop
Oktober 30th, 2015
University Heidelberg
Other organizers: Olivier Guichard, Enrico Leuzinger, Anna Wienhard
-
Topology Retreat
Retreat
September 29th - October 3rd, 2015
Będlewo, Poland
Other organizers: Piotr Nowak
-
Heidelberg-Karlsruhe-Strasbourg Geometry Day V
Workshop
June 6th, 2014
Karlsruhe Institute of Technology
Other organizers: Olivier Guichard, Enrico Leuzinger, Anna Wienhard
-
Heidelberg-Karlsruhe-Strasbourg Geometry Day IV
Workshop
January 24th, 2014
University Heidelberg
Other organizers: Olivier Guichard, Enrico Leuzinger, Anna Wienhard
-
Heidelberg-Karlsruhe-Strasbourg Geometry Day III
Workshop
October 18th, 2013
Université de Strasbourg
Other organizers: Olivier Guichard, Enrico Leuzinger, Anna Wienhard
-
GGT-Conference 2013
Conference
October 7th - 11th, 2013
Karlsruhe Institute of Technology
[poster]
Other organizers: Wilderich Tuschmann, Gabriela Weitze-Schmithüsen
-
Heidelberg-Karlsruhe-Strasbourg Geometry Day II
Workshop
May 24th, 2013
Karlsruhe Institute of Technology
Other organizers: Olivier Guichard, Enrico Leuzinger, Anna Wienhard
-
Heidelberg-Karlsruhe-Strasbourg Geometry Day I
Workshop
Januar 18th, 2013
University of Heidelberg
Other organizers: Olivier Guichard, Enrico Leuzinger, Anna Wienhard
-
"Action-now" - Group Actions, their Dynamics and Geometry
Workshop
October 11th - 12th, 2012
University of Berlin
[poster]
Other organizers: Tsachik Gelander, Holger Reich
-
Research Seminar on geometric group theory
Research Seminar
September 24th - 27th, 2012
University of Münster
Other organizers: Petra Schwer
-
Flows on homogeneous spaces
Minerva Summer School
September 2nd - 7th, 2012
Technion in Haifa/Israel
Other organizers: Uri Bader, Francoise Dal'Bo
-
New Horizons for Simplicial Volume and The Barycenter Method
AIM Square Program
August 6th - 10th, 2012
American Institute of Mathematics, Palo Alto
Other organizers: Michelle Bucher, Chris Connell, Jean Lafont, Ben Schmidt
-
Geometry and Rigidity of Groups
Summer School
August 24th - 28th, 2009
University of Münster
Other organizers: Arthur Bartels, Wolfgang Lück
-
L²-Invariants, Measure Theory and Geometric Group Theory
Workshop
March 8th - 12th, 2004
University of Münster
[Booklet]
Other organizers: Damien Gaboriau, Wolfgang Lück, Andrzej Zuk