Publications

Book projects

• $ℓ^2$-Invariants - n years after (working title)
  Wolfgang Lück, Roman Sauer, Thomas Schick, 2030 [link].

• Metric topology of aspherical manifolds (MFO seminar series)
  Clara Löh, Roman Sauer, 2025 [link].

Preprints

• Higher Brin–Thompson groups are Kazhdan
  Roman Sauer, Eduard Schesler – with an appendix by Francesco Fournier Facio
  arxiv:2610.09524, 2026. [arXiv]
  For the messy history behind the search for non-hyperlinear groups, of which Brin-Thompson groups are arguably the first naturally occurring examples, we recommend Francesco Fournier-Facio’s account.

• Fixed point properties and cohomology of Banach representations of arithmetic groups
  Saar Bader, Shaked Bader, Uri Bader, Roman Sauer
  arxiv:2609.24951, 2026. [arXiv]
  This unusual collaboration was featured in this podcast. Talks by my coauthor Uri Bader on that work: IHES and INI Cambridge.

• On the unitary cohomology of semisimple groups
  Uri Bader, Michael Glasner, Yuval Gorfine, Roman Sauer
  arxiv:2609.08652, 2026. [arXiv]

• Polynomial homological Dehn functions from non-proper actions
  Roman Sauer, Jannis Weis
  arxiv:2606.25897, 2026. [arXiv]

• Non-uniform exponential growth and the decay of growth rates in growing dimensions
  Roman Sauer, Eduard Schesler
  arxiv:2605.30163, 2026. [arXiv]
  This preprint merges, extends and supersedes arXiv:2605.30163v1 and arXiv:2606.15945v1.

• Kazhdan groups of dimension $16$ with prescribed second $\ell^2$-Betti number
  Francesco Fournier-Facio, Roman Sauer
  arxiv:2601.00074, 2025. [arXiv]
  Here is a talk on that paper at the University of Krakow from 2026: YouTube.

• Higher property T and below-rank phenomena of lattices
  Uri Bader, Roman Sauer
  arxiv:2511.20192, 2025. [arXiv]
  This survey is a (very extended) version of Uri’s abstract for the ICM 2026. Here is the video of Uri’s ICM talk: YouTube.

• The cheap embedding principle: Dynamical upper bounds for homology growth
  Kevin Li, Clara Löh, Marco Moraschini, Roman Sauer, Matthias Uschold
  arxiv:2508.01347, 2025. [arXiv]
  Here is a talk by my coauthor Clara Löh on that paper at the ESI in Vienna: YouTube.

• Higher Kazhdan property and unitary cohomology of arithmetic groups
  Uri Bader, Roman Sauer
  arxiv:2308.06517, 2023. [arXiv]
  My course at the IHES Summer School: Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5.

Published

• Uniform waist inequalities in codimension two for manifolds with Kazhdan fundamental group
  Uri Bader, Roman Sauer
  Geom. Funct. Anal. (GAFA), 2026. [Journal] [arXiv] [MathSciNet] [zbMATH]
  Here is a talk by Misha Gromov about waist inequalities from 2025 that briefly discusses this paper: YouTube.

• The algebraic cheap rebuilding property
  Kevin Li, Clara Löh, Marco Moraschini, Roman Sauer, Matthias Uschold
  Transactions of the American Mathematical Society, 2025. [Journal] [arXiv] [MathSciNet] [zbMATH]

• On homological properties of the Schlichting completion
  Laura Bonn, Roman Sauer
  Mathematical Proceedings of the Cambridge Philosophical Society, 2025. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Stability and instability of lattices in semisimple groups
  Uri Bader, Alexander Lubotzky, Roman Sauer, Shmuel Weinberger
  J. Anal. Math., 2023. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Amenable covers and integral foliated simplicial volume
  Clara Löh, Marco Moraschini, Roman Sauer
  New York J. Math., 2022. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Volume and macroscopic scalar curvature
  Sabine Braun, Roman Sauer
  Geom. Funct. Anal. (GAFA), 2021. [Journal] [arXiv] [MathSciNet] [zbMATH]
  Here is a talk about that paper at the Hausdorff Institute in Bonn: YouTube.

• Profinite invariants of arithmetic groups
  Holger Kammeyer, Steffen Kionke, Jean Raimbault, Roman Sauer
  Forum Math. Sigma, 2020. [Journal] [arXiv] [MathSciNet] [zbMATH]

• S-arithmetic spinor groups with the same finite quotients and distinct $ℓ^2$-cohomology
  Holger Kammeyer, Roman Sauer
  Groups Geom. Dyn., 2020. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Bounded cohomology of amenable covers via classifying spaces
  Clara Löh, Roman Sauer
  Enseign. Math., 2020. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Homology and homotopy complexity in negative curvature
  Uri Bader, Tsachik Gelander, Roman Sauer
  J. Eur. Math. Soc. (JEMS), 2020. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Lattice envelopes
  Uri Bader, Alex Furman, Roman Sauer
  Duke Math. J., 2020. [Journal] [arXiv] [MathSciNet] [zbMATH]

• An adelic arithmeticity theorem for lattices in products
  Uri Bader, Alex Furman, Roman Sauer
  Math. Z., 2019. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Counting maximally broken Morse trajectories on aspherical manifolds
  Caterina Campagnolo, Roman Sauer
  Geom. Dedicata, 2019. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Vanishing of $ℓ^2$-Betti numbers of locally compact groups as an invariant of coarse equivalence
  Roman Sauer, Michael Schrödl
  Fund. Math., 2018. [Journal] [arXiv] [MathSciNet] [zbMATH]

• $ℓ^2$-Betti number of discrete and non-discrete groups
  Roman Sauer
  London Math. Soc. Lecture Note Ser., 447 (Book chapter), 2018. [Journal] [arXiv] [MathSciNet] [zbMATH]

• $ℓ^2$-Betti numbers of totally disconnected groups and their approximation by Betti numbers of lattices
  Henrik Densing Petersen, Roman Sauer, Andreas Thom
  J. Topol., 2018. [Journal] [arXiv] [MathSciNet] [zbMATH]
  Here is a talk on that paper from 2017 at the Newton Institute in Cambridge: YouTube.

• Topological models of finite type for tree almost automorphism groups
  Roman Sauer, Werner Thumann
  Int. Math. Res. Not. IMRN, 2017. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Cantor systems and quasi-isometry of groups
  Kostya Medynets, Roman Sauer, Andreas Thom
  Bull. Lond. Math. Soc., 2017. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Integral foliated simplicial volume of aspherical manifolds
  Roberto Frigerio, Clara Löh, Cristina Pagliantini, Roman Sauer
  Israel J. Math., 2016. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Volume and homology growth of aspherical manifolds
  Roman Sauer
  Geom. Topol., 2016. [Journal] [arXiv] [MathSciNet] [zbMATH]

• On the structure and arithmeticity of lattice envelopes
  Uri Bader, Alex Furman, Roman Sauer
  C. R. Math. Acad. Sci. Paris, 2015. [Journal] [arXiv] [MathSciNet] [zbMATH]

• $ℓ^2$-invisibility and a class of local similarity groups
  Roman Sauer, Werner Thumann
  Compos. Math., 2014. [Journal] [arXiv] [MathSciNet] [zbMATH]

• On the growth of Betti numbers in p-adic analytic towers
  Nicolas Bergeron, Peter Linnell, Wolfgang Lück, Roman Sauer
  Groups Geom. Dyn., 2014. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Weak notions of normality and vanishing up to rank in $ℓ^2$-cohomology
  Uri Bader, Alex Furman, Roman Sauer
  Int. Math. Res. Not. IMRN, 2014. [Journal] [arXiv] [MathSciNet] [zbMATH]

• On the cohomology of weakly almost periodic group representations
  Uri Bader, Christian Rosendal, Roman Sauer
  J. Topol. Anal., 2014. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Integrable measure equivalence and rigidity of hyperbolic lattices
  Uri Bader, Alex Furman, Roman Sauer
  Invent. Math., 2013. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Efficient subdivision in hyperbolic groups and applications
  Uri Bader, Alex Furman, Roman Sauer
  Groups Geom. Dyn., 2013. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Spectral distribution and $ℓ^2$-isoperimetric profile of Laplace operators on groups
  Alexander Bendikov, Christophe Pittet, Roman Sauer
  Math. Ann., 2012. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Euler characteristics of categories and homotopy colimits
  Fiore, Thomas M., Wolfgang Lück, Roman Sauer
  Doc. Math., 2011. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Finiteness obstructions and Euler characteristics of categories
  Thomas M. Fiore, Wolfgang Lück, Roman Sauer
  Adv. Math., 2011. [Journal] [arXiv] [MathSciNet] [zbMATH]

• The limit of F_p-Betti numbers of a tower of finite covers with amenable fundamental groups
  Peter Linnell, Wolfgang Lück, Roman Sauer
  Proc. Amer. Math. Soc., 2011. [Journal] [arXiv] [MathSciNet] [zbMATH]

• ℓ²-torsion, the measure-theoretic determinant conjecture, and uniform measure equivalence
  Wolfgang Lück, Roman Sauer, Christian Wegner
  J. Topol. Anal., 2010. [Journal] [arXiv] [MathSciNet] [zbMATH]

• A spectral sequence to compute $ℓ^2$-Betti numbers of groups and groupoids
  Roman Sauer, Andreas Thom
  J. Lond. Math. Soc. (2), 2010. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Amenable covers, volume and $ℓ^2$-Betti numbers of aspherical manifolds
  Roman Sauer
  J. Reine Angew. Math., 2009. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Simplicial volume of Hilbert modular varieties
  Clara Löh, Roman Sauer
  Comment. Math. Helv., 2009. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Degree theorems and Lipschitz simplicial volume for nonpositively curved manifolds of finite volume
  Clara Löh, Roman Sauer
  J. Topol., 2009. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Volume and $ℓ^2$-Betti numbers of aspherical manifolds
  Roman Sauer
  Trends in mathematics. Proceedings of the Courant Colloquium, University of Göttingen, 2008. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Homological invariants and quasi-isometry
  Roman Sauer
  Geom. Funct. Anal. (GAFA), 2006. [Journal] [arXiv] [MathSciNet] [zbMATH]
  Lecture 2 of a two-part minicourse at the ENS Pisa is available on YouTube, starting at 3:39:37. Lecture 1 was not recorded.

• $ℓ^2$-Betti numbers of discrete measured groupoids
  Roman Sauer
  Internat. J. Algebra Comput., 2005. [Journal] [arXiv] [MathSciNet] [zbMATH]

• Power series over the group ring of a free group and applications to Novikov-Shubin invariants
  Roman Sauer
  Proceedings of the School, ICTP, Trieste, on High-dimensional manifold topology, 2003. [Journal] [arXiv] [MathSciNet] [zbMATH]