Filippo Sarti - Research

In am interested in the dynamic of measure prerving actions of groups on measure spaces and on their (co)homological invariant. This is the main topic of Measured Group Theory, a field lying at the interline between dynamic, ergodic theory and geometric group theory. I recommend Furman's survey for a beatiful introduction to this topic.

My research interests include rigidity of measurable cocycles, measured groupoids and equivalence relations, boundaries and boundary maps, (continuous) bounded cohomology and simplicial volume, foliations with transverse measure, R-spaces, R-covers, R-simplicial complexes, measure and orbit equivalences.

Preprints

• Superrigidity for representations of transverse measured groupoids (with A. Savini), (2026), arXiv.
• Bounded cohomological induction for transverse measured groupoids (with T. Hartnick), (2025), arXiv.
• Simplicial volume via foliated simplices and duality, (2025), arXiv.

• Bounded cohomology of t-discrete measured groupoids via resolutions (with A. Savini), (2025), arXiv.
• Measurable bounded cohomology of measured groupoids (with A. Savini), (2023), arXiv.

Published or accepted papers

• Boundaries and equivariant maps of ergodic groupoids (with A. Savini), Glasgow Mathematical Journal, (2025), arXiv, DOI.

• Boundary maps and reducibility for cocycles into the isometries of CAT(0)-spaces (with A. Savini), Groups, Geometry, and Dynamics, (2025), arXiv, DOI.
• Bounded cohomology classes of exact forms (with L. Battista, Stefano Francaviglia, Marco Moraschini and A. Savini), Proceedings of the American Mathematical Society, (2024), arXiv, DOI.
• Parametrized Kahler class and Zariski dense orbital 1-cohomology (with A. Savini), Mathematical Research Letters (2023), arXiv, DOI.
• Superrigidity of maximal measurable cocycles of complex hyperbolic lattices (with A. Savini), Mathematische Zeitschrift, (2022), arXiv, DOI.
• Counting surface branched cover (with C. Petronio), Studia Scientiarum Mathematicarum Hungarica, (2019), arXiv, DOI.

Book chapters

• The Proportionality Principle via Hyperbolic Geometry chapter in the book Bounded Cohomology and Simplicial Volume, London Mathematical Society Lecture Note Series (2023), DOI.

Thesis

• Numerical invariants for measurable cocycles, PhD thesis, University of Bologna (2022), pdf.