Research 

My research interests are focused mainly on rigidity properties of lattices in semisimple Lie groups. 

1. Rigidity at infinity of representations of lattices in semisimple Lie groups:

Keywords: character variety, ideal points, numerical invariants for representations and bounded cohomology, Mostow rigidity type theorems. 

2. Numerical invariants and natural maps for measurable cocycles:

Keywords: rank one lattices, measurable cocycles, numerical invariants and bounded cohomology, Margulis/Zimmer rigidity/superrigidity type theorems, algebraic hull and reducibility, tautness and measure equivalence, maximal cocycles and mapping degree.

3.  Parametrized class and Eilenberg Mac-Lane cohomology:

Keywords: Eilenberg-MacLane cohomology with measurable coefficients, Euler/Kahler parametrized class, Ghys correspondence type theorems.

4. Virtual actions on dendrites:

Keywords: dendrites, elementarity of virtual actions, unitary representations in Bochner spaces, Monod cocycle.

5. Measurable cohomology of groups:

Keywords: measurable cohomology of Lie groups and their boundaries, Monod's conjecture. 

6. Measurable cohomology of measured groupoids: 

Keywords: measured and ergodic groupoids, measurable cohomology, amenability, Poisson boundaries for reflected measures, algebraic representability.

Here you can find my arXiv profile . I report below a list of my papers:

• Published Papers

1. A. Savini, The omega-Borel invariant for representations into SL(n,C_omega), Groups Geom. Dyn 13 (2019), n.3, 767-1131. [DOI link].

2. A. Savini, Rigidity at infinity for lattices in rank-one Lie groups, J. Top. Anal. 12 (2020), n. 1, 113-130. [DOI link].

3. S. Francaviglia, A. Savini, Volume rigidity at ideal points of the character variety of hyperbolic 3-manifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci. XX (2020), issue 4, 1325-1344.

4. A. Savini, Entropy rigidity for foliations by strictly convex projective manifolds, Pure Appl. Math. Q. 17 (2021), n. 1, 575-589.

5. A. Savini, Algebraic hull of maximal measurable cocycles of surface groups into Hermitian Lie groups, Geom. Dedicata 213 (2021), n.1, 375-400 [DOI link].

6. A. Savini, Equivariant maps for measurable cocycles with value into higher rank Lie groups, Pacific J. Math. 312 (2021), n. 2, 505-525 [DOI link].

7. F. Sarti, A. Savini, Superrigidity of maximal measurable cocycles of complex hyperbolic lattices,  Math. Z. 300 (2022), n. 1, 421-443 [DOI link].

8. A. Savini, A note on elementarity of virtual dendro-morphisms of higher rank lattices, Proc. of Amer. Math. Soc. 150 (2022), n. 11, 4995-5008 [DOI link].

9.  M. Moraschini, A. Savini, Multiplicative constants and maximal measurable cocycles in bounded cohomology, Ergodic Theory Dynam. Systems 42 (2022), n. 11, 3490-3525 [DOI link].

10. M. Moraschini, A. Savini, A Matsumoto-Mostow result for Zimmer's cocycles of hyperbolic lattices, Trans. Group 27 (2022), n. 4, 1337-1392 [DOI link]. 

11. A. Savini, "Continuous bounded cohomology, representations and multiplicative constants", in the collection "Bounded cohomology and simplicial volume", LMS lecture notes 479 (2022) [DOI link].

12. A. Savini, Natural maps for measurable cocycles of compact hyperbolic manifolds, J. Math. Inst. Jussieu 22 (2023), n.1, 421-448 [DOI link].

13. A. Savini, Rigidity at infinity for the Borel function of the tetrahedral reflection lattices,  Algeb. Geom. Topology 23 (2023), n. 4, 1583-1600.

14. F. Sarti, A. Savini, Parametrized Kahler class and Zariski dense orbital 1-cohomology, Math. Res. Lett. 30 (2023), n. 6, 1895-1929.

15. L. Battista, S. Francaviglia, M. Moraschini, F. Sarti, A. Savini,  Bounded cohomology of exact forms, Proc. Amer. Math. Soc 152 (2024), n.1 , pp. 71–80

16. A. Savini, On trivializability of rank-one cocycles with a invariant field of projective measures, European J. Math. 10 (2024), n. 1 [DOI link]. 

• Accepter Papers

1. A. Savini, Borel invariant for Zimmer cocycles of 3-manifold groups, to appear on J. Top. Anal. [DOI link].

2. A. Savini, Orbital cohomology and Kahler rigidity, to appear in the Sémin. Théor. Spectr. Géom. [arXiv link].

• Submitted Papers

1. F. Sarti, A. Savini, Boundary maps and reducibility of cocycles into the isometries of CAT(0)-spaces [arXiv link].

2. A. Savini, Parametrized Euler class and semicohomology theory [arXiv link].

3. M. Bucher, A. Savini,  Some explicit cocycles on the Furstenberg boundary for products of isometries of hyperbolic spaces and SL(3,K) [arXiv link].

4. F. Sarti, A. Savini, Measurable bounded cohomology of measured groupoids [arXiv link].

5. M. Bucher, A. Savini, Alternating cochains on Furstenberg boundaries and measurable cohomology [arXiv link].

6. M. Bucher, A. Savini, Kernels in measurable cohomology for transitive actions [arXiv link].

7. F. Sarti, A. Savini, Boundaries and equivariant maps for ergodic groupoids [arXiv link].