My research interests lie in mathematical methods in quantum mechanics, with particular emphasis on geometric and topological effects in condensed matter physics.
A selection of topics on which my research is focused includes:
Analysis of periodic Schrödinger operators and Hamiltonians;
Classification of phases of topological quantum matter;
Novel materials, as e.g. graphene and topological insulators;
Quantum transport of interacting and non-interacting fermions.
You can browse my preprints and publications also on arXiv and Google Scholar.
More information concerning my publications is accessible through MathSciNet, ORCID, Scopus, Web of Science, and zbMATH.
6. Absolute and relative invariants for low-dimensional topological insulators (with Federico Manzoni and Gabriele Peluso). Preprint at arXiv:2609.32442.
5. The colored Hofstadter butterfly as a many-body quantum Hall phase diagram (with Giovanna Marcelli, Tadahiro Miyao, Stefan Teufel, and Marius Wesle). Preprint at arXiv:2606.26256.
4. Universality of the Hall conductivity for a weakly interacting magnetic fermionic gas in the Hartree-Fock approximation (with Horia Cornean, Emanuela Giacomelli and Mikkel Hviid Thorn). Preprint at arXiv:2602.15522.
3. Vanishing of power-law corrections to Kubo's formula for the Hall current at incommensurate magnetic fields (with Gabriele Mazzini). Preprint at arXiv:2601.21417.
2. Derivation of Hartree-Fock dynamics and semiclassical commutator estimates for fermions in a magnetic field (with Niels Benedikter, Chiara Boccato, and Ngoc Nhi Nguyen). Preprint at arXiv:2503.16001.
1. The Localization Dichotomy for gapped periodic quantum systems (with Gianluca Panati, Adriano Pisante, and Stefan Teufel). Preprint at arXiv:1612.09557.
27. Zak phase and bulk-boundary correspondence in a generalized Dirac-Kronig-Penney model (with Giuliano Angelone and Gabriele Peluso). Accepted for publication in New Journal of Physics (2026). Preprint at arXiv:2602.03378.
26. The Zak phase in topologically insulating chains: invariants and limitations (with Federico Manzoni and Gabriele Peluso). Accepted for publication in Advances in Theoretical and Mathematical Physics (2026). Preprint at arXiv:2603.14995.
25. Splitting obstructions and Z2 invariants in time-reversal symmetric topological insulators (with Alessandro Ferreri and Gabriele Peluso). Complex Analysis and Operator Theory 20, art. no. 111 (2026). Preprint at arXiv:2511.10444.
24. Near linearity of the macroscopic Hall current response in infinitely extended gapped fermion systems (with Marius Wesle, Giovanna Marcelli, Tadahiro Miyao, and Stefan Teufel). Communications in Mathematical Physics 406, Issue 8 (2025), 199. Preprint at arXiv:2411.06967.
23. Effective quantum dynamics for magnetic fermions (with Margherita Ferrero). Open Communications in Nonlinear Mathematical Physics 4 (2024), 157–187. Preprint at arXiv:2406.15041.
22. A Z2 invariant for chiral and particle–hole symmetric topological chains (with Gabriele Peluso). Journal of Mathematical Physics 64, Issue 4 (2023), 041904. Preprint at arXiv:2303.08464.
21. Topology vs localization in synthetic dimensions (with Thaddeus Roussigné). Journal of Mathematical Physics 64, Issue 1 (2023), 011902. Preprint at arXiv:2210.04809.
20. Purely linear response of the quantum Hall current to space-adiabatic perturbations (with Giovanna Marcelli). Letters in Mathematical Physics 112, Issue 5 (2022), 91. Preprint at arXiv:2112.03071.
19. From charge to spin: analogies and differences in quantum transport coefficients (with Giovanna Marcelli). Journal of Mathematical Physics 63, Issue 7 (2022), 072102. Preprint at arXiv:2203.08044.
18. Symmetric Fermi projections and Kitaev's table: topological phases of matter in low dimensions (with David Gontier and Solal Perrin-Roussel). Journal of Mathematical Physics 63, Issue 4 (2022), 041902. Preprint at arXiv:2201.01576 .
17. Beyond Diophantine Wannier diagrams: Gap labelling for Bloch-Landau Hamiltonians (with Horia Cornean and Massimo Moscolari). Journal of the European Mathematical Society 23, Issue 11 (2021), 3679–3705 . Preprint at arXiv:1810.05623.
16. Středa formula for charge and spin currents (with Massimo Moscolari). Reviews in Mathematical Physics 33, Issue 1 (2021), 2060003. Proceedings issue for the conference "QMath14: Mathematical Results in Quantum Physics", August 12-16, 2019, Aarhus (Denmark). Preprint at arXiv:2002.02419.
15. Spin Hall conductivity in insulators with non-conserved spin (with Lara Ulčakar). Physical Review B 102, Issue 12 (2020), 125138. Preprint at arXiv:2006.12071.
14. Parseval frames of exponentially localized magnetic Wannier functions (with Horia Cornean and Massimo Moscolari). Communications in Mathematical Physics 371, Issue 3 (2019), 1179–1230. Preprint at arXiv:1704.00932.
13. Localised Wannier functions in metallic systems (with Horia Cornean, David Gontier, and Antoine Levitt). Annales Henri Poincaré 20, Issue 4 (2019), 1367–1391. Preprint at arXiv:1712.07954.
12. Adiabatic currents for interacting electrons on a lattice (with Stefan Teufel). Reviews in Mathematical Physics 31, Issue 3 (2019), 1950009. Preprint at arXiv:1707.01852.
11. The Haldane model and its localization dichotomy (with Giovanna Marcelli, Massimo Moscolari, and Gianluca Panati). Rendiconti di Matematica e delle sue Applicazioni 39, Issue 2 (2018), 307–327. Extended preprint at arXiv:1909.03298.
10. Optimal decay of Wannier functions in Chern and Quantum Hall insulators (with Gianluca Panati, Adriano Pisante, and Stefan Teufel). Communications in Mathematical Physics 359, Issue 1 (2018), 61–100. Preprint at arXiv:1612.09552.
9. Chern and Fu-Kane-Mele invariants as topological obstructions. Chapter 12 in: G. Dell'Antonio and A. Michelangeli (eds.), Advances in Quantum Mechanics: Contemporary Trends and Open Problems, vol. 18 in Springer INdAM Series (2017). Proceedings volume for the INdAM meeting "Contemporary Trends in the Mathematics of Quantum Mechanics", July 4-8, 2016, Rome (Italy). Preprint at arXiv:1705.06534.
8. On the construction of Wannier functions in topological insulators: the 3D case (with Horia Cornean). Annales Henri Poincaré 18, Issue 12 (2017), 3863–3902. Preprint at arXiv:1703.06308.
7. Gauge-theoretic invariants for topological insulators: A bridge between Berry, Wess-Zumino, and Fu-Kane-Mele (with Clément Tauber). Letters in Mathematical Physics 107, Issue 7 (2017), 1315–1343. Preprint at arXiv:1611.05691.
6. Wannier functions and Z2 invariants in time-reversal symmetric topological insulators (with Horia Cornean and Stefan Teufel). Reviews in Mathematical Physics 29, Issue 2 (2017), 1730001. Preprint at arXiv:1603.06752.
5. Z2 invariants of topological insulators as geometric obstructions (with Domenico Fiorenza and Gianluca Panati). Communications in Mathematical Physics 343, Issue 3 (2016), 1115–1157. Preprint at arXiv:1408.1030.
4. Stability of closed gaps for the alternating Kronig-Penney Hamiltonian (with Alessandro Michelangeli). Analysis and Mathematical Physics 6, Issue 1 (2016), 67–83. Preprint at SISSA Digital Library 16/2015/MATE.
3. Construction of real-valued localized composite Wannier functions for insulators (with Domenico Fiorenza and Gianluca Panati). Annales Henri Poincaré 17, Issue 1 (2016), 63–97. Preprint at arXiv:1408.0527.
2. Symmetry and localization in periodic crystals: triviality of Bloch bundles with a fermionic time-reversal symmetry (with Gianluca Panati). Acta Applicandae Mathematicae 137, Issue 1 (2015), 185–203. Proceedings issue for the conference "Symmetry and Perturbation Theory 2014", May 25 - June 1, 2014, Cala Gonone (Italy). Preprint at SISSA Digital Library and at arXiv:1601.02906.
1. Topological invariants of eigenvalue intersections and decrease of Wannier functions in graphene (with Gianluca Panati). Journal of Statistical Physics 155, Issue 6 (2014), 1027–1071. Preprint at arXiv:1306.3904.
5. Tampone positivo, e ora? La matematica dei test diagnostici. Sapere Scienza (2021).
4. Esagoni, cerchi e tangenti: al ristorante con Lagrange. Prisma Magazine 21 (2020), 36-37.
3. Fase 2: la disposizione ottimale dei clienti usando la matematica. Sapere Scienza (2020).
2. Client packing: in tempo di pandemia, una ristorazione in regola... e ottimale. Blog post for Math is in the air (2020).
1. KK-theory, gauge theory and topological phases (with Francesca Arici). Nieuw Archief voor Wiskunde 5/18, Issue 4 (2017), 257–262.
Geometric phases in graphene and topological insulators. Thesis in partial fulfillment of the requirements for the degree of Philosophiæ Doctor in Mathematical Physics (SISSA, Trieste, Italy, 2015). Available at the SISSA Digital Library.
A geometric approach to the decay of Wannier functions in graphene. Thesis in partial fulfillment of the requirements for the Master degree in Mathematics (SAPIENZA Università degli Studi di Roma, Rome, Italy, 2011).
Euler's equation (a geometric description). Thesis in partial fulfillment of the requirements for the Bachelor degree in Mathematics (SAPIENZA Università degli Studi di Roma, Rome, Italy, 2009).