I am interested in mathematical problems arising from condensed matter physics, specially related to charge and spin (topological) transport in quantum systems.
More recently, I have become interested in spectral and dynamical aspects related to certain non-integer base expansions, and machine learning area: in particular the connection between feedforward neural networks and approximation theory.
13) Spin transport and lack of quantisation in the AII class on the honeycomb structure
L. Fresta, G. Marcelli. Preprint (2025). Submitted.
12) Longitudinal conductivity at integer quantum Hall transitions
G. Marcelli, L. Pigozzi, M. Porta. Preprint (2025). Under Revision in Lett. Math. Phys. (2025).
11) Spectral and dynamical results related to certain non-integer base expansions on the unit interval
H. D. Cornean, I. W. Herbst, G. Marcelli. Preprint (2025). Accepted in Journal of Spectral Theory (2025).
M. Wesle, G. Marcelli, T. Miyao, D. Monaco, S. Teufel. Commun. Math. Phys. (2025).
9) On the self-consistent Landauer-Büttiker formalism
H. D. Cornean, G. Marcelli. Commun. Math. Phys. (2024).
8) Adiabatic evolution of low-temperature many-body systems
R. L. Greenblatt, M. Lange, G. Marcelli, M. Porta. Commun. Math. Phys. (2024).
7) Purely linear response of the quantum Hall current to space-adiabatic perturbations
G. Marcelli, D. Monaco. Lett. Math. Phys. (2022).
6) From charge to spin: analogies and differences in quantum transport coefficients
G. Marcelli, D. Monaco. J. Math. Phys. (2022).
5) Improved energy estimates for a class of time-dependent perturbed Hamiltonians
G. Marcelli. Lett. Math. Phys. (2022).
4) Localization of generalized Wannier bases implies Chern triviality in non-periodic insulators
G. Marcelli, M. Moscolari, G. Panati. Ann. Henri Poincaré (2022).
3) A new approach to transport coefficients in the quantum spin Hall effect
G. Marcelli, G. Panati, S. Teufel. Ann. Henri Poincaré (2020). Extended preprint at arXiv:2004.00956 .
2) Spin conductance and spin conductivity in topological insulators: analysis of Kubo-like terms
G. Marcelli, G. Panati, C. Tauber. Ann. Henri Poincaré (2019).
1) The Haldane model and its localization dichotomy
G. Marcelli, D. Monaco, M. Moscolari, G. Panati. Rend. Mat. Appl. (2018). Extended preprint at arXiv:1909.03298 .