Publications
Papers
M. Girotti, T. Grava, K. McLaughlin, J. Najnudel, Law of Large Numbers and Central Limit Theorem for random sets of solitons of the focusing nonlinear Schrodinger equation, submitted, 2024.
A. Mousavi-Hosseini, S. Park, M. Girotti, I. Mitliagkas, M. Erdogdu, Neural Networks Efficiently Learn Low-Dimensional Representations with SGD, International Conference on Learning Representations (ICLR), 2023 (notable-top-25%).
(spotlight presentation at the Workshop on Optimization for Machine Learning OPT 2022 - NeurIPS)
M. Girotti, T. Grava, R. Jenkins, K. McLaughlin, A. Minakov, Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation, Comm. Pure Appl. Math., 10.1002/cpa.22106, 2023.
M. Girotti, I. Mitliagkas, G. Gidel, Convergence Analysis and Implicit Regularization of Feedback Alignment for Deep Linear Networks, 2021.
(spotlight talk at the workshop Beyond First-Order Methods in ML Systems - ICML 2021)
C. Guille-Escuret, B. Goujaud, M. Girotti, I. Mitliagkas, A Study of Condition Numbers for First-order Optimization, Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1261-1269, 2021.
(spotlight presentation and Student Paper Award at the Workshop on Optimization for Machine Learning OPT 2020 - NeurIPS)
M. Girotti, T. Grava, R. Jenkins, K. McLaughlin, Rigorous asymptotics of a KdV soliton gas, Comm. Math. Phys., https://doi.org/10.1007/s00220-021-03942-1, 2021.
M. Cafasso, T. Claeys, M. Girotti, Fredholm determinant solutions of the Painlevé II hierarchy and gap probabilities of determinantal point processes, Internat. Math. Res. Notices, rnz168, 2019.
T. Claeys, M. Girotti, D. Stivigny, Large gap asymptotics at the hard edge for product random matrices and Muttalib-Borodin ensembles, Internat. Math. Res. Notices, rnx202, 2017.
M. Girotti, Riemann-Hilbert approach to gap probabilities for the Bessel process, Physica D, 295-296C, 103-121, 2015.
M. Girotti, Asymptotics of the Tacnode process: a transition between the gap probabilities from the Tacnode to the Airy process, Nonlinearity 27, 1937-1968, 2014.
M. Girotti, Riemann-Hilbert approach to gap probabilities for the Generalized Bessel process, Math. Phys. Anal. Geom. 17 (1), 183-211, 2014.
M. Girotti, Vanishing time-relaxation for a phase-field model with entropy balance, Adv. Math. Sci. Appl., 22(2), 553-575, 2012.
Ph.D. thesis
My Ph.D. thesis investigates gap probabilities of some universal kernels that appear in Random Matrix Theory.
Riemann-Hilbert approach to Gap Probabilities of Determinantal Point Processes, Concordia University, 2014.
Master and Bachelor theses
My Master (Laurea Magistrale) thesis investigates well-posedness and uniqueness of the solution of a system of PDEs describing the evolution of a first-order phase transition in the regime as a time coefficients vanishes. The results have also been published (see above).
Time-relaxation for a phase-field model with entropy balance, Università degli Studi di Milano, 2010 (in Italian).
My Bachelor (Laurea Triennale) thesis is a review of the classical theory of magnetic monopole, who was originally introduced by P.A.M. Dirac in 1931.
Dirac’s magnetic monopole, Università degli Studi di Milano, 2008 (in Italian).
