Teaching at UNIPI

(Deep) Learning Theory) (PhD course in mathematics, 2023/24)
Statistica I (Ingegneria Gestionale, a.a. 2022/23)
Research Interests
I am interested in applied probability theory, more specifically in interacting particle systems for real world applications. I have worked on scaling limits for models of chemical reaction networks, focusing on the relations between their dynamics and their structure. More recently, I have worked on the dynamics of scaling limits of machine learning algorithms seen as interacting particle systems, and on dynamics of fluid models.
 Global optimality of Elmantype recurrent neural networks in the meanfield regime, with J. Lu and S. Mukherjee, International Conference on Machine Learning (2023)
 Random Splitting of Fluid Models: Positive Lyapunov Exponents, with O. Melikechi and J. Mattingly, arXiv:2210.02958
 Random Splitting of Fluid Models: Ergodicity and Convergence, with O. Melikechi and J. Mattingly, Communications in Mathematical Physics (2023)
 A homotopic approach to policy gradients for linear quadratic regulators with nonlinear controls, with C. Chen, IEEE Proceedings of of Conference on Decision and Control (2022)
 Large deviations with Markov jump processes with uniformly diminishing rates, with L. Andreis, M. Renger, R. Patterson, Stochastic Processes and Their Applicatons (2022)
 Global optimality of softmax policy gradient with single hidden layer neural networks in the meanfield regime, with J. Lu, International Conference on Learning Representations, 2021
 Temporal Difference Learning with nonlinear function approximation in the lazy training regime, with J. Lu, Proceedings of Machine Learning Research, Mathematical and Scientific Machine Learning, 2021
 Seemingly stable chemical kinetics can be stable, marginally stable or unstable, with J. Mattingly, Comm. Math. Sci. 18 (6), 1605  1642 (2020)
 Large Deviations Theory for Markov Jump Models of Chemical Reaction Networks, with A. Dembo and J.P. Eckmann, Ann. Appl. Prob. 28 (3), 18211855 (2018)
 On the Geometry of Chemical Network Theory: Lyapunov Function and Large Deviations Theory, with A. Dembo and J.P. Eckmann, J. Stat. Phys. 172 (2), 321352 (2018)
 The Colored Hofstadter Butterfly for the Honeycomb Lattice, with G. M. Graf and J.P. Eckmann, J. Stat. Phys. 156 (3), 417426 (2014)
Teaching
 Statistical Learning Theory (STATS 303, Duke)
 Stochastic Calculus (MATH 545, Duke)
 Introducton to Probabilty and Statistics (STATS 210, Duke)
 Probability theory (MATH 230, Duke)