The optimal transport measures given by Wigner measures of Schrödinger dynamics.
Schrödinger spectra and the Hamilton-Jabobi homogenization.
The study of quasimodes and eigenfunctions for Schrödinger operators on the torus associated to weak solutions of Hamilton-Jacobi equations.
Global Fourier Integral Operators
The global FIO setting. The problem of continuity. The notion of infinite dimensional FIO.
Schrödinger equation
The global FIO structure of the evolution operator. Multivalued semiclassical WKB approximation outside resonant times. The analytical properties of the kernel.
Symplectic geometry
Global generating functions for the graph of Hamiltonian flows. Minimax and geometric solutions of Hamilton-Jacobi equations.
Professional Activity
May 2016 - April 2018 : Postdoctoral position, Department of Mathematics, University of Padova.
May 2015 - April 2016 : Postdoctoral position, Department of Industrial Engineering, University of Padova.
Oct 2013 - Dec 2014 : Postdoctoral position, Department of Mathematics, University of Padova.
(7) L. Zanelli: Mather measures in semiclassical Analysis.
Proceedings of the 14 th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 24 - 29 june 2012. AIMS on Applied Mathematics Vol. 8.
(6) O. Bernardi, A. Parmeggiani, L. Zanelli. Mather measures associated with a class of Bloch wave functions.
Annales Henri Poincarè. Volume 13, Issue 8 (2012), Page 1807-1839.
(5) S. Graffi, L. Zanelli. The geometric approach to the Hamilton-Jacobi equation and global parametrices for the Schrödinger propagator.
Reviews in Mathematical Physics, vol 23, issue 9, 2011.
(4) S. Graffi, L. Zanelli. Global parametrices for the Schrödinger propagator and geometric approach to the Hamilton-Jacobi equation.
(3) P. Guiotto, L. Zanelli. The Geometry of Generating Functions for a class of Hamiltonian flows in the non compact case.
Journal of Geometry and Physics, vol. 60, pp 1381-1401, 2010.
(2) O. Bernardi, F. Cardin, M. Guzzo, L. Zanelli. A PDE approach to finite time indicators in ergodic theory.
Journal of Nonlinear Mathematical Physics, vol. 16, issue 2, 2009.
(1) F. Cardin, P. Guiotto, L. Zanelli. Integral representations of the Schrödinger propagator.
Reports on Mathematical Physics, vol. 62, issue 1, 2008.
Referee Reports
Journal of Mathematical Physics
Journal of Physics A: Mathematical and Theoretical
Conferences and Seminars
Communication at XVII Italian Meeting on Hyperbolic Equations, University of Pavia, 06 - 08 september 2017.
Title: Schroedinger dynamics and optimal transport problems.
Communication at the Workshop Assemblea Scientifica GNFM 2017, Montecatini Terme, 04 - 06 may 2017.
Title: Schroedinger spectra and the effective Hamiltonian of the weak KAM theory
Communication at the Workshop Assemblea Scientifica GNFM 2015, Montecatini Terme, 22 - 24 october 2015.
Title: Schroedinger dynamics and optimal transport of measures on the torus.
Communication at the Workshop: Problemi attuali in teoria dei sistemi dinamici, Department of Mathematics, Milano-Bicocca University, 22 - 23 may 2014.
Title: On the dynamics of WKB wave functions whose phase are weak KAM solutions of H-J equation.
Communication at Assemblea Scientifica GNFM 2014, Montecatini Terme, 15 - 17 may 2014.
Title: On the localization of the semiclassical Wave Front Set for Schroedinger eigenfunctions on the flat torus.
Seminar at the Institut Henri Poincaré,Paris,16 november 2012.
Title: Some applications of the Aubry-Mather theory in semiclassical Analysis.
Seminar at Assemblea Scientifica GNFM 2012, Montecatini Terme, 4 - 6 october 2012.
Title: Wigner measures supported on weak KAM tori.
Communication at the Congress: 14 th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, University of Padova,24 - 29 june 2012.
Title: Mather measures in semiclassical Analysis.
Seminar at the Department of Mathematics University of Padova, 13 december 2011.
Title: The weak KAM theory in semiclassical analysis.
Communication at the Congress: Mathematical Methods in Quantum Mechanics, Bressanone, 14 - 19 february 2011.
Title: Global Fourier Integral Operators and quantum dynamics.
Communication at the Congress: "Classical and weak KAM theorem: the Aubry-Mather sets, a break-trough in the study of dynamical systems" Montegrotto 14-19 february 2010.
Title: The Geometry of Generating Functions for a class of Hamiltonian flows in the non compact case.
Seminar at the Department of Mathematics University of Bologna, 23 november 2009.
Title: Operatori Integrali di Fourier globali e Propagatore di Schrödinger.
Seminar at the Department of Mathematics University of Bologna, 29 september 2008.
Title: Funzioni generatrici quadratiche all'infinito di flussi Hamiltoniani.
Communication at the Congress: Assemblea Scientifica GNFM 2007, Montecatini Terme, 11 - 13 october 2007.
Title: Rappresentazioni Globali del Propagatore di Schrödinger.
Communication at the Congress: Mathematical Modeling, Mechanics and Materials, Bressanone, 19 march 2007.
Title: On the Evolution Operator of the Fokker-Planck equation.
Communication at the Congress: Mathematical Methods in Quantum Mechanics, Bressanone, 26 february - 3 march 2007.
Title: The Schrödinger Propagator.
Communication at the Congress: Problemi Matematici in Meccanica Quantistica, Università di Modena,05 - 07 october 2006.
Title: Integral representations of the Schrödinger Propagator.
Seminar at the Department of Physics University Roma 3, 24 june 2005.
Title: Rappresentazione Integrale Finita Esatta del Propagatore di Schrödinger.
Seminar at the Summer School of Mathematical Physics,Ravello, september 2005.
Title: Forze di Contatto e di Bulk.
Seminar at the Summer School of Mathematical Physics,Ravello, september 2004.
Title: A lower bound for Von Karman Energy Functional.
Communication at the Congress: Mathematical Problems in Quantum Mechanics, Università di Modena, 19 - 21 december 2003.
Title: Rappresentazione Integrale Finita Esatta del Propagatore di Schrödinger e di Fokker Planck.
Past Teaching Activity (theory and exercises)
Meccanica Razionale, master degree course, a.a. 2017/18, Department of Industrial Engineering, University of Padova.
Meccanica Razionale, master degree course, a.a. 2016/17, Department of Industrial Engineering, University of Padova.
Fisica Matematica, master degree course, a.a. 2015/16, Department of Mathematics, University of Padova.
Meccanica Razionale, master degree course, a.a. 2015/16, Department of Industrial Engineering, University of Padova.
Analisi Matematica, summer course 2014 in Bressanone (I - week) organized by University of Padova.
Fisica Matematica, master degree course, a.a. 2010/11, Department of Mathematics, University of Bologna.
Matematica 1, master degree course, a.a. 2009/10, Department of Chemistry, University of Bologna.
Matematica 1, master degree course, a.a. 2007/08, Department of Biotechnology, University of Padova.
Istituzioni di Analisi Matematica 2, master degree course, a.a. 2006/07, Department of Statistics, University of Padova.
Matematica 1, master degree course, a.a. 2005/06, Department of Physics, University of Padova.
Fisica Matematica, master degree course, a.a. 2005/06, Department of Mathematics, University of Padova.