Marco Falconi's Math Page
Department of Mathematics
Politecnico di Milano
E-mail: marco.falconi [AT] polimi.it
MathSciNet profile , GoogleScholar profile , ArXiv profile
Itinerant Quantum Math Meetings
Recent Advances in Quantum and Statistical Mechanics - Hausdorff School
Research interests
- Wigner measures and Egorov-type Theorems in infinite dimensions
- Quasi-Classical Systems
- Renormalization in Quantum Field Theory
- Lattice Quantum ElectroDynamics
- Open Quantum Systems
- Scattering theory for linear and nonlinear evolution systems
- Rigorous derivation of effective theories in condensed matter
- Pseudodifferential calculus in infinite dimensions
Publications & Preprints
In reverse chronological order:
2023
- M.F., A. Olgiati, N. Rougerie
- Convergence of states for polaron models in the classical limit, Preprint
Abstract & Metadata
- Convergence of states for polaron models in the classical limit, Preprint
- M. Correggi, M.F., M. Olivieri
- Ground State Properties in the Quasi-Classical Regime, Anal. PDE 16(8), 1745-1798
Abstract & Metadata
- Ground State Properties in the Quasi-Classical Regime, Anal. PDE 16(8), 1745-1798
- M. Correggi, M.F., M. Olivieri
- Quasi-Classical Dynamics, J. Eur. Mat. Soc. 25(2), 731-783
Abstract & Metadata
- Quasi-Classical Dynamics, J. Eur. Mat. Soc. 25(2), 731-783
- Z. Ammari, M.F., M. Olivieri
- Semiclassical analysis of quantum asymptotic fields in the Yukawa theory, J. Differential Equations 357, 236-274
Abstract & Metadata
- Semiclassical analysis of quantum asymptotic fields in the Yukawa theory, J. Differential Equations 357, 236-274
- M. F., N. Leopold
- Derivation of the Maxwell–Schrödinger equations: A note on the infrared sector of the radiation field, J. Math. Phys. 64, 011901
Abstract & Metadata
- Derivation of the Maxwell–Schrödinger equations: A note on the infrared sector of the radiation field, J. Math. Phys. 64, 011901
- M. F., N. Leopold, D. Mitrouskas, S. Petrat
- Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model, Rev. Math. Phys. 33, 2350006
Abstract & Metadata
- Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model, Rev. Math. Phys. 33, 2350006
2022
- M. Dalmonte, V. Eisler, M.F., B. Vermersch
- Entanglement Hamiltonians - from field theory, to lattice models and experiments, Ann. Phys. (Berlin) 534(11), 202200064
Abstract & Metadata
- Entanglement Hamiltonians - from field theory, to lattice models and experiments, Ann. Phys. (Berlin) 534(11), 202200064
- Z. Ammari, M.F., F. Hiroshima
- Towards a derivation of Classical ElectroDynamics of charges and fields from QED, Preprint
Abstract & Metadata
- Towards a derivation of Classical ElectroDynamics of charges and fields from QED, Preprint
2021
- R. Carlone, M. Correggi, M.F., M. Olivieri
- Emergence of Time-Dependent Point Interactions in Polaron Models, SIAM J. Math. Anal. 53(4), 4657-4691
Abstract & Metadata
- Emergence of Time-Dependent Point Interactions in Polaron Models, SIAM J. Math. Anal. 53(4), 4657-4691
- M.F., E.L. Giacomelli, C. Hainzl, M. Porta
- The dilute Fermi gas via Bogoliubov theory, Ann. Henri Poincaré 22(7), 2283-2353
Abstract & Metadata
- The dilute Fermi gas via Bogoliubov theory, Ann. Henri Poincaré 22(7), 2283-2353
- D. Dimonte, M.F., A. Olgiati
- Some rigorous aspects of fragmented condensation, Nonlinearity 34(1), 1-32
Abstract & Metadata
- Some rigorous aspects of fragmented condensation, Nonlinearity 34(1), 1-32
2019
- M. Correggi, M.F., M. Olivieri
- Magnetic Schrödinger Operators as the Quasi-Classical Limit of Pauli-Fierz-type Models, J. Spectr. Theory 9(4), 1287-1325
Abstract & Metadata
- Magnetic Schrödinger Operators as the Quasi-Classical Limit of Pauli-Fierz-type Models, J. Spectr. Theory 9(4), 1287-1325
2018
- M.F.
- Cylindrical Wigner measures, Doc. Math. 23, 1677-1756
Abstract & Metadata - Concentration of cylindrical Wigner measures, Commun. Contemp. Math. 20(5), 1750055
Abstract & Metadata
- Cylindrical Wigner measures, Doc. Math. 23, 1677-1756
- M. Correggi, M.F.
- Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit, Ann. Henri Poincaré 19(1), 189-235
Abstract & Metadata
- Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit, Ann. Henri Poincaré 19(1), 189-235
2017
- Z. Ammari, M.F.
- Bohr's correspondence principle for the renormalized Nelson model, SIAM J. Math. Anal. 49(6), 5031-5095
Abstract & Metadata
- Bohr's correspondence principle for the renormalized Nelson model, SIAM J. Math. Anal. 49(6), 5031-5095
- M.F., J. Faupin, J. Froehlich, B. Schubnel
- Scattering theory for Lindblad master equations, Comm. Math. Phys. 350(3), 1185-1218
Abstract & Metadata
- Scattering theory for Lindblad master equations, Comm. Math. Phys. 350(3), 1185-1218
2016
- Z. Ammari, M. F., B. Pawilowski
- On the rate of convergence for the mean field approximation of Bosonic many-body quantum dynamics, Commun. Math. Sci. 14(5), 1417-1442
Abstract & Metadata
- On the rate of convergence for the mean field approximation of Bosonic many-body quantum dynamics, Commun. Math. Sci. 14(5), 1417-1442
- Z. Ammari, M.F.
- Bohr's correspondence principle in quantum field theory and classical renormalization scheme: the Nelson model, Preprint
Abstract & Metadata
- Bohr's correspondence principle in quantum field theory and classical renormalization scheme: the Nelson model, Preprint
2015
- M.F.
- Self-Adjointness criterion for operators in Fock spaces, Math. Phys. Anal. Geom. 18(1)
Abstract, Intro & Metadata
- Self-Adjointness criterion for operators in Fock spaces, Math. Phys. Anal. Geom. 18(1)
2014
- Z. Ammari, M. F.
- Wigner measures approach to the classical limit of the Nelson model: Convergence of dynamics and ground state energy, J. Stat. Phys. 157(2), 330-364
Abstract, Intro & Metadata
- Wigner measures approach to the classical limit of the Nelson model: Convergence of dynamics and ground state energy, J. Stat. Phys. 157(2), 330-364
2013
- M.F.
- Global Solution of the Electromagnetic Field-Particle System of Equations, J. Math. Phys. 55, 101502
Abstract, Intro & Metadata - Mean field limit of bosonic systems in partially factorized states and their linear combinations, Preprint
Abstract, Intro & Metadata
- Global Solution of the Electromagnetic Field-Particle System of Equations, J. Math. Phys. 55, 101502
2012
- M.F.
- Classical limit of the Nelson model with cut off, J. Math. Phys. 54, 012303
Abstract & Metadata
- Classical limit of the Nelson model with cut off, J. Math. Phys. 54, 012303
2008
- R. Bonezzi, M.F.
- Mode Regularization for N = 1, 2 SUSY Sigma Model, J. High Energy Phys. 10 (2008) 019
Abstract & Metadata
- Mode Regularization for N = 1, 2 SUSY Sigma Model, J. High Energy Phys. 10 (2008) 019
Affiliations
Current employment
Senior Tenure-Track Researcher at DMat, Politecnico di Milano.
Education
- Ph.D. in Mathematics. Alma Mater Studiorum, Università di Bologna.
- Dissertation : Classical limit of the Nelson model. pdf
- Advisor : Giorgio Velo.
- Committee : Piero D'Ancona, Alberto Parmeggiani, Marco Peloso.
- Defense : June 8, 2012.
- Master Degree in Theoretical Physics. Alma Mater Studiorum, Università di Bologna.
- Dissertation : On the regularization of phase-space path integral in curved manifolds. pdf
- Advisor : Fiorenzo Bastianelli.
- Grade : 110/110 with honours.
- Bachelor Degree in Physics. Alma Mater Studiorum, Università di Bologna.
- Dissertation : Sulla nozione di distinguibilità e degenerazione (in italian).
- Advisor : Loris Ferrari.
- Grade : 110/110 with honours.
Chronology
- September 2019 - Present. Researcher (RTDa) at Rome 3 University, Italy.
- January 2018 - August 2019. Postdoc at Eberhard Karls Universität Tübingen, Germany.
- April 2017 - December 2017. Postdoc at Universität Zürich, Switzerland.
- April 2016 - March 2017. Postdoc at Rome 3 University, Italy.
- October 2015 - March 2016. Research assistant at Universität Stuttgart, Germany.
- January 2014 - September 2015. Postdoc at CHL/IRMAR Rennes, France.
- July 2012 - June 2013. Postdoc at Mathematics Department, Bologna University, Italy.
- January 2009 - June 2012. Ph.D. student, Bologna University, Italy.
- September 2005 - December 2007. Master student, Bologna University, Italy.
- September 2002 - September 2005. Bachelor student, Bologna University, Italy.
Since October 2014 I am member of the International Association of Mathematical Physics (IAMP), of the French Mathematical Society (SMF), and of the European Mathematical Society (EMS). From January 2016, I am also member of the American Mathematical Society (AMS).
Teaching & Dissemination
Research Activities
- Hausdorff School
- Recent Advances in Quantum and Statistical Mechanics. Hausdorff School at HCM Bonn, organized together with C. Brennecke and S. Cenatiempo. Website
- INdAM Intensive Period
- INdAM Quantum Meetings 22. Research Trimester with focus on the Mathematical Methods of Quantum Mechanics. March-May 2022, Politecnico di Milano. Website
- Workshop
- Quantum Before Christmas. December 20-22, 2021. Università degli Studi di Milano. Website
- Local Seminar
- Itinerant Quantum Math Meetings. Local seminar, delocalized in Polimi, Statale, and Insubria. Website
- Italian Quantum Seminar
- MCQM Seminar. Italian quantum seminar. Website
Teaching
- Tübingen
- Minicorso Sapienza
- Froehlich lectures in La Sapienza
- Cours de scattering - Giorgio Velo
- Cours doctoral
- Relations de commutation canoniques: représentations en systèmes fini ou infini-dimensionnels. Programme Notes du cours (manuscrites)
Scientific Presentations
- Renormalization at any order of lattice infrared QED\(_4\). Probability Seminar, HCM Bonn + Mathematical Quantum Matter. slides
- A Quantum detour: regularizing classical electrodynamics by means of QED. Seminar of Mathematical Physics, Tohoku University + Quantissima in the Serenissima IV. slides
- Variational Problems in Quasi-Classical Systems. Seminar Analysis and Mathematical Physics, Basel + SMAQ Seminar, L'Aquila. slides
- Quasi-Classical Dynamics. Nonlinear Dynamics in Quantum Mechanics, Bremen. website slides
- Ground State Energy of Interacting Fermions at Low Density. Seminario di Fisica Matematica, Roma. slides
- Limiti Quasi-Classici in Meccanica Quantistica. XXI Congresso U.M.I., Pavia. website slides
- Semiclassical Analysis in AQFT. AQFT: Where Operator Algebra Meets Microlocal Analysis, Cortona. website slides
- Cylindrical Wigner Measures in Bosonic QFTs. 4th SwissMAP General Meeting, Grindelwald. website slides
- Potenziali effettivi nell'approssimazione quasi-classica. Assemblea Scientifica GNFM 2017. website slides (in italian)
- External Potentials Generated by the Interaction with a Semiclassical Field. Spectral Days 2017, Stuttgart. website slides
- Bohr's correspondence principle in the Nelson model. Mathematical quantum field theory and related topics, IMI Kyushu. pdf website
- Scattering theory in open quantum systems: Lindblad-type evolutions. Mathematical Challenges in Quantum Mechanics, Bressanone. pdf website
- Semiclassical Analysis in Infinite Dimensions: Wigner Measures. Seminari di Analisi Matematica Bruno Pini, Dipartimento di Matematica, Universita' di Bologna. To appear in BPMAS 2016 notes
- Bohr's correspondence principle and classical dressing renormalization in the Nelson model. 3rd Meeting ANR SQFT, Ile de Porquerolles (France). June 11th, 2015. pdf website
- Bounds on the convergence towards mean field dynamics for systems of many bosons. Rencontre LODIQUAS, Saint-Malo (France). December 9th, 2014. pdf website (lodiquas)
- Schrödinger-Klein-Gordon system as the classical limit of a Quantum Field Theory dynamics. Workshop on Dispersive equations with nonlocal dispersion - III, WPI Vienna. October 10th, 2014. pdf website
- Classical and mean field limit of field-particle systems. GDR DynQua annual meeting 2014, Roscoff. February 5th, 2014. pdf website
Some fun (thanks to Quino and R. Munroe)
