Marco Falconi's Math Page

Department of Mathematics
Politecnico di Milano

E-mail: marco.falconi [AT] polimi.it

CV(english)

MathSciNet profile , GoogleScholar profile , ArXiv profile

Itinerant Quantum Math Meetings

MCQM Seminar

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:

2024

M.F., L. Fratini
- Abstract semiclassical analysis of the van Hove model, Preprint
  Abstract & Metadata
S. Breteaux, M. Correggi, M.F., J. Faupin
- Quantum Point Charges Interacting with Quasi-classical Electromagnetic Fields, Preprint
  Abstract & Metadata
Z. Ammari, M.F., F. Hiroshima
- Towards a derivation of Classical ElectroDynamics of charges and fields from QED, Ann. Inst. Fourier, in press
  Abstract & Metadata

2023

M.F., A. Olgiati, N. Rougerie
- Convergence of states for polaron models in the classical limit, Preprint
  Abstract & Metadata
M. Correggi, M.F., M. Olivieri
- Ground State Properties in the Quasi-Classical Regime, Anal. PDE 16(8), 1745-1798
  Abstract & Metadata
M. Correggi, M.F., M. Olivieri
- Quasi-Classical Dynamics, J. Eur. Mat. Soc. 25(2), 731-783
  Abstract & Metadata
Z. Ammari, M.F., M. Olivieri
- Semiclassical analysis of quantum asymptotic fields in the Yukawa theory, J. Differential Equations 357, 236-274
  Abstract & Metadata
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
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

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

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
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
D. Dimonte, M.F., A. Olgiati
- Some rigorous aspects of fragmented condensation, Nonlinearity 34(1), 1-32
  Abstract & Metadata

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

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
M. Correggi, M.F.
- Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit, Ann. Henri Poincaré 19(1), 189-235
  Abstract & Metadata

2017

Z. Ammari, M.F.
- Bohr's correspondence principle for the renormalized Nelson model, SIAM J. Math. Anal. 49(6), 5031-5095
  Abstract & Metadata
M.F., J. Faupin, J. Froehlich, B. Schubnel
- Scattering theory for Lindblad master equations, Comm. Math. Phys. 350(3), 1185-1218
  Abstract & Metadata

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
Z. Ammari, M.F.
- Bohr's correspondence principle in quantum field theory and classical renormalization scheme: the Nelson model, Preprint
  Abstract & Metadata

2015

M.F.
- Self-Adjointness criterion for operators in Fock spaces, Math. Phys. Anal. Geom. 18(1)
  Abstract, Intro & Metadata

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

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

2012

M.F.
- Classical limit of the Nelson model with cut off, J. Math. Phys. 54, 012303
  Abstract & Metadata

2008

R. Bonezzi, M.F.
- Mode Regularization for N = 1, 2 SUSY Sigma Model, J. High Energy Phys. 10 (2008) 019
  Abstract & Metadata

Affiliations

Current employment

Associate Professor 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
- Non-Linear Dispersive Partial Differential Equations (2019). Website Exercise Sheets: 1 2 3 4
- Non-Linear Dispersive Partial Differential Equations (2018). Website Exercise Sheets: 1 2 3 4 5
Minicorso Sapienza
- Lecture notes
Froehlich lectures in La Sapienza
- Slides and lecture notes
Cours de scattering - Giorgio Velo
- Détails et notes du cours (en anglais)
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)