Marco Falconi's Math Page

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Department of Mathematics
Politecnico di Milano

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

CV(english)

MathSciNet profile , GoogleScholar profile , ArXiv profile

INdAM Quantum Meetings (IQM22)(poster)(workshop I)

Quantum Before Christmas

Itinerant Quantum Math Meetings

MCQM Seminar

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:

2022

  • M. Dalmonte, V. Eisler, M.F., B. Vermersch
    • Entanglement Hamiltonians - from field theory, to lattice models and experiments, Ann. Phys. (Berlin), in press
      Abstract & Metadata
  • M. Correggi, M.F., M. Olivieri
    • Ground State Properties in the Quasi-Classical Regime, Anal. PDE, in press
      Abstract & Metadata
  • M. Correggi, M.F., M. Olivieri
  • Z. Ammari, M.F., F. Hiroshima
    • Towards a derivation of Classical ElectroDynamics of charges and fields from QED, Preprint
      Abstract & Metadata

2021

  • Z. Ammari, M.F., M. Olivieri
    • Semiclassical analysis of quantum asymptotic fields in the Yukawa theory, Preprint
      Abstract & Metadata
  • M. F., N. Leopold, D. Mitrouskas, S. Petrat
    • Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model, Preprint
      Abstract & Metadata
  • 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.
  • M. Correggi, M.F.
    • Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit, Ann. Henri Poincaré 19(1), 189-235
      Abstract & Metadata
  • M.F.
    • Concentration of cylindrical Wigner measures, Commun. Contemp. Math. 20(5), 1750055
      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

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

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

  • 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

Scientific Presentations

  • 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)

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Last updated in August 2021 by MF using Emacs 27.2 (Org mode 9.4.6's html-export)