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Carfora Mauro

Professore ordinario
ogni giorno su appuntamento
carfora (at) pv.infn.it
Dipartimento di Fisica Nucleare e Teorica

Elenco corsi

Elettrodinamica e relatività (Fisica)
Elettrodinamica e relatività (Scienze fisiche)
Elettrodinamica e relatività (Fisica)
Relatività generale

+ Altri anni accademici

Elettrodinamica e relatività (Scienze fisiche)
Elettrodinamica e relatività (Fisica)
Elettrodinamica e relatività (Fisica)
Relatività generale
Elettrodinamica e relatività
Relatività generale
Elettrodinamica e relatività
Relatività generale
Elettrodinamica e relatività
Relatività generale
Teorie relativistiche
Elettrodinamica e relatività
Relatività generale

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  •  Ph.D. Physics, May 1981 University of Texas at Dallas (Supervisor W. Rindler)
  • M.A. Physics, (Cum Laude), February 1977, University of Rome "La Sapienza", Rome (Supervisor C. Cattaneo)


  •  University of Pavia, Full Professor of Mathematical Physics, 2001 - Present
  • University of Pavia, Associate Professor of Theoretical Physics, 1997-2001
  • International School for Advanced Studies (ISAS-SISSA), Associate Professor of Mathematical Physics, 1992-1997
  •  University of Pavia, Researcher (Theoretical Physics), 1985-1992
  • University of Rome "La Sapienza", Researcher (Theoretical Physics), 1981-1985


  • Dean of Graduate Studies in Physics of the University of Pavia, 2007-present
  • Vice-Director of the Department of Nuclear and Theoretical Physics of the University of Pavia, 2001-2012
  • Coordinator of the theoretical group of the Pavia section of the INFN (Italian National Institute for Nuclear Physics) (1987-1993);
  • Local coordinator (Pavia) of the research projects (PRIN): "Geometry of Integrable systems I" (2000-2001 e 2002-2003). "Geometry of Integrable systems II" (2004-2005)  “Moduli spaces, inegrable structures, and PDE of evolutive type” (2006-2007). "Evolutive PDEs" (2008-2010).
  • Local coordinator (Pavia) of the INFN research projects "Differential geometrical methods in field and string theory", (1985-present)
  • Local coordinator (Pavia) of the European HCM project Constrained Dynamical Systems (1993-96);
  • Member of the Scientific Committee of  SIGRAV (Italian Society for Relativity and Gravitational Physics).
  • Member of the Scientific Committee of the SIGRAV Graduate School in Contemporary Relativity and Gravitational Physics.
  • Member of the American Mathematical Society
  • Organizer (together with: Zindine Djadli, Gerhard Huisken, Lei Ni, Eric Woolgar) of the International Workshop: "Geometric flows in mathematics and physics" BIRS (Banff International Research Station- 5 days workshop 11w5010) Banff Centre (Canada), (17/04/2011 - 22/04/2011).
  • Member of the Advisory Board of the: XXXV International Conference of Theoretical Physics "Matter to the Deepest", Ustron, Poland, 12-18 Settembre 2011
  • Member of the Scientific Committee of "The jubilee 40th Symposium on Mathematical Physics: "Geometry and Quanta", June 25-28, 2008, Torun, Poland
  • President (together with Bruno Bertotti) of the Scientific Committee of the International Conference "Spacetime in Action: one hundred years of Relativity" (Pavia March 29- April 2, 2005), framed within the UNESCO World Year of Physics 2005 Programme.
  • Member of the Scientific Committee of the meeting "Problemi Attuali di Fisica Teorica" (Vietri, 2001, 2004, 2005, 2006, 2007, 2008,2010, 2012); Chair of the Quantum  Gravity workshop.
  • Chairman of the Classical and Quantum Gravity workshop of the Italian Meeting on General Relativity and Gravitational Physics (2004, 2006).
  • Review (at large) for  Physical Review Letters, Physical Review D, Classical and Quantum Gravity, Journal of Geometry and Physics, Journal of Differential Geometry,  Physics Letters (A and B), Journal of Physics A, Journal of Mathematical Analysis and Applications, and many other journals.
  • Acted as Committee Member for various  Institutions abroad (USA, Germany, France, Australia) for academic position evaluation.
  • Acted as expert Evaluator for some National Science Foundation  projects


  • Winner of the Bruno Finzi Prize for Mathematical Physics of the Istituto Lombardo di Scienze (1997)
  • 2nd Prize of The Gravity Research Foundation (with C. Rovelli and A. Bareira, 1996)
  • Member elected of the Scientific Committee of the National Group of Mathematical Physics (GNFM) of the National Institute of Advanced Mathematics (INDAM), (2001-Present)
  • Profile of Success (together with Rebecca Bishop and Joseph P. Estrera) as testimonial of the Graduate School in Physics of the University of Texas at Dallas (2011).


He has held visiting positions in many universities and research institutions abroad, among these: University of California, Berkeley (Physics Dept); KITP at the University of California, Santa Barbara; University of Texas at Dallas, Ludwig-Maximilians-Universität München, N. Copernicus Astronomical Centre Warsaw, Banach Institute Warsaw; University of Oregon, Eugene; N. Bohr Institute, Copenhagen.


  • "Changes of scale, Dicretizations & Quantum Geometry", Invited Talk at CECAM-ETH Zurigo, 27-29  June 2011
  • "(Quantum) Glimpses of Spacetime Geometry " Invited talk at 87e rencontre entre physiciens théoriciens et mathématiciens : Géométrie de Lorentz en mathématiques et en physique 16-18 juin 2011, (IRMA), Strasbourg, France.
  • "Ricci Flow: A Theoretical Physics Perspective" and "Ricci flow conjugation and Initial data sets for Einstein Equations" Invited talks at the: Numerical Ricci Flow in Computer Science, Geometry, and Physics, Pacific Institute for Mathematical Sciences, Vancouver 14-16 July 2011.
  • "Ricci Flow and Quantum Field Theory Landscaping"
    Invited talk at: XXI Fall Workshop on Geometry and Physics, Madrid 31 August-3 September, 2011.
  • "QFT landscaping and the Ricci Flow" Invited talk at the: "The moon of Einstein-The scientific legacy of Ruggiero de Ritis", Istituto Italiano di Studi Filosofici, Napoli 1-3 October 2010
  • "Back and Forth with the Ricci flow" Invited talk at the: XIX SIGRAV Conference, Scuola Normale Superiore, 27 September-1 October  2010
  • "Ricci flow and Einstein equations" Invited talk at the: "Aspects géométriques at porbabilistes de la théorie de la relativité", 10-12 juin 2010, (IRMA), Strasbourg, France
  • "Einstein Equations, Lorentzian Geometry, and Ricci Flow Conjugation"
    Invited talk at the Workshop "Geometric Evolutions and Minimal Surfaces in Lorentzian Manifolds", Centro DeGiorgi, SNS Pisa, 7 September - 10 September 2010
  • "Ricci flow in Mathematical and Theoretical Physics"
    A two--weeks course during the trimester: "Geometric Flows and Geometric Operators" organized by the Scuola Normale Superiore (SNS), in collaboration with INdAM. 02 May 2009 - 30 July 2009, Centro DeGiorgi, SNS Pisa
  • "Quantum fluctuations and Riemannian Geometry: The case of the Ricci flow"
    Invited lecture at: ADVANCES IN NUMBER THEORY AND GEOMETRY, 150 years of Riemann Hypothesis,  April 19-24, 2009, RISM (Riemann International School of Mathematics), Verbania (Italy). Speakers: (MiniCourses by: E. Bombieri, J. Cheeger, J. P. Demailly,
    P. Sarnak; Lectures by: W. Ballmann, M. Bertolini, M. Carfora, A. Granville, E. Kowalski, R. Narasimhan, A. Perelli, M. Rasetti, H. Rosenberg, N. Snaith, G. Thorbergsson, C. Voisin)
  • "Averaging and back-reaction in relativistic cosmology I & II"
    A series of two lectures at: SIGRAV School in Cosmology and INFN Formation School "Coarse-Grained Cosmology", 26-29 January, 2009, The Galileo Galilei Institute for Theoretical Physics (GGI), Arcetri, Florence (Lectures by  E.J. Copeland, G.F.R. Ellis, E. W. Kolb, M. Carfora, P.K.S. Dunsby)
  • "Green functions for the Ricci flow and their applications" Invited talk at: "Workshop on Field Theory and Geometric Flows", November  24 - 28, 2008, Ludwig-Maximilians-Universität München (LMU),  Arnold-Sommerfeld-Center, Munich,
    (Speakers:  G. Tian, D. Friedan, N. Manton, M. Petropoulos, G. Huisken, H-D. Cao, I. Brunner, C. Bachas, E. Kuwert, S. Shatashvili, E. Wolgar, L. Ni, J. Isenberg, M. Gaberdiel, C. Warnick, T. Olyinyk, D.H. Phong, K. Skenderis, M. Carfora)
  • "Physical and Mathematical applications of the Conjugate Ricci Flow"
    Invited talk at: කème rencontre entre physiciens théoriciens et mathématiciens : Le flot de Ricci en mathématique et en physique"  11-13 septembre 2008,Institut de Recherche Mathématique Avancée (IRMA), Strasbourg, France (Speakers: M. Carfora, P. Topping, E. Woolgar, J. Keller,     
    G. Besson, I. Bakas, D. Friedan, F. Luo, W. Graf, B. Wilking)
  • "Quantum Fluctuations and Geometry: From Graphs Counting to Ricci Flow" 
    Invited talk at: The jubilee 40th Symposium on Mathematical Physics,
    "Geometry and Quanta",  June 25-28, 2008, Torun, Poland, (Speakers:  N. O'Murchadha, E.T. Newman, M.Carfora, J. Pullin, Ch. Fleischhack)
  • "Quantum fluctuations and Geometry"
    Invited talk at: the conference More Geometrico 3, "De l'univers au monde quantique : structure géométriques et topologiques" 5-10 May, 2008, Fondation des Treilles,TOURTOUR , France
  • "Conjugate linearized Ricci Flow, heat content and deformation of GR initial data sets"
    invited talk at: Conference on "Geometric Flows in Mathematics and Physics", 13–18 April 2008, Banff International Research Station (BIRS), Banff, Canada,( Speakers: H-D. Cao, L. Ni, M. Simon, G. Holzegel, C. Warnick, I. Bakas, M. Carfora, D. Friedan, D. Morrison, J. Gegenberg, V. Suneeta, X. Dai, P. Miao, J-F. Li, R. Bartnik, J. Lamm, J. Streets, N. Sesum, S. Anco, M. Athanassenas, J. Metzger, F. Schulze). 
  • “Physical Applications of Ricci flow” Geometric Analysis Lecture Series,  Mathematical Physics Seminar at The University of Arizona December 5, 2007,  Department of Mathematics, The University of Arizona, Tucson
  • “The conjugate linearized Ricci flow” Geometric Analysis Lecture Series, Analysis and Its Applications Seminar at The University of Arizona, December 4, 2007, Department of Mathematics, The University of Arizona, Tucson
  • “Fokker-Planck equation and Ricci flow” Geometric Analysis Lecture Series seminar at The University of Arizona, December 3, 2007,Department of Mathematics, The University of Arizona, Tucson 
  • "The conjugate Linearized Ricci Flow and its (nice) properties"
    invited talk at: "Workshop on Renormalization Group Flow and Ricci flow", October 22-25, 2007,E. Schroedinger International Institute for Mathematical Physics (ESI), Wien, Austria
    (Speakers: R. McCann, G. Huisken, C. Kopper, M. Carfora, A. Grigor'yan, V. Schomerus, B. Wilking);
  • "Changes of scale, quantum gravity and quantum geometry" invited talk at: "II ème Rencontre "More geometrico" Changement d'échelle - changement de niveau", May 2-4, 2007, Université René Descartes - Paris 5, Paris, (Speakers: P-P. Vidal, P. Viviani, C. Sinigaglia, J. Droulez, K. Cullen, P. Mamassian, Y. Bouligand, L. Nottale, J-F. Sadoc, A. Soto, M. Ladjimi, U. Bruzzo, C. Bartocci, M. Carfora, J-P. Luminet, T. Paul)
  • "Ricci flow, entropies and the averaging of cosmological spacetimes"
    invited talk at: "Workshop on Geometric and Renormalization Group Flows", November 22-24, 2006, Max Planck Institute for Gravitational Physics, (Albert Einstein Institute) Potsdam, Germany
     (Speakers: A. Tseytlin, A. Zamolodchikov, M. Carfora, K. Smoczyk, E. Kuwert, K. Ecker, I. Bakas, E. Woolgar, B. Wilking);
  • "Applications of the Hamilton-Perelman flow in theoretical physics" invited talk at: "Geometric Evolutions and Applications", 18-19 December 2006, Pisa, Centro di ricerca matematica E. DeGiorgi, Scuola Norm. Sup.
  • “Ricci flow, Perelman’s entropy and FLRW templates in Relativistic Cosmology”
    invited talk at: “Heat Equation and Curvature Flows”,  September 24-25, 2004,Università di Roma “La Sapienza” ( Speakers:  M. Carfora,  K. Ecker, R.S. Hamilton, C. Sinestrari, T. Coulhon, A. Grigor’yan, G. Huisken).


Temi di ricerca



  • Geometrical methods and non linear analysis in theoretical and mathematical Physics.
  • General relativity and quantum gravity.
  • Relativistic Cosmology.
  • Ricci flow on Riemannian manifolds.
  • Applications of geometric flows to theoretical and mathematical Phyics.
  • Renormalization group flow and geometrical flows.
  • Simplicial techniques in quantum gravity, moduli space theory, and String Theory.


Progetti di ricerca

Local coordinator  of the research projects (PRIN):


  • "Geometry of Integrable systems I" (2000-2001)
  • "Geometry of Integrable systems I"(2002-2003).
  • "Geometry of Integrable systems II" (2004-2005) 
  • “Moduli spaces, inegrable structures, and PDE of evolutive type” (2006-2007).
  • "Evolutive PDEs" (2008-2010).
  • Local coordinator  of the INFN research projects "Differential geometrical methods in field and string theory", (1985-present)
  • Local coordinator  of the European HCM project Constrained Dynamical Systems (1993-96);



 Author of more than 90  research papers in leading journals and proceedings; two Springer Lecture Notes Monographs, and editor of numerous proceedings. He is also a known scientific illustrator,  the book Flat and Curved Space-times by G.F.R. Ellis and R. M. Williams, the Springer Lecture Notes The Geometry of Dynamical Triangulations by J. Ambjorn, M. Carfora, and A. Marzuoli, and the official  Italian stamp for the Italian celebration of the Unesco World Year of Physics (2005) provide a few examples.


Some Recent and Relevant Publications

  • M. Carfora, A. Marzuoli (2012). Quantum Triangulations: Moduli spaces, Strings, and Quantum Computing. Lecture Notes in Physics, Springer Verlag Heidelberg Monographs Vol. 845, pXV-280, ISBN: 978-3-642-24439-1
  • M. Carfora (2012-in stampa). Ricci flow conjugated initial data sets for Einstein Equations. Advances in Theor. and Math. Phys. 
  • M. Carfora (2010). Renormalization group and the Ricci flow. Milan Jour. of  Mathematics, vol. 78; p. 319-353, ISSN: 1424-9286, doi: 10.1007/s00032-010-0110-y
  • M. Carfora (2009). The Conjugate Linearized Ricci Flow on Closed 3-Manifolds. Annali della Scuola Norm. Sup. di  Pisa. CL. di  Scienze, vol. Vol. VIII; p. 1-44, ISSN: 0391-173
  • M. Carfora. (2009). Quantum fluctuations and geometry: from graph counting to Ricci flow. Reports on  Math. Phys., vol. 64; p. 185-203, ISSN: 0034-487
  • M. Carfora, A. Marzuoli, M. Rasetti (2009). Quantum Tetrahedra. Journ. of Physical Chemistry  A., vol. 113, ISSN: 1089-5639, doi: 10.1021/jp909824h
  •  M. Carfora, T. Buchert (2008). On the curvature of the present-day universe
    Class. Quantum Grav. 25 (2008) 1–35.
  • M. Carfora, T. Buchert (2008). Ricci flow deformation of cosmological
    inital data sets
    . WASCOM 2007,14th conference on Waves and Stability in Continuous
    Media (pp. 118-127), World Sci.
  • M. Carfora (2007). Fokker-Planck Dynamics and Entropies for the normalized
    Ricci Flow
    . Adv. in Theor. and Math. Phys. vol. 11, pp. 635-681 ISSN: 1095-0761.
  • M. Carfora, C. Dappiaggi, V. L. Gili (2007). Boundary Conformal Field
    Theory and Ribbon Graphs: A Tool for open/closed string dualities
    . Jour.
    Of High Energy Phys. vol. 07, pp. 021 ISSN: 1126-6708. doi:10.1088/1126-
  • M. Carfora, C. Dappiaggi, V. L. Gili (2006). Triangulated surfaces in
    twistor space: a kinematical set up for open/closed string duality
    . Jour. Of
    High Energy Phys. vol. 017, pp. 1-33 ISSN: 1126-6708. doi:10.1088/1126-
  • M. Carfora (2004). Discretized Gravity and the SU(2) WZW model. Class.
    and Quant. Grav. vol. 21, pp. S109-S126 ISSN: 0264-9381.
  • G. Arcioni, M. Carfora, C. Dappiaggi, A. Marzuoli (2004). The WZW
    model on random Regge triangulations
    . Jour. of Geom. and Phys. vol. 52,
    pp. 137-173 ISSN: 0393-0440.
  • T. Buchert, M. Carfora (2003). Cosmological Parameters are dressed. Phys.
    Rev. Lett. vol. 90, pp. 031101-1,4 ISSN: 0031-9007.
  • J.Ambjørn, M.Carfora, A.Marzuoli, The Geometry of Dynamical Triangulations,
    Lectures Notes in Physics, New Series: Monographs, m50. Springer-
    Verlag, Berlin, 1997. viii+197 pp.
  • M.Bareira, M.Carfora, C.Rovelli Physics with nonperturbative quantum gravity:
    radiation from quantum black holes
    , General Relativity and Gravit. 28,
  • M.Carfora, G.F.R. Ellis The geometry of classical change of signature, Intern.
    Journ. of Modern Physics D, 4 (1995), 175-187.
  • M.Carfora, A. Marzuoli Holonomy and Entropy estimates for dynamically
    triangulated manifolds
    , Journ.Math.Phys. 36 6353-6376 (1995).
  • M.Carfora, A.Marzuoli Finiteness theorems in Riemannian geometry and
    lattice quantum gravity
    , Contemporary Mathematics 132, 171-211 (1992).
  • M.Carfora, J.Isenberg, M.Jackson, Convergence of the Ricci flow for a class
    of riemannian metrics with indefinite Ricci curvature
    , Journ. of Differential
    Geometry 31 249-263 (1990).
  • M.Carfora, A.Marzuoli, Functional Measures on the space of n-dimensional
    riemannian geometries
    Phys.Rev.Letters 62 1339-1342 (1989).
  • M.Carfora, A. Marzuoli, Model geometries in the space of Riemannian
    structures and Hamilton’s flow
    Class.Quantum Grav. 5 659-693 (1988)
  • M.Carfora, A.Marzuoli, Smoothing out spatially closed cosmology, Phys.
    Rev. Lett. 53 2445-2448 (1984)


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