Matteo FOCARDI

Ruolo attuale:: Professore Ordinario
SSD:: MATH-03/A - Analisi matematica
Afferenza organizzativa:: Dipartimento di Matematica e Informatica 'Ulisse Dini'

Recapiti

	0552751442
	matteo.focardi(AT)unifi.it

Ulteriori Recapiti

	Stanza 205
	0552751442
	matteo.focardi(AT)unifi.it
	http://web.math.unifi.it/users/focardi/

Matteo FOCARDI

Orario di ricevimento (aggiornato al 30/08/2022)

Elementi di Matematica e Statistica (corso B): da concordare all'inizio delle lezioni. Per un ricevimento in orari e giorni diversi contattare il docente per e-mail o a lezione,
Analisi Funzionale: su appuntamento contattando il docente.

Matteo FOCARDI

Biografia

** DATI ANAGRAFICI

  nome e cognome: MATTEO FOCARDI.

  codice fiscale: FCRMTT73T27D612P.

  luogo e data di nascita: Firenze 27 Dicembre 1973, cittadinanza italiana.

  ruolo: Professore Ordinario in Analisi Matematica, presso la Università degli Studi di Firenze.

  indirizzo: DiMaI ``Ulisse Dini'', V.le Morgagni 67/A, 50134, Firenze, Italy.

  telefono/fax: +39-055-4237136, +39-055-4222695

  e-mail: matteo.focardi@unifi.it

  homepage: https://people.dimai.unifi.it/focardi/index.html




** ISTRUZIONE

1987-1992: Diploma di Maturita' Scientifica presso il liceo Scientifico 
``A.M.E. Agnoletti'' di Sesto Fiorentino (FI), con la votazione di 60/60; 

1992-1996: Laurea in Scienze Matematiche presso l'UNIFI (votazione 110/110 con lode). 
Relatrice Prof.ssa E. Mascolo, titolo della tesi ``Semicontinuità di Funzionali 
Vettoriali nella Classe di Orlicz-Sobolev'' (discussione 25.10.96); 

1997: Borsa di Studio junior INdAM, presso l'Universita' ``La Sapienza'' di Roma; 

1998-2000: Perfezionamento in Matematica presso SNS di Pisa (votazione 70/70 con 
lode). Relatore Prof. L. Ambrosio, titolo della tesi ``Variational Approximation 
of Vectorial Free-Discontinuity Problems: the Discrete and Continuous case'' 
(discussione 14.06.2002). 


* POSIZIONI 

1.09.21-oggi: Professore Ordinario presso il DiMaI, UNIFI;

1.11.14-30.08.21: Professore Associato presso il DiMaI, UNIFI; 

1.09.00-31.10.14: Ricercatore presso il DiMaI, UNIFI; 
 
2003: Postdoc presso il Max Planck Institut fur Mathematik in den 
Naturwissenschaften a Lipsia (D)

Matteo FOCARDI

Curriculum

MATTEO FOCARDI'S CURRICULUM VITAE

Matteo Focardi, born in 1973 in Firenze (Italy), Italian citizen

** Positions

2021-today: Full Professor at the U. Firenze
2017: National Italian habilitation as Full Professor in Mathematical Analysis
2014-2021: Associate Professor at the U. Firenze
2000-2014: Research associate at the U. Firenze
2013: Research fellow at the Max Planck Institut für Mathematik in den Naturwissenschaften in Leipzig
2013: National Italian habilitation as Associate Professor in Mathematical Analysis
2003: Postdoc at the Max Planck Institut für Mathematik in den Naturwissenschaften in Leipzig
2002: Perfezionamento in Matematica (Ph.D.) at the Scuola Normale Superiore di Pisa
1996: Master Degree in Mathematics at the U. Firenze

** Teaching

I have been teaching since the a.y. 2000-01 in the ensuing Corsi di Laurea (undergraduate and/or master)
of the U. Firenze: Biotecnologie, Fisica, Matematica, Scienze Biologiche

* Ph.D. courses and schools
2021: “Γ-convergenza e applicazioni alla teoria dell’elasticità”, 20/40 ore, Dottorato in Matematica, Informatica e Statistica, DiMaI, U. Firenze, U. Perugia, INdAM.
2018: “An introduction to BV functions and Γ-convergence”, ModeMat - Escuela Politècnica Nacional, Quito (EC)
2014: “School on Free Discontinuity problems”, Centro De Giorgi Pisa
2008: “Una introduzione alla Γ-convergenza”, Dottorato in Matematica, Dipartimento di Matematica, U. Firenze

* Mentoring
2 Postdocs
1 Ph.D. student
3 master students
2 undergraduate students

** Research

I am (co-)author of about 50 papers published in international journals on Calculus of Variations, Geometric Measure Theory, and PDEs.

* Bibliometric information on my publications:
- 52 articles in scientific journals
- 2 articles in conference proceedings
- 1 chapter in collective volumes
- 1 editorial

* Citations (as of 18/02/2022):
- Scopus: 50 cited documents, 488 citations (h-index 13), 393 citations excluding self citations (h-index 10),
355 citations excluding self-citations of all authors (h-index 10)
- ISI Web of Knowledge: 44 cited documents, 414 citations (h-index 11), 267 citing articles,
353 citations excluding self-citations, 237 citing articles without self-citations
- MR Citation Database: 53 publications, 430 citations by 282 authors

* Main contributions
- Homogenization of non-local obstacle functionals
- Regularity for the jump set of Mumford-Shah (almost-)minimizers
- Phase-field approximation via Gamma-convergence of models in fracture mechanics
- Free boundary regularity for thin and thick obstacle problems

* Collaborators
M. Cicalese (TUM München), S. Conti (HCM Bonn), G. Cupini (U. Bologna), C. De Lellis (IAS Princeton),
N. Fusco (U. Napoli), A. Garroni (U. Roma La Sapienza), M.S. Gelli (U. Pisa), F. Iurlano (CNRS, Sorbonne U.),
F. Leonetti (U. L’Aquila), P. Marcellini (U. Firenze), P.M. Mariano (U. Firenze), E. Mascolo (U. Firenze), M. Ponsiglione (U. Roma La Sapienza), E. Spadaro (U. Roma La Sapienza), N. Van Goethem (U. Lisboa), C.I. Zeppieri (U. Münster)

* Scientific visits
- Universities: Zürich, Marne-la-Vallèe, Minnesota, Carnegie Mellon Univ. Pittsburgh, Roma Tor Vergata, EPFL Lausanne, Politécnica de Madrid, Napoli Federico II, Würzburg, Parma, The Univ. of Texas at Austin, Roma La Sapienza, TU München, Leipzig, Pavia, Torino, Univ. of Sussex

- Istitutions: Max Planck Institut für Mathematik in den Naturwissenschaften Leipzig, Centro De Giorgi Pisa, Hausdorff Center for Mathematics Bonn

* Workshops and invited talks (last 3 years)
2021:
- “On the regularity of singular sets of minimizers for the Mumford-Shah energy”, Regularity Theory for Free Boundary and Geometric Variational Problems, Levico Terme
- “On the regularity of singular sets of minimizers for the Mumford-Shah energy”, Nonlinear Potential Theoretic Methods in Partial Differential Equations, Banff, online meeting
- “On the regularity of singular sets of minimizers for the Mumford-Shah energy”, SIAM Conference on Mathematical Aspects of Materials Science - MS21, online meeting
- “On the regularity of singular sets of minimizers for the Mumford-Shah energy”, Seminario de Investigación del Centro de Modelización Matemática - Modemat de la EPN
- “On the regularity of singular sets of minimizers for the Mumford-Shah energy”, Mathematics Colloquium, Universität Münster
2020:
- “On the regularity of singular sets of minimizers for the Mumford-Shah energy”, Incontri di Analisi Matematica tra Firenze, Pisa e Siena, online meeting
2019:
- “How a minimal surface leaves a thin obstacle”, workshop “Modeling of Crystalline Interfaces and Thin Film Structures”, Erwin Schrödinger Institute, Wien
- “How a minimal surface leaves a thin obstacle”, workshop “Regularity aspects in linear growth problems”, Augsburg
- “How a minimal surface leaves a thin obstacle”, Turkey-Italy Colloquium on Applied Analysis and Differential Equations, Hacettepe U., Ankara
- “The measure and the structure of the free boundary in the lower dimensional obstacle problem”, Topics in Nonlinear Analysis and Calculus of Variations, U. Torino
- “The measure and the structure of the free boundary in the lower dimensional obstacle problem”, U. Pavia
- “How a minimal surface leaves a thin obstacle”, Levico Terme (TN)

* Organization of schools and workshops
2022:
- “Advances in Calculus of Variations”, Naples
2019:
- “Two days in CalcVar&PDEs”, Bologna
- “Geometric Measure Theory and Applications. From Geometric Analysis to Free Boundary Problems”, CIME Summer School, Cetraro
2018:
- “Workshop on dynamical systems, calculus of variations and control”, Firenze
2017:
- “New Trends on Calculus of Variations and PDE’s”, Firenze-Montecatini
- “Harnack’s inequalities and nonlinear operators”, Cortona
2009:
- “Workshop on Calculus of Variations and PDEs”, Firenze
2005:
- “Weekend di Calcolo delle Variazioni - Workshop a Firenze”, Firenze

* Coordination of research projects
- PRIN 2015 - “Calcolo delle Variazioni”, Firenze local unit coordinator (9.11.2017-5.02.20)
- Bando Ricerca Scientifica e Tecnologica 2020, Fondazione Cassa di Risparmio di Firenze -
“Struttura della frontiera libera per soluzioni di problemi di ostacolo sottile”, progetto individuale
- Bando Ricerca Scientifica e Tecnologica 2015, Ente Cassa di Risparmio di Firenze -
“Materiali intelligenti: l’analisi matematica al servizio delle applicazioni”, coordinatore negli a.a. 2017-2019
- GNAMPA 2020 - “Regolarità per problemi variazionali: vincoli unilaterali ed equazioni non uniformemente ellittiche”
- GNAMPA 2017 - “Regolarità per problemi variazionali d’ostacolo e libero”
- GNAMPA 2015 - “Regolarità per problemi di Analisi Geometrica e del Calcolo delle Variazioni”
- GNAMPA 2013 - “Semicontinuità e regolarità in problemi variazionali”
- GNAMPA 2013 - programma Professori Visitatori, guest Prof. E. Spadaro
- GNAMPA 2010 - “Semicontinuità di funzionali definiti su mappe multivoche, vettoriali e problemi collegati”

* Participation in research projects
- PRIN 2015 - “Calcolo delle Variazioni”
- PRIN 2010 - “Calcolo delle Variazioni”
- PRIN 2008 - “Equazioni ellittiche: problemi vettoriali e regolarità”
- PRIN 2006 - “Equazioni ellittiche e paraboliche: problemi vettoriali e regolarità”
- PRIN 2004 - “Calcolo delle variazioni: problemi vettoriali e regolarità”
- PRIN 2002 - “Equazioni e sistemi differenziali nonlineari degeneri: esistenza e regolarità”
- PRIN 2000 - “Calcolo delle Variazioni”
- GNAMPA 2019 - “Regolarità per equazioni non uniformemente ellittiche e nel Calcolo delle Variazioni”
- GNAMPA 2018 - “Regolarità per problemi ellittici e del calcolo delle variazioni: non convessi, discontinui, degeneri, singolari”
- GNAMPA 2016 - “Regolarità per problemi ellittici e di teoria geometrica della misura”
- GNAMPA 2014 - “Metodi variazionali per la meccanica e i materiali”
- GNAMPA 2012 - “Esistenza e regolarità per problemi vettoriali e variazionali”
- GNAMPA 2011 - “Regolarità per problemi variazionali non lineari e questioni connesse”
- GNAMPA 2008 - “Analisi di stati stazionari e fenomeni di evoluzione dissipativa nei corpi complessi”
- GNAMPA 2004 - “Tecniche di omogeneizzazione e metodi asintotici per problemi a scale multiple”
- GNAMPA 2003 - “Tecniche di omogeneizzazione e metodi asintotici per problemi a scale multiple”
- GNAMPA 2002 - “Tecniche di omogeneizzazione e metodi asintotici per problemi a scale multiple”

* Miscellaneous scientific activities
- I have participated in several committees of evaluation of Ph.D. candidates
- Referee for the ensuing journals: SIAM Journal on Mathematical Analysis, ESAIM COCV, DCDS-B, ZAMM, MMAS, Physica D,
IFB, JDE, Applicable Analysis, IFB, Calc. Var. & PDEs, CPDE, ARMA, Advances in Calculus of Variations, JFA, Annali della Scuola Normale Superiore di Pisa, The Proceedings of the Royal Society of Edinburgh: Section A, IMRN, Philosophical Transactions A, JNLS, Advances in Mathematics, Indiana University Mathematics Journal, Duke Mathematical Journal, Journal für die Reine und Angewandte Mathematik, AMPA, JEMS, Publications mathématiques de l’IHÉS, Mathematische Annalen, Journal de Mathématiques Pures et Appliquées.

** Service

* Ph.D. School in Mathematics, Computer Science and Statistics - U. Firenze, U. Perugia, INdAM
2021-today: Coordinator
2013-2021: Member of the board and Mathematics Curriculum Referent

* Corso di Laurea in Matematica
2016-2021: Gruppo del Riesame (coordinator)
2016-2021: Commissione Tesi
2016-2021: Commissione Compiti Didattici
2014-2015: Gruppo del Riesame (member)

* Mathematics and Computer Science Department
2018-2021: Commissione Internazionalizzazione
2012-today: Commissione Sicurezza

A complete an up-to-dated version of the CV can be found at the link 
https://people.dimai.unifi.it/focardi/curriculum/Focardi_Vitae.pdf

Matteo FOCARDI

Interessi

My research is devoted to Calculus of Variations and Geometric Measure Theory.

I first studied both the lower semicontinuity properties of integral functionals

having non-standard growth and the asymptotic analysis by means of

Gamma-convergence of some variational problems coming from applied sciences.

In particular, in my PhD Thesis I focused on the variational approximation of

free-discontinuity problems for vector valued maps, both in a discrete and a continuous setting.

My interests were then driven towards naturally related homogenization and relaxation

problems.

More recently, apart from continuing the issues quoted above, I started to investigate new topics:

(i) convergence problems for variational numerical schemes,

(ii) homogenization for obstacle problems for non-local energies,

(iii) lower semicontinuity properties for quasiconvex energies defined on Sobolev maps

taking values in non-flat spaces,

(iv) regularity properties for minimizers of the Mumford-Shah energy,

(v) regularity properties for solutions of the classical obstacle problems in case

the matrix of the coefficients of the relevant quadratic form is only Lipschitz continuous,

(vi) lower semicontinuity properties for non-coercive polyconvex energies in the limit case

for the admissible weak topology,

(vii) variational approximation of cohesive fracture (type) models in Fracture Mechanics and

related issues,

(viii) abstract regularity results, i.e. stratification of the singular set for solutions to

variational problems or of PDEs arising in problems of geometric analysis,

(ix) a variational approach to Weiss' epiperimetric inequality for obstacle problems,

(x) regularity for minimizers of the thin obstacle problems.

In addition, I wrote an up-to-date survey paper on $Gamma$-convergence theoryand a survey paper on some sharp regularity properties for local minimizers of the Mumford-Shah energy. Moreover, a simplied proof of a classical lower semicontinuity result dating back to Morrey has been provided.

I am author of about fifty research papers published on international journals.

Matteo FOCARDI

Pubblicazioni

Legenda

Contributo su rivista |

Articolo su libro |

Libro |

Contributo in atti di convegno (proceeding) |

Brevetto |

Curatela | Altro

Altro |

Tesi di Dottorato

Conti, Sergio; Focardi, Matteo; Iurlano, Flaviana (2025). Approximation of SBV functions with possibly infinite jump set. JOURNAL OF FUNCTIONAL ANALYSIS, vol. 288, pp. 1-58, ISSN:0022-1236 DOI Accesso ONLINE all'editore

Conti, Sergio; Focardi, Matteo; Iurlano, Flaviana (2024). Phase-Field Approximation of a Vectorial, Geometrically Nonlinear Cohesive Fracture Energy. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, vol. 248, pp. 1-60, ISSN:0003-9527 DOI Accesso ONLINE all'editore

Andreucci G.; Focardi M. (2023). The classical obstacle problem with Hölder continuous coefficients. NONLINEAR ANALYSIS, vol. 226, pp. 1-17, ISSN:0362-546X DOI Accesso ONLINE all'editore

Focardi M.; Spadaro E. (2021). Introduction. In: Guido De Philippis, Xavier Ros-Oton, Georg Weiss. Lecture Notes in Mathematics, pp. 1-3, GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND: Springer Science and Business Media Deutschland GmbH, ISBN:978-3-030-65798-7. DOI

Cicalese M.; Focardi M.; Zeppieri C.I. (2021). Phase-Field Approximation of Functionals Defined on Piecewise-Rigid Maps. JOURNAL OF NONLINEAR SCIENCE, vol. 31, pp. 1-25, ISSN:0938-8974 DOI Accesso ONLINE all'editore

De Lellis C.; Focardi M.; Ghinassi S. (2021). Endpoint regularity for 2d Mumford-Shah minimizers: On a theorem of Andersson and Mikayelyan. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, vol. 155, pp. 83-110, ISSN:0021-7824 DOI Accesso ONLINE all'editore

Matteo Focardi, Emanuele Spadaro (2020). How a minimal surface leaves a thin obstacle. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, vol. 37, pp. 1017-1046, ISSN:0294-1449 DOI Accesso ONLINE all'editore

Marco Caroccia, Matteo Focardi, Nicolas Van Goethem (2020). On the integral representation of variational functionals on BD. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, vol. 52, pp. 422-467, ISSN:0036-1410 DOI Accesso ONLINE all'editore

Focardi M.; Spadaro E. (2020). The local structure of the free boundary in the fractional obstacle problem. ADVANCES IN CALCULUS OF VARIATIONS, vol. 0, pp. 1-27, ISSN:1864-8258 DOI Accesso ONLINE all'editore

Matteo Focardi, Francesco Geraci, Emanuele Spadaro (2020). Quasi-Monotonicity Formulas for Classical Obstacle Problems with Sobolev Coefficients and Applications. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, vol. 184, pp. 125-138, ISSN:1573-2878 DOI Accesso ONLINE all'editore

Giovanni Cupini, Matteo Focardi, Francesco Leonetti, Elvira Mascolo, (2020). On the Hölder continuity for a class of vectorial problems. ADVANCES IN NONLINEAR ANALYSIS, vol. 9, pp. 1008-1025, ISSN:2191-9496 DOI Accesso ONLINE all'editore

Sergio Conti, Matteo Focardi, Flaviana Iurlano (2019). Approximation of fracture energies with $p$-growth via piecewise affine finite elements. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, vol. 25, pp. 1-12, ISSN:1262-3377 DOI Accesso ONLINE all'editore

Sergio Conti, Matteo Focardi, Flaviana Iurlano (2019). A note on the Hausdorff dimension of the singular set of solutions to elasticity type systems. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, vol. 21, pp. 1-58, ISSN:0219-1997 DOI Accesso ONLINE all'editore

Sergio, Conti, Matteo Focardi, Flaviana Iurlano (2019). Existence of strong minimizers for the Griffith static fracture model in dimension two. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, vol. 36, pp. 455-474, ISSN:0294-1449 DOI Accesso ONLINE all'editore

Matteo Focardi; Emanuele Spadaro (2018). On the measure and the structure of the free boundary of the lower dimensional obstacle problem. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, vol. 230, pp. 125-184, ISSN:1432-0673 DOI Accesso ONLINE all'editore

Cupini, G; Focardi, M; Leonetti, F; Mascolo, E (2018). LOCAL BOUNDEDNESS OF VECTORIAL MINIMIZERS OF NON-CONVEX FUNCTIONALS. BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR, vol. 1, pp. 20-40, ISSN:2240-2829

Matteo Focardi, Sergio Conti, Flaviana Iurlano (2018). Which special functions of bounded deformation have bounded variation?. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS, vol. 148, pp. 33-50, ISSN:0308-2105 DOI Accesso ONLINE all'editore

Conti, Sergio; Focardi, Matteo; Iurlano, Flaviana (2017). Integral representation for functionals defined on $SBD^p$ in dimension two. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, vol. 223, pp. 1337-1374, ISSN:0003-9527 DOI Accesso ONLINE all'editore

Focardi, Matteo; Geraci, Francesco; Spadaro, Emanuele (2017). The classical obstacle problem for nonlinear variational energies. NONLINEAR ANALYSIS, vol. 154, pp. 71-87, ISSN:0362-546X DOI Accesso ONLINE all'editore

Focardi, Matteo (2016). Fine regularity results for Mumford-Shah minimizers: porosity, higher integrability and the Mumford-Shah conjecture. In: Focardi, Matteo. Free Discontinuity Problems, pp. 1-68, Pisa: Edizioni della Normale, ISBN:978-88-7642-592-9.

Sergio, Conti; Matteo, Focardi; Flaviana, Iurlano (2016). Phase field approximation of cohesive fracture models. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, vol. 33, pp. 1033-1067, ISSN:0294-1449 DOI Accesso ONLINE all'editore

Conti, Sergio; Focardi, Matteo; Iurlano, Flaviana (2016). Some recent results on the convergence of damage to fracture. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI, vol. 27, pp. 51-60, ISSN:1120-6330 DOI Accesso ONLINE all'editore

Conti, Sergio; Focardi, Matteo; Iurlano, Flaviana (2016). Existence of minimizers for the 2d stationary Griffith fracture model. COMPTES RENDUS MATHÉMATIQUE, vol. 354, pp. 1055-1059, ISSN:1631-073X DOI Accesso ONLINE all'editore

Focardi, Matteo; Spadaro, Emanuele (2016). An epiperimetric inequality for the thin obstacle problem. ADVANCES IN DIFFERENTIAL EQUATIONS, vol. 21, pp. 153-200, ISSN:1079-9389 Accesso ONLINE all'editore

G. De Philippis; S. Di Marino; M. Focardi (2016). Lower semicontinuity for non-coercive polyconvex integrals in the limit case. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS, vol. 146, pp. 243-264, ISSN:0308-2105 DOI Accesso ONLINE all'editore

Matteo, Focardi; Andrea, Marchese; Emanuele Nunzio, Spadaro (2015). Improved estimate of the singular set of Dir-minimizing Q-valued functions via an abstract regularity result. JOURNAL OF FUNCTIONAL ANALYSIS, vol. 268, pp. 3290-3325, ISSN:0022-1236 DOI Accesso ONLINE all'editore

Matteo Focardi; Paolo Maria Mariano; Emanuele Nunzio Spadaro (2015). Multi-value microstructural descriptors for complex materials: analysis of ground states. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, vol. 217, pp. 899-933, ISSN:0003-9527 DOI Accesso ONLINE all'editore

M. Focardi; M.S. Gelli; E.N. Spadaro (2015). Monotonicity formulas for obstacle problems with Lipschitz coefficients. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, vol. 54, pp. 1547-1573, ISSN:0944-2669 DOI Accesso ONLINE all'editore

Matteo Focardi; Paolo Marcellini (2014). On the lower semicontinuity of quasiconvex integrals. BULLETIN OF INSTITUTE OF MATHEMATICS, ACADEMIA SINICA. NEW SERIES, vol. 9, pp. 245-265, ISSN:2304-7909

M. Focardi;N. Fusco;C. Leone;P. Marcellini;E. Mascolo;A. Verde (2014). Weak lower semicontinuity for polyconvex integrals in the limit case. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, vol. 51, pp. 171-193, ISSN:0944-2669 DOI Accesso ONLINE all'editore

Camillo De Lellis; Matteo Focardi; Berardo Ruffini (2014). A note on the Hausdorff dimension of the singular set for minimizers of the Mumford-Shah energy. ADVANCES IN CALCULUS OF VARIATIONS, vol. 7, pp. 539-545, ISSN:1864-8258 DOI Accesso ONLINE all'editore

Matteo Focardi; Flaviana Iurlano (2014). Asymptotic analysis of Ambrosio-Tortorelli energies in linearized elasticity. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, vol. 46, pp. 2936-2955, ISSN:0036-1410 DOI Accesso ONLINE all'editore

C. De Lellis; M. Focardi (2013). Higher integrability of the gradient for minimizers of the 2d Mumford-Shah energy. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, vol. 100, pp. 391-409, ISSN:1776-3371 DOI Accesso ONLINE all'editore

M. Focardi; E.N. Spadaro (2013). An intrinsic approach to manifold constrained variational problems. ANNALI DI MATEMATICA PURA ED APPLICATA, vol. 192, pp. 145-163, ISSN:0373-3114 DOI Accesso ONLINE all'editore

C. De Lellis; M. Focardi (2013). Density lower bound estimates for local minimizers of the 2d Mumford-Shah energy. MANUSCRIPTA MATHEMATICA, vol. 132, pp. 215-232, ISSN:0025-2611 DOI Accesso ONLINE all'editore

M. Focardi (2012). Vector-valued obstacle problems for non-local energies. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B., vol. 17, pp. 487-507, ISSN:1531-3492 DOI Accesso ONLINE all'editore

Matteo Focardi (2012). Gamma-convergence: a tool to investigate physical phenomena across scales. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol. 35, pp. 1613-1658, ISSN:0170-4214 DOI Accesso ONLINE all'editore

Matteo Focardi; Paolo Maria Mariano (2012). Analytical and geometrical problems in continuum mechanics. American Institute of Mathematical Sciences, pp. 445-733. Accesso ONLINE all'editore

Matteo Focardi (2012). Regularity issues for local minimizers of the Mumford & Shah energy in 2d. BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR, vol. 1, pp. 14-32, ISSN:2240-2829 Accesso ONLINE all'editore

Matteo Focardi; Paolo Maria Mariano (2012). Analytical and geometrical problems in continuum mechanics: Preface. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B., vol. 17, pp. i-v, ISSN:1531-3492 DOI Accesso ONLINE all'editore

M. Barchiesi; M. Focardi (2011). Homogenization of the Neumann problem in perforated domains: an alternative approach. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, vol. 42, pp. 257-288, ISSN:0944-2669 DOI Accesso ONLINE all'editore

C. De Lellis; M. Focardi; E.N. Spadaro (2011). Lower semicontinuous functionals for Almgren's multiple valued functions. ANNALES ACADEMIAE SCIENTIARUM FENNICAE. MATHEMATICA, vol. 36, pp. 393-410, ISSN:1239-629X DOI Accesso ONLINE all'editore

M. Focardi; M.S. Gelli; G. Pisante (2010). On a 1-capacitary type problem in the plane. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, vol. 9, pp. 1319-1334, ISSN:1534-0392 DOI Accesso ONLINE all'editore

M. Focardi (2010). Aperiodic fractional obstacle problems. ADVANCES IN MATHEMATICS, vol. 225, pp. 3502-3544, ISSN:0001-8708 DOI Accesso ONLINE all'editore

Matteo Focardi; Paolo Maria Mariano (2009). Discrete dynamics of complex bodies with substructural dissipation:variational integrators and convergence. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B., vol. 11, pp. 109-130, ISSN:1531-3492 DOI Accesso ONLINE all'editore

M.Focardi; M.S.Gelli; M.Ponsiglione (2009). Fracture mechanics in perforated domains: a variational approach for brittle porous media. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, vol. 19, pp. 2065-2100, ISSN:0218-2025 DOI Accesso ONLINE all'editore

M.Focardi (2009). Homogenization of random fractional obstacle problems via Gamma-convergence. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, vol. 34, pp. 1607-1631, ISSN:0360-5302 DOI Accesso ONLINE all'editore

Matteo Focardi; Paolo Maria Mariano (2008). Convergence of asynchronous variational integrators in linear elastodynamics. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, vol. 75, pp. 755-769, ISSN:0029-5981 DOI Accesso ONLINE all'editore

Matteo Focardi; Paolo Maria Mariano (2008). Convergence of AVI’s for the linear elastodynamics of simple bodies. In: IACM/ECCOMAS 2008, Venezia, 30 giugno - 4 luglio 2008, Iacm/Eccomas, pp. 1-10, ISBN:9788496736559

M. Focardi; M.S. Gelli (2008). RELAXATION OF FREE DISCONTINUITY ENERGIES WITH OBSTACLES. ESAIM. COCV, vol. 14, pp. 879-896, ISSN:1292-8119 DOI Accesso ONLINE all'editore

M. Focardi; A. Garroni (2007). A 1D phase macroscopic phase field model for dislocations anda second order Gamma-limit.. MULTISCALE MODELING & SIMULATION, vol. 6, pp. 1098-1124, ISSN:1540-3459 DOI Accesso ONLINE all'editore

Matteo Focardi; Paolo Maria Mariano (2007). Convergence of asynchronous variational integrators in linear elastodynamics. In: AIMETA 2007, BRESCIA, 11-14.09.07, Starrylink, vol. Aimeta 2007. Atti del 18º COngresso dell'Associazione italiana di meccanica teorica e applicata., pp. 1-8.

M. Focardi; M.S. Gelli (2007). Asymptotic analysis of the Mumford-Shah functional in periodically perforated domains.. INTERFACES AND FREE BOUNDARIES, vol. 9, pp. 107-132, ISSN:1463-9971 DOI Accesso ONLINE all'editore

M. Focardi (2007). Asymptotic analysis and relaxation of Mumford-Shah type energies with obstacles. In: ICIAM, ZURIGO (CH), 16-20.07.07, - WILEY-V C H VERLAG GMBH, PO BOX 10 11 61, WEINHEIM, GERMANY, D-69451 -Johann Ambrosius Barth:Prager Strasse 16 B, D-04103 Leipzig Germany:011 49 341 9781570, Fax: 011 49 341 9781575, vol. PAMM Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007, pp. 1150807-1150808. DOI Accesso ONLINE all'editore

M. Focardi; M.S. Gelli (2003). Approximation results by difference schemes of fracture energies: the vectorial case.. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, vol. 10, pp. 469-495, ISSN:1021-9722 DOI Accesso ONLINE all'editore

R. Alicandro; M. Focardi (2002). Variational approximation of free-discontinuity energies with linear growth. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, vol. 4, pp. 685-723, ISSN:0219-1997 DOI Accesso ONLINE all'editore

B. Bianconi; M. Focardi; E. Mascolo (2002). Existence of minimizers for a class of quasiconvex functionals with nonstandard growth. ANNALI DI MATEMATICA PURA ED APPLICATA, vol. 180, pp. 493-510, ISSN:0373-3114 DOI Accesso ONLINE all'editore

M. Focardi (2002). Variational approximation of vectorial free-discontinuity problems: the discrete and continuous case. (Tutor: Prof. Luigi Ambrosio)

M. FOCARDI (2001). ON THE VARIATIONAL APPROXIMATION OF FREE DISCONTINUITY PROBLEMS IN THE VECTORIAL CASE. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, vol. 11, pp. 663-684, ISSN:0218-2025 DOI Accesso ONLINE all'editore

M. Focardi; E. Mascolo (2001). Lower semicontinuity of quasiconvex functionals with nonstandard growth. JOURNAL OF CONVEX ANALYSIS, vol. 8, pp. 1-22, ISSN:0944-6532 Accesso ONLINE all'editore

R. Alicandro; M. Focardi; M.S. Gelli (2000). Finite-difference approximation of energies in fracture mechanics. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, vol. 29, pp. 671-709, ISSN:0391-173X Accesso ONLINE all'editore

M. Focardi (1997). Semicontinuity of vectorial functionalsin Orlicz-Sobolev spaces. RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE, vol. 29, pp. 141-161, ISSN:0049-4704 Accesso ONLINE all'editore

Matteo FOCARDI

Biography

** PERSONAL DATA 
 
name/surname: MATTEO FOCARDI 

birth place/date:  Firenze 27 Dicembre 1973, 

Italian citizenship 

position: Full Professor in Mathematical Analysis at Università di Firenze. 

address: DiMaI ``U. Dini'', V.le Morgagni 67/A, 50134, Firenze, Italy 

telefono/fax: +39-055-2751442, 

e-mail: matteo.focardi@unifi.it

homepage: https://people.dimai.unifi.it/focardi/index.html



** EDUCATION 
 
1998-2000: Perfezionamento in Matematica at Scuola Normale Superiore di Pisa, 
final grade: summa cum laude. Advisor Prof. Luigi Ambrosio, thesis title 
``Variational Approximation of Vectorial Free-Discontinuity Problems: the Discrete 
and the Continuous case'', defended on 14.06.02

1997: INdAM junior scholarship, courses held at Universita' di Roma ``La Sapienza''

1992-1996: Laurea in Matematica at Università di Firenze, final grade: summa cum laude. 
Advisor Prof. Elvira Mascolo, thesis title "Lower Semicontinuity of vector valued functionals in 
Orlicz-Sobolev spaces'', defended on 25.10.96


** POSITIONS

1.09.21-Present: Full Professor at the DiMaI, University of Florence,

2017: national Italian habilitation as Full Professor in Mathematical Analysis

1.11.14-30.08.21: Associate Professor at the DiMaI, University of Florence, 

2012: national Italian habilitation as Associate Professor in Mathematical Analysis

2003: postdoc position at MPI Leipzig, from  16.03.03 to 27.07.03

2000-2014: Assistant Professor at the Department of Mathematics 
of the University of Florence, since 1.09.00 to 31.10.14

Matteo FOCARDI

Curriculum

MATTEO FOCARDI'S CURRICULUM VITAE

Matteo Focardi, born in 1973 in Firenze (Italy), Italian citizen

** Positions

2021-today: Full Professor at the U. Firenze
2017: National Italian habilitation as Full Professor in Mathematical Analysis
2014-2021: Associate Professor at the U. Firenze
2000-2014: Research associate at the U. Firenze
2013: Research fellow at the Max Planck Institut für Mathematik in den Naturwissenschaften in Leipzig
2013: National Italian habilitation as Associate Professor in Mathematical Analysis
2003: Postdoc at the Max Planck Institut für Mathematik in den Naturwissenschaften in Leipzig
2002: Perfezionamento in Matematica (Ph.D.) at the Scuola Normale Superiore di Pisa
1996: Master Degree in Mathematics at the U. Firenze

** Teaching

I have been teaching since the a.y. 2000-01 in the ensuing Corsi di Laurea (undergraduate and/or master)
of the U. Firenze: Biotecnologie, Fisica, Matematica, Scienze Biologiche

* Ph.D. courses and schools
2021: “Γ-convergenza e applicazioni alla teoria dell’elasticità”, 20/40 ore, Dottorato in Matematica, Informatica e Statistica, DiMaI, U. Firenze, U. Perugia, INdAM.
2018: “An introduction to BV functions and Γ-convergence”, ModeMat - Escuela Politècnica Nacional, Quito (EC)
2014: “School on Free Discontinuity problems”, Centro De Giorgi Pisa
2008: “Una introduzione alla Γ-convergenza”, Dottorato in Matematica, Dipartimento di Matematica, U. Firenze

* Mentoring
2 Postdocs
1 Ph.D. student
3 master students
2 undergraduate students

** Research

I am (co-)author of about 50 papers published in international journals on Calculus of Variations, Geometric Measure Theory, and PDEs.

* Bibliometric information on my publications:
- 52 articles in scientific journals
- 2 articles in conference proceedings
- 1 chapter in collective volumes
- 1 editorial

* Citations (as of 18/02/2022):
- Scopus: 50 cited documents, 488 citations (h-index 13), 393 citations excluding self citations (h-index 10),
355 citations excluding self-citations of all authors (h-index 10)
- ISI Web of Knowledge: 44 cited documents, 414 citations (h-index 11), 267 citing articles,
353 citations excluding self-citations, 237 citing articles without self-citations
- MR Citation Database: 53 publications, 430 citations by 282 authors

* Main contributions
- Homogenization of non-local obstacle functionals
- Regularity for the jump set of Mumford-Shah (almost-)minimizers
- Phase-field approximation via Gamma-convergence of models in fracture mechanics
- Free boundary regularity for thin and thick obstacle problems

* Collaborators
M. Cicalese (TUM München), S. Conti (HCM Bonn), G. Cupini (U. Bologna), C. De Lellis (IAS Princeton),
N. Fusco (U. Napoli), A. Garroni (U. Roma La Sapienza), M.S. Gelli (U. Pisa), F. Iurlano (CNRS, Sorbonne U.),
F. Leonetti (U. L’Aquila), P. Marcellini (U. Firenze), P.M. Mariano (U. Firenze), E. Mascolo (U. Firenze), M. Ponsiglione (U. Roma La Sapienza), E. Spadaro (U. Roma La Sapienza), N. Van Goethem (U. Lisboa), C.I. Zeppieri (U. Münster)

* Scientific visits
- Universities: Zürich, Marne-la-Vallèe, Minnesota, Carnegie Mellon Univ. Pittsburgh, Roma Tor Vergata, EPFL Lausanne, Politécnica de Madrid, Napoli Federico II, Würzburg, Parma, The Univ. of Texas at Austin, Roma La Sapienza, TU München, Leipzig, Pavia, Torino, Univ. of Sussex

- Istitutions: Max Planck Institut für Mathematik in den Naturwissenschaften Leipzig, Centro De Giorgi Pisa, Hausdorff Center for Mathematics Bonn

* Workshops and invited talks (last 3 years)
2021:
- “On the regularity of singular sets of minimizers for the Mumford-Shah energy”, Regularity Theory for Free Boundary and Geometric Variational Problems, Levico Terme
- “On the regularity of singular sets of minimizers for the Mumford-Shah energy”, Nonlinear Potential Theoretic Methods in Partial Differential Equations, Banff, online meeting
- “On the regularity of singular sets of minimizers for the Mumford-Shah energy”, SIAM Conference on Mathematical Aspects of Materials Science - MS21, online meeting
- “On the regularity of singular sets of minimizers for the Mumford-Shah energy”, Seminario de Investigación del Centro de Modelización Matemática - Modemat de la EPN
- “On the regularity of singular sets of minimizers for the Mumford-Shah energy”, Mathematics Colloquium, Universität Münster
2020:
- “On the regularity of singular sets of minimizers for the Mumford-Shah energy”, Incontri di Analisi Matematica tra Firenze, Pisa e Siena, online meeting
2019:
- “How a minimal surface leaves a thin obstacle”, workshop “Modeling of Crystalline Interfaces and Thin Film Structures”, Erwin Schrödinger Institute, Wien
- “How a minimal surface leaves a thin obstacle”, workshop “Regularity aspects in linear growth problems”, Augsburg
- “How a minimal surface leaves a thin obstacle”, Turkey-Italy Colloquium on Applied Analysis and Differential Equations, Hacettepe U., Ankara
- “The measure and the structure of the free boundary in the lower dimensional obstacle problem”, Topics in Nonlinear Analysis and Calculus of Variations, U. Torino
- “The measure and the structure of the free boundary in the lower dimensional obstacle problem”, U. Pavia
- “How a minimal surface leaves a thin obstacle”, Levico Terme (TN)

* Organization of schools and workshops
2022:
- “Advances in Calculus of Variations”, Naples
2019:
- “Two days in CalcVar&PDEs”, Bologna
- “Geometric Measure Theory and Applications. From Geometric Analysis to Free Boundary Problems”, CIME Summer School, Cetraro
2018:
- “Workshop on dynamical systems, calculus of variations and control”, Firenze
2017:
- “New Trends on Calculus of Variations and PDE’s”, Firenze-Montecatini
- “Harnack’s inequalities and nonlinear operators”, Cortona
2009:
- “Workshop on Calculus of Variations and PDEs”, Firenze
2005:
- “Weekend di Calcolo delle Variazioni - Workshop a Firenze”, Firenze

* Coordination of research projects
- PRIN 2015 - “Calcolo delle Variazioni”, Firenze local unit coordinator (9.11.2017-5.02.20)
- Bando Ricerca Scientifica e Tecnologica 2020, Fondazione Cassa di Risparmio di Firenze -
“Struttura della frontiera libera per soluzioni di problemi di ostacolo sottile”, progetto individuale
- Bando Ricerca Scientifica e Tecnologica 2015, Ente Cassa di Risparmio di Firenze -
“Materiali intelligenti: l’analisi matematica al servizio delle applicazioni”, coordinatore negli a.a. 2017-2019
- GNAMPA 2020 - “Regolarità per problemi variazionali: vincoli unilaterali ed equazioni non uniformemente ellittiche”
- GNAMPA 2017 - “Regolarità per problemi variazionali d’ostacolo e libero”
- GNAMPA 2015 - “Regolarità per problemi di Analisi Geometrica e del Calcolo delle Variazioni”
- GNAMPA 2013 - “Semicontinuità e regolarità in problemi variazionali”
- GNAMPA 2013 - programma Professori Visitatori, guest Prof. E. Spadaro
- GNAMPA 2010 - “Semicontinuità di funzionali definiti su mappe multivoche, vettoriali e problemi collegati”

* Participation in research projects
- PRIN 2015 - “Calcolo delle Variazioni”
- PRIN 2010 - “Calcolo delle Variazioni”
- PRIN 2008 - “Equazioni ellittiche: problemi vettoriali e regolarità”
- PRIN 2006 - “Equazioni ellittiche e paraboliche: problemi vettoriali e regolarità”
- PRIN 2004 - “Calcolo delle variazioni: problemi vettoriali e regolarità”
- PRIN 2002 - “Equazioni e sistemi differenziali nonlineari degeneri: esistenza e regolarità”
- PRIN 2000 - “Calcolo delle Variazioni”
- GNAMPA 2019 - “Regolarità per equazioni non uniformemente ellittiche e nel Calcolo delle Variazioni”
- GNAMPA 2018 - “Regolarità per problemi ellittici e del calcolo delle variazioni: non convessi, discontinui, degeneri, singolari”
- GNAMPA 2016 - “Regolarità per problemi ellittici e di teoria geometrica della misura”
- GNAMPA 2014 - “Metodi variazionali per la meccanica e i materiali”
- GNAMPA 2012 - “Esistenza e regolarità per problemi vettoriali e variazionali”
- GNAMPA 2011 - “Regolarità per problemi variazionali non lineari e questioni connesse”
- GNAMPA 2008 - “Analisi di stati stazionari e fenomeni di evoluzione dissipativa nei corpi complessi”
- GNAMPA 2004 - “Tecniche di omogeneizzazione e metodi asintotici per problemi a scale multiple”
- GNAMPA 2003 - “Tecniche di omogeneizzazione e metodi asintotici per problemi a scale multiple”
- GNAMPA 2002 - “Tecniche di omogeneizzazione e metodi asintotici per problemi a scale multiple”

* Miscellaneous scientific activities
- I have participated in several committees of evaluation of Ph.D. candidates
- Referee for the ensuing journals: SIAM Journal on Mathematical Analysis, ESAIM COCV, DCDS-B, ZAMM, MMAS, Physica D,
IFB, JDE, Applicable Analysis, IFB, Calc. Var. & PDEs, CPDE, ARMA, Advances in Calculus of Variations, JFA, Annali della Scuola Normale Superiore di Pisa, The Proceedings of the Royal Society of Edinburgh: Section A, IMRN, Philosophical Transactions A, JNLS, Advances in Mathematics, Indiana University Mathematics Journal, Duke Mathematical Journal, Journal für die Reine und Angewandte Mathematik, AMPA, JEMS, Publications mathématiques de l’IHÉS, Mathematische Annalen, Journal de Mathématiques Pures et Appliquées.

** Service

* Ph.D. School in Mathematics, Computer Science and Statistics - U. Firenze, U. Perugia, INdAM
2021-today: Coordinator
2013-2021: Member of the board and Mathematics Curriculum Referent

* Corso di Laurea in Matematica
2016-2021: Gruppo del Riesame (coordinator)
2016-2021: Commissione Tesi
2016-2021: Commissione Compiti Didattici
2014-2015: Gruppo del Riesame (member)

* Mathematics and Computer Science Department
2018-2021: Commissione Internazionalizzazione
2012-today: Commissione Sicurezza

A complete an up-to-dated version of the CV can be found at the link 
https://people.dimai.unifi.it/focardi/curriculum/Focardi_Vitae.pdf

Matteo FOCARDI

Interest

My research is devoted to Calculus of Variations and Geometric Measure Theory.

I first studied both the lower semicontinuity properties of integral functionals

having non-standard growth and the asymptotic analysis by means of

Gamma-convergence of some variational problems coming from applied sciences.

In particular, in my PhD Thesis I focused on the variational approximation of

free-discontinuity problems for vector valued maps, both in a discrete and a continuous setting.

My interests were then driven towards naturally related homogenization and relaxation

problems.

More recently, apart from continuing the issues quoted above, I started to investigate new topics:

(i) convergence problems for variational numerical schemes,

(ii) homogenization for obstacle problems for non-local energies,

(iii) lower semicontinuity properties for quasiconvex energies defined on Sobolev maps

taking values in non-flat spaces,

(iv) regularity properties for minimizers of the Mumford-Shah energy,

(v) regularity properties for solutions of the classical obstacle problems in case

the matrix of the coefficients of the relevant quadratic form is only Lipschitz continuous,

(vi) lower semicontinuity properties for non-coercive polyconvex energies in the limit case

for the admissible weak topology,

(vii) variational approximation of cohesive fracture (type) models in Fracture Mechanics and

related issues,

(viii) abstract regularity results, i.e. stratification of the singular set for solutions to

variational problems or of PDEs arising in problems of geometric analysis,

(ix) a variational approach to Weiss' epiperimetric inequality for obstacle problems,

(x) regularity for minimizers of the thin obstacle problems.

In addition, I wrote an up-to-date survey paper on $Gamma$-convergence theoryand a survey paper on some sharp regularity properties for local minimizers of the Mumford-Shah energy. Moreover, a simplied proof of a classical lower semicontinuity result dating back to Morrey has been provided.

I am author of about fifty research papers published on international journals.