Andrea Braides

Professor in Mathematical Analysis

Born in Udine on April 12, 1961

 Course `Local minimization, Variational Evolution and Gamma-convergence'

A handbook of Gamma-convergence

Course `From Discrete Systems to Continuum Problems' (Würzburg 2012) - LECTURE NOTES  (will be update as I find mistakes/misprints)

Mini-course `Homogenization of Lattice systems' (INdAM, Rome 2005) - LECTURE NOTES

 Course `From Discrete Systems to Continuous Variational Problems' (Utah 2005) - LECTURE NOTES

Research areasCalculus of Variations, Gamma-convergence, Homogenization, Discrete Variational Problems, Fracture Mechanics, Image Processing, Geometric Measure Theory 

Previous positions:
Associate Professor at SISSA, Trieste 1995-2000
Associate Professor at the University of Brescia, 1992-1995
`Ricercatore' at the University of Brescia, 1988-1992
(`Servizio civile', 1986-1988)
Contract Professor at the University of Udine, 1985-1986
`Perfezionando'(Ph D, adviser E. De Giorgi) at Scuola Normale Superiore, Pisa, 1983-1985
`Laurea' in Mathematics at the University of Pisa, 1983

Visiting positions:
Tata Institute of Fundamental Research, Bangalore, India (1994, 2004), Max-Planck Institute for Mathematics in the Sciences, Leipzig (1998), University of Minnesota, Dept. Aerospace Engr. Mech. (1998), CalTech, Pasadena (1998, 2003,2004), Centre Emile Borel, Paris (1998), Carnegie-Mellon University, Pittsburgh (1999, 2003), Isaac Newton Institute, Cambridge (1999), University Paris VI and XIII (2000, 2001 and 2002), Stanford University (Timoshenko Visiting Scholar 2004), Oxford Mathematical Institute and Mansfield College 2013-2014 (Visiting Professorship and College Fellowship), TU Munich 2015 (von Neumann Professorship).

Ph.D. Theses (Adviser)
R. Alicandro. Approximation of Free-Discontinuity Problems (SISSA, 1999)
M.S. Gelli. Variational Limits of Discrete Systems (SISSA, 1999)
N. Ansini. Homogenization Problems for Multi-dimensional and Multi-scale Structures (SISSA, 2000)
M.Cicalese. Multi-scale analysis for variational problems arising from discrete systems (University of Naples `Federico II', 2003)
C.I Zeppieri Multi-scale analysis via Gamma-convergence (Universita' di Roma La Sapienza, 2006)
L. Sigalotti.
Asymptotic analysis of discrete systems with complex interfacial interactions (Sapienza Universita' di Roma, 2010)
G. Scilla Variational motion of discrete interfaces (Sapienza Universita' di Roma)
V. Vallocchia. (Università di Roma Tor Vergata) ongoing
L. Kreutz. (GSSI, L'Aquila) ongoing

I also had the pleasure of collaborating to the following theses:
M. Solci  A Variational Model for Phase Separation (Pavia 2003, adviser E.Vitali).

Editorial Board:

Networks and Heterogeneous Media
Archive for Rational Mechanics and Analysis

Mathematics and Mechanics of Complex Systems

Journal de l'Ecole Polytechnique

Encyclopedia of Mathematical Physics

Some Publications
(see also my web page at Scuola Normale Superiore, Pisa)

Books and Lecture Notes

A. Braides.
An Introduction to Homogenization and Gamma-convergence.
In:  G. Allaire, A. Braides, G. Buttazzo, A. Defranceschi, L.V. Gibiansky.
School on Homogenization. Lecture Notes of the Courses held at ICTP,
Trieste, 4--17 September 1993


A. Braides and A. Defranceschi.
Homogenization of Multiple Integrals
Oxford University Press, Oxford, 1998.

A. Braides. 
Approximation of Free-Discontinuity Problems
Lecture Notes in Mathematics No. 1694, Springer Verlag, Berlin, 1998.
LNM 1694      LNM1694

A. Braides and M.S. Gelli.
From Discrete to Continuum: a Variational Approach.
Lecture Notes. SISSA, Trieste, 2000.(file pdf)

A. Braides
Gamma-convergence for Beginners.
Oxford University Press, 2002

A. Braides
From discrete to continuous variational problems: an introduction
Lecture Notes. School on Homogenization Techniques and Asymptotic Methods for Problems with Multiple Scales.
Torino, September 2001

appeared as part of

A. Braides and M.S. Gelli.
From discrete systems to continuous variational problems: an introduction.
Topics on concentration phenomena and problems with multiple scales, 3--77, Lect. Notes Unione Mat. Ital., 2, Springer, Berlin, 2006.

A. Braides
A handbook of Gamma-convergence
in Handbook of Differential Equations. Stationary Partial Differential Equations, Volume 3 (M. Chipot and P. Quittner, eds.) Elsevier 2006.

A. Braides
Local minimization, Variational Evolution and Gamma-convergence
Lecture Notes in Mathematics No. 2094, Springer Verlag, Berlin, 2013
LNM 2094

Editorial Activity

Topics on concentration phenomena and problems with multiple scales.
Edited by Andrea Braides and Valeria Chiadò Piat.
Lecture Notes of the Unione Matematica Italiana, 2.
Springer-Verlag, Berlin, 2006. xii+316

Recent Papers (see also my web page at CVGMT)


Picture Gallery