Summer School , Pisa, May 2014

Scientific and Organizing Committee

Andrew Comech, Scipio Cuccagna, Vladimir Georgiev, Atanas Stefanov, Nicola Visciglia

and Anna Rita Giammetta

Objectives and Format







To provide an up-to-date intensive course on methods to establish stability of solitary waves for Schrodinger and wave type equations. The equations and models of this type have important applications in different fields: quantum mechanics, biology, medicine. The main goal of the school is to introduce Master Degree Students and PhD Students to the main math tools to study the asymptotic behavior (stability and instability) of the solitary and traveling wave and to have contact and to make mini projects in collaboration with established specialists in the field from Europe, USA and Japan.

· Target group

the Course is oriented preferentially to students and PhD students in Mathematics and Physics.


Weak for possible preliminary work on arguments supposed to be known: 12-17 May 2014, arguments supposed to be known:  Linear, nonlinear stability for ordinary differential equations and classical fields modeled with evolution partial differential equations, asymptotic stability and a priori estimates to establish asymptotic stability, spectral theory.

Intensive week: Daily intensive lecturing (6 hours / day from May 19th to May 23th, Monday to Friday), among lecturer: Michael Sigal, Andrew Comech, Dmitry Pelinovsky.

Workshop week: Daily intensive lecturing from May 26th to May 30th.

Week of individual work on suggesting and introducing to some concrete mini projects: individual work with tutors in the week 2-6 June.

The school will provide total number of lectures - 36 and an overall number of 6 credits (after attendance of the overall Course and submission of a project within December 31st, 2014 with evaluation by a memeber of the scientific comeetee of the Workshop). Partial attendance to the Course will give right to a number of credits proportionally reduced.


Among lecturer: Israel Sigal, Andrew Comech, Claude Zuily, Dmitry Pelinovsky and Alim Sukhtayev.

Lecture Notes:

Lecture Notes of prof. Israel Michael Sigal

Sigal: Lectures on Mean Curvature Flow

Sigal: On Singularity Formation Under Mean Curvature

Sigal: Magnetic Vortices, Nielsen-Olesen - Nambu
Strings and Abrikosov Lattices

Lecture Notes of prof. Andrew Comech Lecture Notes of prof. Andrew Comech
Lecture Notes of prof. Dmitri Pelinovski Lecture Notes of prof. Pelinovski
Lecture Notes of prof. Claude Zuily: Zuily: Le systeme de ondes de surface


Some funds are available to offer financial support to a limited number of selected students (up to 20 in shared double rooms) and young researchers (post-docs in studios for two persons). Deadline for application is 11 April 2014.

In order to apply, please send:

  • your curriculum vitae
  • your publication list
  • a recommendation letter(optional)


Centro di Ricerca Matematica Ennio De Giorgi
Collegio Puteano, Scuola Normale Superiore
Piazza dei Cavalieri, 3
I - 56100 PISA

Your C.V. and the publication list can also be sent by e-mail to the address:

In order to complete the financial support form you can go to the page financial support of Centro di Ricerca Matematica Ennio De Giorgi.





Partially supported by Contract FIRB "Dinamiche Dispersive: Analisi di Fourier e Metodi Variazionali.", 2012, NSF Contract No. 1419217, Centro di Ricerca Matematica Ennio De Giorgi, Universita' di Pisa and and Comenius project "Dynamat" 2010