Collaborators: Paolo Baroni (Uppsala), Alessio Figalli (Austin), Giovanni Franzina (Erlangen), Tuomo Kuusi (Aalto University), Adriano Pisante (Sapienza Roma), Yannick Sire (LATP Marseille), Enrico Valdinoci (WIAS Berlin)

Visitors:

- Manuel Del Pino (Universidad de Chile), Pisa, February 17-23, 2014, [Talk: Examples of fractional minimal surfaces, February 20, 2014]

- Maria del Mar Gonzalez (UPC Barcelona), Pisa, February 16-23, 2014, [Talk: The CR fractional Laplacian, February 21, 2014]

- Adriano Pisante (Sapienza Universita di Roma), Parma, May 15-16, 2013 [Talk: Improved Sobolev embeddings and concentration-compactness for fractional Sobolev spaces, May 16, 2013]

- Yannick Sire (LATP Marseille), SISSA, Jan 14-22, 2014 [Talk: Non local phase transitions and a non local version of De Giorgi conjecture, Jan 15, 2014]

- Enrico Valdinoci (WIAS Berlin), Pisa, February 18-22, 2014 [Talk: Dislocation dynamics in crystals, February 21, 2014]

Visiting:

- Paolo Baroni in Mittag-Leffler Institut, Stockholm, November 29 - December 13, 2013
- Tuomo Kuusi in Aalto University, Helsinki, April 7-16, 2014

Events:

- Workshop on Partial Differential Equations and Applications, University of Pisa, February 20-21, 2014

Seminars:

- Serena Dipierro, Seminar on Differential Geometry and Analysis, Institut fur Analysis und Numerik, Magdeburg, Germany [Talk: Asymptotics of the nonlocal perimeter functionals, May 13, 2013]

- Serena Dipierro, Department of Mathematics, University of Padova, Italy, [Talk: Asymptotics of fractional perimeter functionals, May 22, 2013]

- Serena Dipierro, Spring School "Rate-independent evolutions and hysteresis modelling", Politecnico di Milano and University of Milano, Italy, [Talk: Asymptotics of fractional perimeter functionals, May 27, 2013]

- S. Dipierro, G. Palatucci: Asymptotics of the nonlocal perimeter functionals - Recent advances in partial differential equations and applications, Milano, June 17--22, 2013. Also, in SIAM@PoliMI, Politecnico di Milano, June 28, 2013 -
*poster here*

- Serena Dipierro, Summer School "Non local equations of elliptic type", Palazzone di Cortona, Italy, [Talk: Asymptotics of fractional perimeter functionals, Jul 3, 2013]

- Giampiero Palatucci, “Mathematical Analysis, Modelling, and Applications”, SISSA, Trieste, Italy, [Talk: Improved Sobolev embeddings and concentration-compactness for fractional Sobolev spaces, Jul 12, 2013]
- Giampiero Palatucci, “Mathematical Congress of the Americas 2013”, Guanajuato, Mexico, [Talk: Improved Sobolev embeddings and concentration-compactness for fractional Sobolev spaces, Aug 8, 2013]

- Serena Dipierro, Seminario Ecuaciones en Derivadas Parciales, Universidad de Chile, Santiago, Chile, [Talk: Asymptotics of a reaction-diffusion equation driven by the fractional Laplacian, Aug 14, 2013]

- Giampiero Palatucci, Dipartimento di Matematica, Università di Trento, Italy, [Talk: Disuguaglianze di Sobolev migliorate e concentrazione-compattezza per spazi di Sobolev frazionari, Nov 18, 2013]

- Serena Dipierro, Seminar on Differential Geometry and Analysis, Universidad Autonoma de Madrid, Spain [Talk: Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting, Dec 11, 2013]

- Giampiero Palatucci, Junior Analysis Seminars, SISSA, Trieste, Italy [Talk: Nonlocal perimeter functionals, Feb 5, 2014]
- Serena Dipierro, Analysis Seminars, School of Mathematics, University of Edinburgh [Talk: Dislocation dynamics in crystals, Feb 10, 2014]

- Giampiero Palatucci, Seminario di Equazioni Differenziali, Università di Tor Vergata, Roma, Italy [Talk: Sul comportamento locale delle estremali degli integrali non locali, Apr 8, 2014]

- G. Palatucci, School of Science, Aalto University, Helsinki, Finland [Talk: Nonlocal perimeter functionals, Apr 14, 2014]

Pubblications:

- J. Davila, M. del Pino, S. Dipierro, E. Valdinoci: Concentration phenomena for the nonlocal Schrodinger equation with Dirichlet datum -
*preprint here* - A. Di Castro, T. Kuusi, G. Palatucci: Local behavior of fractional $p$-minimizers -
*preprint here*

- A. Di Castro, T. Kuusi, G. Palatucci: Nonlocal Harnack inequalities -
*preprint here*

- S. Dipierro: Asymptotics of fractional perimeter functionals -
*preprint here* - S. Dipierro, A. Figalli, E. Valdinoci: Strongly nonlocal dislocation dynamics in crystals -
*Comm. Partial Differential Equations*-*preprint here**.*

- S. Dipierro, G. Palatucci, E. Valdinoci: Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting -
*Comm. Math. Phys.*-*preprint here**.*

- G. Franzina, G. Palatucci: Fractional $p$-eigenvalues -
*Riv. Mat. Univ. Parma -**preprint here*

- G. Palatucci, A. Pisante: Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces -
*Calc. Var. Partial Differential Equations*-*preprint here* - G. Palatucci, A. Pisante, Y. Sire: Subcritical approximation of Yamabe type non local equation: a Gamma-convergence approach -
*Ann. Sc. Norm. Super. Pisa Cl. Sci.*-*preprint here*

- S. Dipierro, O. Savin, E. Valdinoci: All functions are locally $s$-harmonic up to a small error -
*preprint here*