PIMS 20th Anniversary Celebration at the University of Calgary

In this talk I will explain basic ideas concerning fractional Laplacians (in particular, their relation with Lévy flights in Probability) and I will present the essential tools to treat nonlinear equations involving fractional Laplacians and other integro-differential operators. We will review their Lagrangian and Hamiltonian structures -- two important tools in the study of fractional semilinear elliptic equations. The last part of the talk will concern fractional perimeters and nonlocal minimal surfaces -- a fractional extension of the classical theory of minimal surfaces.