Abstract: 

In this talk, we explore the asymptotic behavior of sphere-valued Sobolev maps as their p-energy approaches the critical Sobolev exponent. Based on a recent work joint with Mattia Freguglia and Nicola Picenni, we show compactness and Gamma-convergence of the p-energy to the area functional of the suitable dimension. Our result establishes the analog for the p-energy of a celebrated work by Alberti, Baldo, and Orlandi for the Ginzburg-Landau energy in general dimension and codimension.