Brian Freidin

Brown University; Visitor, School of Mathematics

December 11, 2018

In the 90's, Gromov and Schoen introduced the theory of

harmonic maps into singular spaces, in particular Euclidean buildings,

in order to understand p-adic superrigidity. The study was quickly

generalized in a number of directions by a number of authors. This

talk will focus on the work initiated by Korevaar and Schoen on

harmonic maps into metric spaces with curvature bounded above in the

sense of Alexandrov. I will describe the variational characterization

of harmonic maps into such spaces, some analytic consequences, and in

particular a Bochner formula capturing the role of both the domain and

target curvatures

harmonic maps into singular spaces, in particular Euclidean buildings,

in order to understand p-adic superrigidity. The study was quickly

generalized in a number of directions by a number of authors. This

talk will focus on the work initiated by Korevaar and Schoen on

harmonic maps into metric spaces with curvature bounded above in the

sense of Alexandrov. I will describe the variational characterization

of harmonic maps into such spaces, some analytic consequences, and in

particular a Bochner formula capturing the role of both the domain and

target curvatures