Monday May 18, PUC, sala 1 Matematicas

16h

Jun Yang (Central China Normal University)

Vortex structures for maps from pseudo-Euclidean spaces

For some geometric flows (such as wave map equations, Schrödinger flows) from pseudo-Euclidean spaces to a unit sphere contained in a three dimensional Euclidean space, we construct solutions with various vortex structures(vortex pairs, vortex circles and helices). The approaches base on the transformations associated with the symmetries of the nonlinear problems, which will lead to two dimensional elliptic problems with resolution theory given by the finite dimensional Lyapunov-Schmidt reduction method in nonlinear analysis.

16h50

Weiwei Ao (University of British Columbia)

Refined Finite-dimensional Reduction Method and Applications to Nonlinear Elliptic Equations

I will talk the refined finite dimensional reduction method and its application to nonlinear elliptic equations. We use this refined reduction method to get optimal bound on the number of interior spike solutions of the singularly perturbed Neumann problem as well as the boundary spike solutions. I will also talk about the entire solutions for nonlinear Schrodinger equations.