Noncompact Problems at the Intersection of Geometry, Analysis, and Topology

Conformal deformations of Riemannian metrics via "critical point theory at infinity": The conformally flat case with umbilic boundary by M. O. Ahmedou Cubic quasilinear wave equation and bilinear estimates by H. Bahouri and J.-Y. Chemin Ginzburg-Landau functionals, phase transitions and vorticity by F. Bethuel and G. Orlandi On the topology of conformally compact Einstein 4-manifolds by S.-Y. A. Chang, J. Qing, and P. Yang On loop spaces of configuration spaces, and related spaces by F. R. Cohen Global energy minimizers for free boundary problems and full regularity in three dimensions by L. A. Caffarelli, D. Jerison, and C. E. Kenig Stability and instability of the Reissner-Nordstrom Cauchy horizon and the problem of uniqueness in general relativity by M. Dafermos Nonlinear elliptic equations of critical Sobolev growth from a dynamical viewpoint by E. Hebey Hamiltonian formalisms for multidimensional calculus of variations and perturbation theory by F. Helein Revisit the topology of Sobolev maps by F. H. Lin Review on blow up and asymptotic dynamics for critical and subcritical gKdV equations by Y. Martel and F. Merle Recent advances in the global theory of constant mean curvature surfaces by R. Mazzeo On some properties of $S^1$-valued fractional Sobolev spaces by P. Mironescu Homoclinics for a semilinear elliptic PDE by P. H. Rabinowitz Vortices for Ginzburg-Landau equations: With magnetic field versus without by S. Serfaty and E. Sandier Some regularity problems of stationary harmonic maps by G. Tian.