Trends in Mathematics / Extended Abstracts Fall 2013

Part I: Conference on Geometrical Analysis.- Foreword.- A Positive Mass Theorem in Three Dimensional Cauchy-Riemann Geometry.- On the Rigidity of Gradient Ricci Solitons.- Geometric Structures Modeled on Affine Hypersurfaces and Generalizations of the Einstein-Weyl and Affine Sphere Equations.- Submanifold Conformal Invariants and a Boundary Yamabe Problem.- Variation of the Total Q-Prime Curvature in CR Geometry.- Conformal Invariants from Nullspaces of Conformally Invariant Operators.- Rigidity of Bach-Flat Manifolds.- Uniformizing Surfaces with Conical Singularities.- Recent Results and Open Problems on Conformal Metrics on Rn with Constant Q-Curvature.- Isoperimetric Inequalities for Complete Proper Minimal Submanifolds in Hyperbolic Space.- Total Curvature of Complete Surfaces in Hyperbolic Space.- Constant Scalar Curvature Metrics on Hirzebruch Surfaces.- Isoperimetric Inequalities for Extremal Sobolev Functions.- Part II: Type Theory, Homotopy Theory and Univalent Foundations.- Foreword.- Univalent Categories and the Rezk Completion.- Covering Spaces in Homotopy Type Theory.- Towards a Topological Model of Homotopy Type Theory.- Made-to-Order Weak Factorization Systems.- A Descent Property for the Univalent Foundations.- Classical Field Theory via Cohesive Homotopy Types.- How Intensional is Homotopy Type Theory.