The two parts of the present volume contain extended conference abstracts corresponding to selected talks given by participants at the "Conference on Geometric Analysis" (thirteen abstracts) and at the "Conference on Type Theory, Homotopy Theory and Univalent Foundations" (seven abstracts), both held at the Centre de Recerca Matemàtica (CRM) in Barcelona from July 1st to 5th, 2013, and from September 23th to 27th, 2013, respectively. Most of them are brief articles, containing preliminary presentations of new results not yet published in regular research journals. The articles are the result of a direct collaboration between active researchers in the area after working in a dynamic and productive atmosphere.
The first part is about Geometric Analysis and Conformal Geometry; this modern field lies at the intersection of many branches of mathematics (Riemannian, Conformal, Complex or Algebraic Geometry, Calculus of Variations, PDE's, etc) and relates directly to the physical world, since many natural phenomena posses an intrinsic geometric content. The second part is about Type Theory, Homotopy Theory and Univalent Foundations.
The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.
Author(s): M. del Mar González, P. C. Yang, N. Gambino, J. Kock (eds.)
Series: Research Perspectives CRM Barcelona (Trends in Mathematics) 3
Publisher: Birkhaüser
Year: 2015
Language: English
Pages: vi, 110
City: Basel
Front Matter ....Pages i-vi
Front Matter ....Pages 1-2
A Positive Mass Theorem in Three Dimensional Cauchy–Riemann Geometry (Jih-Hsin Cheng, Andrea Malchiodi, Paul Yang)....Pages 3-8
On the Rigidity of Gradient Ricci Solitons (Manuel Fernández-López, Eduardo García-Río)....Pages 9-13
Geometric Structures Modeled on Affine Hypersurfaces and Generalizations of the Einstein–Weyl and Affine Sphere Equations (Daniel J. F. Fox)....Pages 15-19
Submanifold Conformal Invariants and a Boundary Yamabe Problem (A. Rod Gover, Andrew Waldron)....Pages 21-26
Variation of the Total Q-Prime Curvature in CR Geometry (Kengo Hirachi)....Pages 27-29
Conformal Invariants from Nullspaces of Conformally Invariant Operators (Dmitry Jakobson)....Pages 31-33
Rigidity of Bach-Flat Manifolds (Seongtag Kim)....Pages 35-39
Uniformizing Surfaces with Conical Singularities (Andrea Malchiodi)....Pages 41-44
Recent Results and Open Problems on Conformal Metrics on ℝn with Constant Q-Curvature (Luca Martinazzi)....Pages 45-49
Isoperimetric Inequalities for Complete Proper Minimal Submanifolds in Hyperbolic Space (Sung-Hong Min, Keomkyo Seo)....Pages 51-55
Total Curvature of Complete Surfaces in Hyperbolic Space (Jun O’Hara, Gil Solanes)....Pages 57-59
Constant Scalar Curvature Metrics on Hirzebruch Surfaces (Nobuhiko Otoba)....Pages 61-66
Isoperimetric Inequalities for Extremal Sobolev Functions (Jesse Ratzkin, Tom Carroll)....Pages 67-71
Front Matter ....Pages 73-74
Univalent Categories and the Rezk Completion (Benedikt Ahrens, Krzysztof Kapulkin, Michael Shulman)....Pages 75-76
Covering Spaces in Homotopy Type Theory (Kuen-Bang Hou)....Pages 77-82
Towards a Topological Model of Homotopy Type Theory (Paige North)....Pages 83-86
Made-to-Order Weak Factorization Systems (Emily Riehl)....Pages 87-92
A Descent Property for the Univalent Foundations (Egbert Rijke)....Pages 93-97
Classical Field Theory via Cohesive Homotopy Types (Urs Schreiber)....Pages 99-103
How Intensional Is Homotopy Type Theory? (Thomas Streicher)....Pages 105-110
Erratum to: Univalent Categories and the Rezk Completion (Benedikt Ahrensm, Krzysztof Kapulkin, Michael Shulman)....Pages E1-E1
