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Extended Abstracts Fall 2013

Geometrical Analysis; Type Theory, Homotopy Theory and Univalent Foundations

  • Conference proceedings
  • © 2015

Overview

Editors:
  1. Maria del Mar González

    1. Departament de Matemàtica Aplicada, Universitat Politècnica de Catalunya, Barcelona, Spain

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  2. Paul C. Yang

    1. Department of Mathematics, Princeton University, Princeton, USA

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  3. Nicola Gambino

    1. School of Mathematics, University of Leeds, Leeds, United Kingdom

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  4. Joachim Kock

    1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain

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Part of the book series: Trends in Mathematics (TM)

Part of the book sub series: Research Perspectives CRM Barcelona (RPCRMB)

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Table of contents (21 papers)

  1. Front Matter

    Pages i-vi
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  2. Geometrical Analysis

    1. Front Matter

      Pages 1-2
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    2. A Positive Mass Theorem in Three Dimensional Cauchy–Riemann Geometry

      • Jih-Hsin Cheng, Andrea Malchiodi, Paul Yang
      Pages 3-8

    3. On the Rigidity of Gradient Ricci Solitons

      • Manuel Fernández-López, Eduardo García-Río
      Pages 9-13

    4. Geometric Structures Modeled on Affine Hypersurfaces and Generalizations of the Einstein–Weyl and Affine Sphere Equations

      • Daniel J. F. Fox
      Pages 15-19

    5. Submanifold Conformal Invariants and a Boundary Yamabe Problem

      • A. Rod Gover, Andrew Waldron
      Pages 21-26

    6. Variation of the Total Q-Prime Curvature in CR Geometry

      • Kengo Hirachi
      Pages 27-29

    7. Conformal Invariants from Nullspaces of Conformally Invariant Operators

      • Dmitry Jakobson
      Pages 31-33

    8. Rigidity of Bach-Flat Manifolds

      • Seongtag Kim
      Pages 35-39

    9. Uniformizing Surfaces with Conical Singularities

      • Andrea Malchiodi
      Pages 41-44

    10. Recent Results and Open Problems on Conformal Metrics on ℝn with Constant Q-Curvature

      • Luca Martinazzi
      Pages 45-49

    11. Isoperimetric Inequalities for Complete Proper Minimal Submanifolds in Hyperbolic Space

      • Sung-Hong Min, Keomkyo Seo
      Pages 51-55

    12. Total Curvature of Complete Surfaces in Hyperbolic Space

      • Jun O’Hara, Gil Solanes
      Pages 57-59

    13. Constant Scalar Curvature Metrics on Hirzebruch Surfaces

      • Nobuhiko Otoba
      Pages 61-66

    14. Isoperimetric Inequalities for Extremal Sobolev Functions

      • Jesse Ratzkin, Tom Carroll
      Pages 67-71

  3. Type Theory, Homotopy Theory, and Univalent Foundations

    1. Front Matter

      Pages 73-74
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    2. Univalent Categories and the Rezk Completion

      • Benedikt Ahrens, Krzysztof Kapulkin, Michael Shulman
      Pages 75-76

    3. Covering Spaces in Homotopy Type Theory

      • Kuen-Bang Hou
      Pages 77-82

    4. Towards a Topological Model of Homotopy Type Theory

      • Paige North
      Pages 83-86

    5. Made-to-Order Weak Factorization Systems

      • Emily Riehl
      Pages 87-92
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Keywords

About this book

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.

Editors and Affiliations

  • Departament de Matemàtica Aplicada, Universitat Politècnica de Catalunya, Barcelona, Spain

    Maria del Mar González

  • Department of Mathematics, Princeton University, Princeton, USA

    Paul C. Yang

  • School of Mathematics, University of Leeds, Leeds, United Kingdom

    Nicola Gambino

  • Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain

    Joachim Kock

Bibliographic Information

  • Book Title: Extended Abstracts Fall 2013

  • Book Subtitle: Geometrical Analysis; Type Theory, Homotopy Theory and Univalent Foundations

  • Editors: Maria del Mar González, Paul C. Yang, Nicola Gambino, Joachim Kock

  • Series Title: Trends in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-21284-5

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Softcover ISBN: 978-3-319-21283-8Published: 13 November 2015

  • eBook ISBN: 978-3-319-21284-5Published: 12 November 2015

  • Series ISSN: 2297-0215

  • Series E-ISSN: 2297-024X

  • Edition Number: 1

  • Number of Pages: VI, 110

  • Topics: Differential Geometry, Algebraic Topology

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