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.
