The Conference on Special Metrics in Complex Geometry will be held at Florida International University from January 7-10, 2021. Complex manifolds are higher-dimensional surfaces that are defined using the complex numbers. Recently, there has been significant progress in the study of "metrics" on complex manifolds, objects that endow these spaces with a shape or more precisely, curvature. The study of these metrics lies at the nexus of complex geometry and geometric analysis. The aim of this conference is to gather together experts working in these two fields to discuss these new and exciting developments. Even though lately there have been many conferences in complex geometry, none have really been organised to address these recent discoveries. This conference serves to fulfill this necessity. In doing so, it will promote collaboration across many areas of the aforementioned fields of complex geometry and geometric analysis. The latest breakthroughs in these two fields will be presented to a new generation of mathematicians, with a particular emphasis on women and those from minority groups. The conference will provide a forum for senior mathematicians to interact with graduate students through the organisation of an optional poster presentation for graduate students which will take place in a non-intimidating and relaxed environment. Ample opportunity will also be provided to women speakers to present their research, with at least one talk per day scheduled for a female speaker. Moreover, the conference will provide a platform for postdocs and junior researchers to present their work. Participants will be brought up-to-date with all of the current developments in the field and will be presented with new avenues of research in the enticing environment that Miami provides in the Winter. More specifically, the Conference on Special Metrics in Complex Geometry will concentrate on the interplay between complex geometry and geometric analysis, with an emphasis being given to equations arising in the construction of hermitian and Kahler metrics with prescribed curvature properties, for example, the complex Monge-Ampere equation in Kahler geometry. These equations are among the most important appearing in geometric analysis and understanding their structure and the techniques involved in their solution are paramount for further progress in the field. Recent breakthroughs include, among others, the independent construction of non-flat Ricci-flat Kahler metrics with maximal volume growth on complex affine space of dimensions three and greater by Li, Conlon-Rochon, and Szekelyhidi, the construction of new examples of gradient expanding and steady Kahler-Ricci solitons by Conlon-Deruelle and Biquard-Macbeth respectively, the solution by Chen-Cheng of a major conjecture of Tian stating the equivalence between the existence of constant scalar curvature Kahler metrics on a compact Kahler manifold and the properness of Mabuchi's K-energy, and the recent families of Ricci-flat Kahler metrics exhibited by Hein-Sun-Viaclovsky-Zhang on K3 surfaces which collapse to an interval with Tian-Yau and Taub-NUT metrics occurring as bubbles. These topics will all form part of the conversation at the conference in January 2021. More details will be available at http://faculty.fiu.edu/~rconlon/conference.htmThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
