Conference: Canonical Metrics in Differential Geometry

This award provides support for participants of the workshop Canonical Metrics in Differential Geometry, hosted at the University of Wisconsin-Madison in April 2025. Differential geometry is a branch of mathematics that studies the local and global shapes of spaces using various approaches such as analytic methods, metric methods, algebraic methods, and more.

The workshop will primarily focus on several active topics in this subject. This event seeks to establish several major scientific goals. First, it will bring leading specialists from different subject areas together and the participants will discuss recent groundbreaking results in the field.

Second, the workshop will provide an opportunity for graduate students and junior researchers in neighboring institutions to explore forefront outstanding questions and new technical tools. Third, the proposed expository lecture will help undergraduate students of the hosting institution, local high school students and general audience to understand current status and global pictures of several cutting-edge research fields, sparking interests in overall STEM fields.

The workshop will feature long and short research talks at various levels, as well as an expository lecture. The proposed workshop will be incubating new research activities and educating interested personnel of all backgrounds in the Midwest area.

The specific emphasis of the workshop will be on the canonical metrics of smooth and non-smooth spaces, which arise in various contexts of geometry. In addition to numerous substantial breakthroughs, the active and intensive study of canonical metrics has been stimulating entirely novel techniques, which have, in turn, opened up new directions for research.

The main research topics of the workshop include Einstein metrics, the Ricci flow and Ricci solitons, canonical metrics in complex geometry and conformal geometry. The workshop will also provide an environment and support for interdisciplinary communication in differential geometry. Investigations from different perspectives may inspire significant developments in the subjects and generate interesting open problems.

An overall goal of the workshop is to create a welcoming environment for sharing new ideas and tools, highlighting important progress in various fields, building an active network, and inspiring new collaborations. https://geometryworkshop.wiscweb.wisc.edu/

This 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.