Organized by:
Luigi Ambrosio (Pisa)
Andrea Mondino (Oxford)
Raquel Perales (CIMAT)
Christina Sormani (CUNYGC and Lehman College)
In the nearly twenty-five years since the publication of Ambrosio-Kirchheim’s seminal paper, Currents on Metric Spaces, there have been significant applications of this generalization of Geometric Measure Theory (GMT) that deepen our understanding of both Geometry and Physics. These applications include a deepening of our understanding of the Plateau Problem in a variety of ambient spaces, a new approach to Pu’s Conjecture and the filling of Riemannian manifolds, the intrinsic definition of a flat convergence for sequences of Riemannian manifolds, and new approaches to understanding low regularity and weak convergence in General Relativity. After many exciting applications presented at a variety of workshops at the Simons Center, the Institute for Advanced Study, and the Fields Institute, new questions have arisen which require the attention of experts in Geometric Measure Theory.
For this reason, we will bring together the leading experts and postdocs specializing in GMT for the first workshop held focusing on this field. The workshop will have talks on Monday describing the key questions that have arisen in Geometry and in Physics. Then Tuesday through Friday, experts in Geometric Measure Theory will present their results. After each talk, there will be a discussion as to how these results might be applied or adapted to answer the questions from physics and geometry. Teams will be formed to encourage continued collaboration on these projects.
This Workshop is associated with the program: Geometry and Convergence in Mathematical General Relativity: August 25 – Oct 3, 2025.