Geometric Measure Theory on Metric Spaces with Applications to Physics and Geometry: September 15-19, 2025

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Participant ListView VideosSchedule
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.

Talk Schedule


Time Title Speaker Location
9:30am Regular Lagrangian Flows, 20 years later Luigi Ambrosio SCGP 102
11:00am Harmonic Maps into Euclidean Buildings Chikako Mese SCGP 102
12:00pm Lunch  N/A SCGP Cafe
1:30pm On the boundary regularity of solutions to the oriented Plateau problem Reinaldo Resende SCGP 102
2:30pm Minimal surfaces in the infinite-dimensional sphere Antoine Song SCGP 102
3:30pm Tea Time  N/A SCGP Cafe
4:00pm Decomposition of integral metric currents Giacomo Del Nin SCGP 102

Time Title Speaker Location
9:30am Trading linearity for ellipticity – a novel approach to global Lorentzian geometry Nicola Gigli SCGP 102
11:00am The mass angular momentum inequality Gilbert Weinstein SCGP 102
12:00pm Lunch  N/A SCGP Cafe
2:30pm Minimizing surfaces in the Heisenberg group Robert Young SCGP 102
3:30pm Tea Time  N/A SCGP Cafe
4:00pm The Spacetime Penrose Inequality with Suboptimal Constant Brian Allen SCGP 102

Time Title Speaker Location
9:30am Ricci Curvature Lower Bounds and Orientability Elia Brue SCGP 102
11:00am Coarse tangent fields Sylvester Eriksson-Bique SCGP 102
12:00pm Lunch  N/A SCGP Cafe
1:30pm Positive Scalar Curvature and Convergence of Manifolds Paul Sweeney SCGP 102
2:30pm Introducing notions of distances between spacetimes Anna Sakovich SCGP 102
3:30pm Tea Time  N/A SCGP Cafe
4:00pm Capacity, semicontinuity, and general relativistic mass Jeff Jauregui SCGP 102

Time Title Speaker Location
9:30am Uniformly rectifiable metric spaces Raanan Schul SCGP 102
11:00am From almost smooth spaces to RCD spaces Shouhei Honda SCGP 102
12:00pm Lunch  N/A SCGP Cafe
1:30pm Reduction Arguments via Asymptotic Correspondence of Initial Data Sets Anna Sancassani SCGP 102
2:30pm Rigidity of mass-preserving 1–Lipschitz maps from integral current spaces into Euclidean space Raquel Perales SCGP 102
3:30pm Tea Time  N/A SCGP Cafe
4:00pm Stability for a class of three-tori with small negative scalar curvature Edward Bryden SCGP 102

Time Title Speaker Location
9:30am Mass Lower Bounds for asymptotically locally flat 4-manifolds Marcus Khuri & Jian Wang SCGP 102
11:00am Gromov’s dihedral rigidity and index theory on polyhedra Jinmin Wang SCGP 102
12:00pm Lunch  N/A SCGP Cafe
1:30pm From linear potential theory to the inverse mean curvature flow: monotonicity formulas Alessandra Pluda SCGP 102
2:30pm From linear potential theory to the inverse mean curvature flow: applications to Riemannian Penrose-type inequalities Luca Benatti SCGP 102
3:30pm Tea Time  N/A SCGP Cafe
4:00pm Towards a definition of energy and its positivity in spacetimes with an expanding flat de Sitter background Anachiara Piubello SCGP 102


This Workshop is associated with the program: Geometry and Convergence in Mathematical General Relativity: August 25 – Oct 3, 2025.