Organized by:
Marcus Khuri (Stony Brook)
Michael Kunzinger (U Vienna)
Andrea Mondino (University of Oxford)
Raquel Perales (CIMAT)
Richard Schoen (UC Irvine)
Christina Sormani (CUNYGC and Lehman College)
Guoliang Yu (TAMU)
In the past decade, significant advances in the understanding of spaces arising in General Relativity have been achieved using techniques from Metric Geometry, Optimal Transport, and Geometric Measure Theory. Mathematicians have combined these geometric methods with great success in the past to develop low regularity notions of convergence and limits for Riemannian Manifolds with Ricci and Scalar curvature bounds, like Gromov-Hausdorff, metric measure, and Intrinsic flat convergence to metric spaces, RCD spaces, and integral current spaces respectively. These geometric techniques are now being applied to develop low regularity notions of convergence and limits for the space-times and initial data sets satisfying Einstein’s Equations or the Positive Energy Condition.
This program and its accompanying workshop, Geometric Measure Theory on Metric Spaces with Applications to Physics and Geometry, will bring together experts in Metric Geometry, Geometric Measure Theory, and Optimal Transport to communicate with leaders in Mathematical General Relativity to explore how the classical low regularity techniques from Partial Differential Equations and Functional Analysis can be combined with these new geometric methods to build a stronger understanding of the geometry and causal structures of sequences of space-times which do not converge smoothly. We will explore how these techniques can be applied together to understand the stability of various standard models from FLRW spacetimes to Minkowski and Kerr spacetimes even in settings where there are many gravity wells and black holes preventing one from constructing a diffeomorphism and using smoother notions of convergence.
Program Schedule:
Monday 8/25/25 11:15AM – Seminar Room – 313
Speaker: Stacey Harris
Title: An Intuitive Approach to Issues in Lorentzian Geometry and Beyond
Monday 8/25/25 2:00PM – Seminar Room – 313
Speaker: Ettore Minguzzi
Title: Mini-course: Classical Causality Theory: An overview of causality theory in the smooth Lorentzian setting, emphasizing its role in global results such as singularity theorems (Part 1).
Tuesday 8/26/25 10:00AM – Seminar Room – 313
Speaker: Lan-Hsuan Huang
Title: Einstein Constraint Equations, ADM Conserved Quantities, and Positive Mass Theorems
Tuesday 8/26/25 11:15AM – Seminar Room – 313
Speaker: Shin-ichi Ohta
Title: Splitting theorems for weighted Finsler spacetimes
Tuesday 8/26/25 2:00PM – P-131 Math Tower
Speaker: Mathias Braun
Title: Spacetime reconstruction and measured Lorentz-Gromov-Hausdorff convergence
Wednesday 8/27/25 11:15AM – Seminar Room – 313
Speaker: Robert McCann
Title: Mini-course: Part I of Optimal Transport and Synthetic Ricci Curvature Bounds: Trading linearity for ellipticity: a low regularity Lorentzian splitting theorem
Thursday 8/28/25 11:15AM – Seminar Room – 313
Speaker: Robert McCann
Title: Mini-course: Part II of Optimal Transport and Synthetic Ricci Curvature Bounds: Metric-measure spacetimes: a nonsmooth approach to Einstein’s theory of gravity
Thursday 8/28/25 2:00PM – Seminar Room – 313
Speaker: Ettore Minguzzi
Title: Mini-course: Causality Theory for Cone Structures: Extensions to more general cone distributions on manifolds, including cases of upper semi-continuous, $C^0$, and Lipschitz regularity, as well as the Lorentz-Finsler generalization (Part 2).
Friday 8/29/25 11:15AM – Seminar Room – 313
Speaker: Robert McCann
Title: Mini-course: Part III of Optimal Transport and Synthetic Ricci Curvature Bounds: A geometric approach to apriori estimates for optimal transport maps
Friday 8/29/25 2:00PM – Seminar Room – 313
Speaker: Stephan Suhr
Title: Mini-course: Causality Beyond Manifolds: Exploration of causal structures in settings where manifolds are absent, drawing on techniques from topologically ordered spaces and metric geometry (Part 3)
Please note that the center is closed September 1st for the Labor day holiday.
Tuesday 9/2/25: 10:00AM – Seminar Room – 313
Speaker: Karl-Theodor Sturm
Title: Synthetic integral scalar curvature and minimal super-Ricci flows
Tuesday 9/2/25: 11:15AM – Seminar Room – 313
Speaker: Christina Sormani
Title: Mini-course: General Relativity and Intrinsic Flat Convergence: Ambrosio-Kirchheim Theory and Integral Current Spaces (Part 1)
Tuesday 9/2/25: 2:00PM – P-131 Math Tower
Speaker: Michael Kunzinger
Title: Hawking’s singularity theorem for spacetime metrics below C^1
Wednesday 9/3/25 11:15AM – Seminar Room – 313
Speaker: Qiaochu Ma
Title: Small Scale Index Theory, Scalar Curvature, and Gromov’s Simplicial Norm
Thursday 9/4/25: 11:15AM – Seminar Room – 313
Speaker: Raquel Perales
Title: Mini-course: General Relativity and Intrinsic Flat Convergence: Almost Rigidity of the Positive Mass Theorem (Part 2)
Thursday 9/4/25: 2:00PM – Seminar Room – 313
Speaker: Eric Woolgar
Title: TBA
Friday 9/5/25 11:15AM – Seminar Room – 313
Speaker: Christina Sormani
Title: Mini-course: General Relativity and Intrinsic Flat Convergence: Causally Null Compactifiable Space-Times (Part 3)
Friday 9/5/25 2:00PM – Seminar Room – 313
Speaker: Yasuaki Fujitani
Title: Lower bounds for the first eigenvalue on minimal hypersurfaces for affine connections
Monday 9/8/25: 11:15AM – Seminar Room – 313
Speaker: Ruobing Zhang
Title: Poincaré-Einstein manifolds: conformal structure meets metric geometry
Monday 9/8/25: 2:00PM – Seminar Room – 313
Speaker: Ariadna Leon Quiros
Title: Vector field approach to proving the Riemannian Positive Mass Theorem
Tuesday 9/9/25: 10:00AM – Seminar Room – 313
Speaker: Roland Steinbauer
Title: Generalizing the Penrose cut-and-paste method: Null shells with pressure and energy flux
Tuesday 9/9/25: 11:15AM – Seminar Room – 313
Speaker: Andrea Mondino
Title: Mini Course: Optimal transport and positive energy conditions in general relativity (Part 1)
Tuesday 9/9/25: 2:00PM – P-131 Math Tower
Speaker: Guoliang Yu
Title: Higher index theory and applications to geometry and topology
Wednesday 9/10/25 11:15AM – Seminar Room – 313
Speaker: Zhizhang Xie
Title: On Gromov’s Dihedral Rigidity Conjecture of Scalar Curvature
Thursday 9/11/25: 11:15AM – Seminar Room – 313
Speaker: Andrea Mondino
Title: Mini-course: Optimal transport and positive energy conditions in general relativity (Part 2)
Thursday 9/11/25: 2:00PM – Seminar Room – 313
Speaker: Gilbert Weinstein
Title: The mass angular momentum inequality
Friday 9/12/25 11:15AM – Seminar Room – 313
Speaker: Andrea Mondino
Title: Mini-course: Optimal transport and positive energy conditions in general relativity (Part 3)
Friday 9/12/25 2:00PM – Seminar Room – 313
Speaker: Roya Mohayaee
Title: Monge-Ampère gravity as a modified theory of gravity
The final week the program will hold a mini course on the following topics:
“Stability Theorems in General Relativity” by Mihalis Dafermos
“Radiative spacetimes in asymptotically-flat and cosmological settings” by Lydia Bieri
In addition there will be weekly seminars where participant will have the opportunity to speak.
This program will also host a workshop: Geometric Measure Theory on Metric Spaces with Applications to Physics and Geometry September 15-19, 2025.
