Recent Advances on Scalar Curvature Problems: June 27 – July 1, 2022

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Organized by:

Alessandro Carlotto (ETH Zurich),

Marcus Khuri (Stony Brook University),

Philippe G. LeFloch (Sorbonne Univ.),

Rafe Mazzeo (Stanford University)

Problems involving the scalar curvature of a Riemannian manifold (prescribed curvature, existence, uniqueness, comparison, convergence, rigidity, regularity, etc.) arise in many areas of mathematics and physics. Over the past decade, there has been spectacular progress on such problems in several fronts in the mathematical research. Beyond their intrinsic relevance in Riemannian geometry, these questions also connect naturally to the description of gravitational forces in the context of general relativity. This workshop will be centered on recent developments on Einstein’s constraint equations, metrics with positive scalar curvature, static Einstein spaces, and mass and rigidity properties.

The organizers have decided to stream this event via https://scgp.stonybrook.edu/live. This event will not be available via zoom.

Talk Schedule

Time Title Speaker Location
9:00am Geometric inequalities and potential theory Lorenzo Mazzieri SCGP 102
10:00am Compactness and Stability Conjectures Christina Sormani SCGP 102
11:00am Coffee Break N/A SCGP Cafe
11:30am Harmonic maps and extremal Schrodinger operators on higher-dimensional manifolds Daniel Stern SCGP 102
12:30pm Lunch N/A SCGP Cafe
2:00pm Dihedral rigidity conjecture and Stoker’s problem Jinmin Wang SCGP 102
3:00pm On Gromov’s dihedral extremality and rigidity conjectures Zhizhang Xie SCGP 102
4:00pm Coffee Break N/A SCGP Cafe

Time Title Speaker Location
9:00am Towards a theory of Ricci flow in dimension 4 (and higher) Richard Bamler SCGP 102
10:00am Decomposing PSC 4-manifolds Christos Mantoulidis SCGP 102
11:00am Coffee Break N/A SCGP Cafe
11:30am Kodaira Dimension and the Yamabe Problem, Revisited Claude LeBrun SCGP 102
12:30pm Lunch N/A SCGP 102
2:00pm Sobolov-Class Asymptotically Hyperbolic Manifolds and the Yamabe Problem David Maxwell SCGP 102
3:00pm Strong Cosmic Censorship and the Stability of AVTD Behavior for Polarized T^2- Symmetric Space-Times Jim Isenberg Zoom
4:00pm Coffee Break N/A SCGP Cafe

Time Title Speaker Location
10:00am Removal of Singularities Joachim Lohkamp SCGP 102
11:00am Coffee Break N/A SCGP Cafe
11:30am The positive mass theorem with boundaries, complete ends, and scalar curvature shields Dan Lee SCGP 102
12:30pm Lunch N/A SCGP Cafe
2:00pm Mass and capacitary potential of asymptotically flat 3-manifolds Pengzi Miao SCGP 102
3:00pm Asymptotic estimates for the Bartnik mass of small metric balls David Wiygul SCGP 102
4:00pm Coffee Break N/A SCGP Cafe

Time Title Speaker Location
9:00am Lipschitz rigidity for scalar curvature Bernhard Hanke SCGP 102
10:00am Higher index theory and scalar curvature Guoliang Yu SCGP 102
11:00am Coffee Break N/A SCGP Cafe
11:30am Comparison geometry and spacetime harmonic functions Demetre Kazaras SCGP 102
12:30pm Lunch N/A SCGP Cafe
2:00pm Distance estimates under lower scalar curvature bounds in the spin setting and beyond Rudolf Zeidler SCGP 102
3:00pm Scalar and mean curvature comparison for Riemannian bands Daniel Räde SCGP 102
4:00pm Coffee Break N/A SCGP Cafe
6:00pm   N/A SCGP Cafe

Time Title Speaker Location
9:00am Coordinates are messy Carla Cederbaum Zoom
10:00am Coffee Break N/A SCGP Cafe
10:30am Local existence and uniqueness of static vacuum extensions of Bartnik boundary data Zhongshan An SCGP 102
11:30am Lunch N/A SCGP Cafe