Notions of Scalar Curvature - Mikhail Gromov
Explore scalar curvature concepts, spin bundles, and rich curves with renowned mathematician Mikhail Gromov in this advanced topology lecture from the Institute for Advanced Study.
How Hard is the Theorem of Stolz - Metrics and Scalar Curvature in Spin Manifolds
Delve into the complexity of Stolz's theorem on positive scalar curvature metrics, exploring metric deformations and manifold transformations through groundbreaking mathematical research findings.
Canonical Kaehler Metrics and Stability of Algebraic Varieties
Explore canonical Kähler metrics, algebraic variety stability, and the Yau-Tian-Donaldson conjecture in complex geometry. Delve into Kähler manifolds, curvature, and pluripotential theory with recent progress and applications.
Curvature of the Determinant Line Bundle for Noncommutative Tori
Explore differential geometry of curved noncommutative tori, including spectral invariants and curvature of determinant line bundle for Dirac operators on noncommutative two tori.
Curvature Bounds and the Length of the Shortest Closed Geodesic
Explore upper bounds for shortest periodic geodesics on Riemannian manifolds, examining curvature's impact on closed geodesic length in various geometric contexts.
Yevgeny Liokumovich - Urysohn Width, Isoperimetric Inequalities and Scalar Curvature
Explore metric spaces, Hausdorff measure, and continuous mappings. Discover connections to isoperimetric inequalities and Riemannian geometry's positive scalar curvature.
Initial Data Rigidity via Dirac-Witten Operators
Explore initial data rigidity in spin settings using Dirac-Witten operators. Derive a rigidity theorem for manifolds with boundary, examining dominant energy conditions and null expansion scalars.
Schoen's Conjecture for Limits of Isoperimetric Surfaces
Explore Schoen's conjecture for asymptotically flat Riemannian manifolds, focusing on area-minimizing hypersurfaces and recent developments in mathematical relativity.
Monotonicity of the Scalar Curvature of the Quantum Exponential Family for Transverse-Field Ising
Explore scalar curvature monotonicity in quantum exponential family for transverse-field Ising chains, examining finite-size effects and implications for Petz conjecture.
Index Pairing and Quantitative Control of Scalar Curvature
Explore index pairing and quantitative scalar curvature control in noncommutative geometry, focusing on direct operators, enlargibility, and metric space theory.
Recent Developments in Constant Mean Curvature Hypersurfaces - Part II
Explore recent developments in constant mean curvature hypersurfaces, focusing on min-max theorems and the half-volume spectrum. Gain insights into advanced geometric analysis concepts.
Scalar Curvature Rigidity in Manifolds
Explore scalar curvature rigidity in manifolds, examining known solutions and current research questions using spinorial techniques.
Scalar Curvature Rigidity and Extremality in Dimension 4
Explore scalar curvature rigidity in 4D using Finsler-Thorpe trick and twisted spinor methods. Discover area-extremal properties of 4-manifolds with nonnegative sectional curvature.
Recent Inequalities on the Mass-to-Capacity Ratio
Explore new inequalities for mass-to-capacity ratio on manifolds with nonnegative scalar curvature, revealing proofs of positive mass theorem and applications in geometry.
Smoothing by Ricci-DeTurck Flow and Applications to Scalar Curvature
Explore Ricci-DeTurck flow's existence theory for non-smooth initial metrics and its applications to scalar curvature rigidity problems in geometry.
Waists Measured via Urysohn Width in Riemannian Manifolds
Explore Urysohn width's role in measuring approximate dimension of Riemannian manifolds and its connection to positive scalar curvature, with insights on slicing manifolds.
Width, Scalar Curvature and Macroscopic Scalar Curvature
Explore the interplay between positive scalar curvature and macroscopic scalar curvature, examining Urysohn width and closed geodesics in PSC and PMSC spaces.
Another Aspect of Gromov's Conjectures on Scalar Curvature
Explore Gromov's scalar curvature conjectures through general relativity, examining partial solutions via the positive mass theorem.
Geometric Variational Methods for Scalar Curvature and Other Curvature Problems
Explore geometric variational problems and their applications to curvature conditions, focusing on Schoen-Yau's approach and recent extensions.
Global Effects of Positive Scalar Curvature in Geometry
Explorez les effets globaux de la courbure scalaire positive, y compris le problème de remplissage de Gromov et les théorèmes de type Llarull sur les variétés complètes.
Index Theory and Applications to Scalar Curvature
Explore index theorems for compact manifolds with boundary and their applications to scalar curvature geometry, focusing on Dirac operators and boundary value problems.