Vietoris-Rips Thickenings - Problems for Birds and Frogs
Explore open problems in Vietoris-Rips complexes, connecting diverse mathematical areas. Suitable for both broad theorists and problem-solving specialists in applied algebraic topology.
Macroscopic Scalar Curvature and Local Collapsing
Exploration of macroscopic scalar curvature in Riemannian geometry, focusing on volume bounds for manifolds with hyperbolic metrics and collapsing techniques in metric geometry.
The Gromov-Hausdorff Distance Between Spheres
Explore upper and lower bounds for Gromov-Hausdorff distances between spheres, including optimal correspondences and topological concepts related to the Borsuk-Ulam theorem.
Urysohn Width
Explore the 100-year history and applications of Urysohn width, a metric invariant quantifying space approximation by simplicial complexes. Discover its role in dimension theory and modern geometric challenges.
Failure of the Curvature-Dimension Condition in Sub-Finsler Manifolds
Explore the failure of curvature-dimension conditions in sub-Finsler manifolds, focusing on recent proofs and implications for sub-Riemannian geometry and the Heisenberg group.
Vector-Valued Concentration on the Symmetric Group
Explore vector-valued concentration inequalities for the symmetric group, examining implications for Banach space geometry and building on recent advancements in discrete hypercube analysis.
Distance, Curvature and Symmetry - A Haphazard Tour Through Metric Geometry
Explore metric geometry through distance, curvature, and symmetry concepts, gaining insights into fundamental mathematical principles and their applications in spatial analysis.
Sharp Stability for the Brunn-Minkowski Inequality for Arbitrary Sets
Explore sharp stability in the Brunn-Minkowski inequality for arbitrary sets, delving into combinatorics and its connections with metric geometry and analysis.
Filling Radius, Positive Scalar Curvature and Quantitative Operator K-Theory
Explore techniques in quantitative operator theory to estimate filling radius, connecting positive scalar curvature and asymptotic dimension in large-scale geometry.
Packing Points in Projective Spaces
Explore optimal point arrangements in projective spaces, surveying current research and open problems in this fundamental area of metric geometry with applications in digital communication.
Alexandrov's Patchwork and the Bonnet-Myers Theorem for Lorentzian Length Spaces
Explore global timelike curvature bounds in Lorentzian length spaces, examining Alexandrov's Patchwork analogue and Bonnet-Myers theorem applications for spacetime geometry.
The Space of Causal Diamonds as a Lorentzian Pre-Length Space
Explore causal diamonds in Mathematical Relativity, examining their geometry and geodesic structure when endowed with Hausdorff distance, and their implications for metric convergence stability.
Non-Regular Spacetime Geometry via Metric Measure Geometry
Explore non-regular spacetime geometry using metric geometry, extending Lorentzian geometry beyond classical differential geometry for low-regularity spacetimes and general spaces.
Metric Geometry of Spaces of Persistence Diagrams
Explore metric geometry of persistence diagram spaces, focusing on synthetic curvature bounds and applications in non-smooth, infinite-dimensional contexts.