Logarithmic Sobolev Inequalities on Homogeneous Spaces
Explore logarithmic Sobolev inequalities on homogeneous spaces with sub-Riemannian structures. Discover how constants depend on Lie group geometry and remain independent of dimension in certain cases.
Topological Recursion: A Recursive Way of Counting Surfaces
Explore topological recursion for enumerating surfaces in combinatorics, geometry, and physics. Learn how this universal method links to integrable systems and random matrices.
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.
Graph Complex Action on Poisson Structures: From Theory to Computation
Explore graph complex action on Poisson structures, from theoretical foundations to computational applications using SageMath's gcaops package for advanced mathematical research.
Periods of Hypersurfaces via Effective Homology
Explore numerical approximations of periods for hypersurfaces using effective homology, enabling computation of algebraic invariants for complex projective varieties.
Spectra of Laplace and Dirac Operators on Noncompact Manifolds
Explore spectra of Laplace and Dirac operators on complete manifolds, including types of spectra, results for special behaviors at infinity, and effects of additional potentials.
On the L^p Spectrum of the Laplacian on Riemannian Manifolds
Explore the $L^p$ spectrum of the Laplacian on manifolds, including resolvent sets, Weyl criterion, and hyperbolic space, with insights on conformally compact manifolds.
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.
Local Systems and Higgs Bundles in p-adic Geometry
Explore the algebraic nature of local systems and Higgs bundles in p-adic geometry, drawing parallels to complex varieties and characteristic p counterparts.
Characteristic Classes of Étale Local Systems
Explore characteristic classes of étale Z_p-local systems on algebraic varieties, their relation to Chern-Simons classes, and connections to Hodge filtration in p-adic settings.
Positive Mass Theorem for Asymptotically Flat Manifolds with Isolated Conical Singularities
Explore recent advancements in positive mass theorem for asymptotically flat manifolds with isolated conical singularities, covering spin and non-spin settings, analysis techniques, and Geroch-type results.
A Stable Version of Gromov's Angle-Shrinking Problem and Its Index Theoretic Applications - Part 1
Explore Gromov's angle shrinking problem and its role in proving the dihedral extremality/rigidity conjecture through a new index theorem for manifolds with polyhedral boundary.
A Stable Version of Gromov's Angle-Shrinking Problem and Its Index Theoretic Applications - Lecture 2
Explore a stable algebraic version of Gromov's angle shrinking problem and its application to dihedral rigidity conjecture, focusing on Fredholm index computation.
Nonnegative Ricci Curvature, Nilpotency, and Hausdorff Dimension
Explore nonnegative Ricci curvature, nilpotency, and Hausdorff dimension in relation to universal covers, minimal representing loops, and asymptotic cones of manifolds.
Stability of Llarull's Theorem in All Dimensions
Explore stability of Llarull's theorem in all dimensions using spin geometry, with results in intrinsic flat and C^0-convergence outside small sets.
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.
Spaces with Ricci Curvature Lower Bounds
Explore recent findings on spaces with nonnegative Ricci curvature, including singular set dimensions, fractal-like Weyl's laws, and nonproper Busemann functions in manifolds.
Ricci Curvature, Fundamental Group and the Milnor Conjecture - Part 2
Explore advanced concepts in topology and geometry, focusing on counterexamples to the Milnor conjecture and their construction using mapping class groups and asymptotic cones.
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.