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#Riemannian Manifolds

Showing: 47 courses
University of Chicago Department of Mathematics

Courant, Bezout, and Persistence - Lecture 2

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Explore spectral geometry through persistence modules and barcodes, examining oscillation of functions and applications to Courant's nodal domain theorem and Bezout's theorem in eigenfunctions.
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1 Lesons
1 hour 9 minutes
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University of Chicago Department of Mathematics

Courant, Bezout, and Persistence in Spectral Geometry - Lecture 1

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Explore spectral geometry and topological persistence, focusing on oscillation of functions, Courant's nodal domain theorem, and Bezout's theorem in the context of eigenfunctions.
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1 Lesons
58 minutes
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Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Sharp Concavity of the Isoperimetric Profile Under Lower Ricci Bounds - Workshop on Synthetic Curvature Bounds

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Explore sharp concavity of isoperimetric profiles in RCD spaces, extending Bavard-Pansu's work on Ricci curvature bounds to non-smooth, finite-dimensional settings.
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1 Lesons
53 minutes
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Paul G. Allen School

Robot Learning From Few Demonstrations by Exploiting Data Structure and Geometry

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Explore robot learning from limited demonstrations, leveraging data structure and geometry. Discover optimal control strategies and intuitive interfaces for efficient skill acquisition in human-robot interaction.
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1 Lesons
59 minutes
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Applied Algebraic Topology Network

Barcodes for the Topological Analysis of Gradient-Like Vector Fields

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Explore topological analysis of gradient-like vector fields using barcodes. Learn about chain complexes, parametrization, and applications in smooth and discrete settings, with insights on stability and approximation.
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1 Lesons
1 hour 6 minutes
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Free-Video
Applied Algebraic Topology Network

Mikhail Katz - Collapsing Surfaces

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Exploring surface collapse in Riemannian geometry, focusing on critical points, intersection theory, and Toponogov comparison. Analyzes fiber homotopy and discrete integration against Euler characteristic.
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10 Lesons
50 minutes
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Applied Algebraic Topology Network

Geodesic Complexity of Riemannian Manifolds

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Explore geodesic complexity in Riemannian manifolds, connecting robot motion planning to topology and geometry. Learn about cut loci, bounds, and applications in this advanced mathematical talk.
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18 Lesons
1 hour 2 minutes
On-Demand
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Fields Institute

Harmonic Maps and Rigidity

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Explore harmonic maps, rigidity theorems, and their applications in geometry. Delve into existence theory, Mostow's strong rigidity, and approaches to rigidity using harmonic maps and the Bochner method.
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23 Lesons
51 minutes
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Simons Institute

Constrained Optimization on Riemannian Manifolds

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Explore advanced mathematical techniques for solving optimization problems on curved spaces, with applications in machine learning and data analysis.
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1 Lesons
37 minutes
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Applied Algebraic Topology Network

Isoperimetric Inequality for Hausdorff Contents and Its Applications

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Explore isoperimetric inequality for Hausdorff contents, its applications in systolic geometry, and new systolic inequalities for non-simply connected Riemannian manifolds.
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1 Lesons
54 minutes
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Institute for Pure & Applied Mathematics (IPAM)

Towards a Theory of Non-commutative Optimization - Geodesic First and Second Order Methods for Moment Maps and Polytopes

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Explore non-commutative optimization theory for geodesically convex problems, unifying diverse applications in computer science, mathematics, and physics through innovative first and second-order methods.
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1 Lesons
32 minutes
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International Mathematical Union

Laurent Saloff-Coste - Breaking Heat Kernel Estimates Into Pieces

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Breaking heat kernel estimates on Riemannian manifolds by analyzing pieces separately and reconstructing the whole. Explores Brownian motion within segments and transitions between them.
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1 Lesons
46 minutes
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Applied Algebraic Topology Network

Metric Reconstruction via Optimal Transport

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Explores metric reconstruction using optimal transport theory, introducing Vietoris-Rips thickening to recover metric information from point samples in metric spaces, with applications to Riemannian manifolds.
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1 Lesons
49 minutes
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Applied Algebraic Topology Network

Exploiting Geometric Structure in Matrix-Valued Optimization

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Exploring optimization on matrix manifolds, introducing Riemannian Frank-Wolfe methods for constrained problems, and discussing applications in machine learning and mathematics.
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1 Lesons
58 minutes
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Applied Algebraic Topology Network

Geodesic Complexity and Fibered Decompositions of Cut Loci

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Explore geodesic complexity in Riemannian manifolds, focusing on cut locus structure and fibered decompositions to establish bounds and applications in projective and lens spaces.
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1 Lesons
55 minutes
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Hausdorff Center for Mathematics

Brunn-Minkowski Inequalities for Sprays on Riemannian Surfaces

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Generalization of Minkowski average on Riemannian manifolds, characterizing curve families on surfaces satisfying Brunn-Minkowski inequality. Explores conditions for constant-speed curves and geodesic curvature.
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1 Lesons
24 minutes
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IMSA

Convergence of Manifolds and Metric Spaces

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Explore Riemannian manifolds, Gromov-Hausdorff and Intrinsic Flat distances, and their applications in solving stability problems in metric spaces.
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1 Lesons
45 minutes
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Fields Institute

Minimal Surfaces in Geometry and General Relativity

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Explore the fascinating intersection of minimal surfaces with geometry and general relativity, delving into their mathematical properties and applications in physics.
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1 Lesons
45 minutes
On-Demand
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Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Nonlinear Hyperbolic Conservation Laws on Manifolds

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Explore nonlinear scalar hyperbolic equations on Riemannian varieties, covering existence, uniqueness, entropy conditions, finite-volume schemes, and numerical results.
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1 Lesons
48 minutes
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Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Schoen's Conjecture for Limits of Isoperimetric Surfaces

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Explore Schoen's conjecture for asymptotically flat Riemannian manifolds, focusing on area-minimizing hypersurfaces and recent developments in mathematical relativity.
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1 Lesons
57 minutes
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Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Quantitative Recurrence for Z-Extension of Three-Dimensional Axiom A Flows

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Explore quantitative recurrence in Z-extension of Axiom A flows, focusing on first return time behavior and applications to geodesic flows on Z-cover of compact surfaces.
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1 Lesons
55 minutes
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Fields Institute

Riemannian Manifolds, Isometries, and Geodesics - Lecture 3

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Explore Riemannian manifolds, isometries, and geodesics, with a focus on the upper half-plane and hyperbolic metric in this advanced geometry lecture.
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1 Lesons
55 minutes
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Institut des Hautes Etudes Scientifiques (IHES)

Lipschitz Constant and Degree of Mappings in Riemannian Manifolds

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Explore the relationship between Lipschitz constant and degree of mappings in Riemannian manifolds, focusing on recent developments and clever mapping techniques.
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17 Lesons
52 minutes
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Stony Brook Mathematics

Mapping Riemannian Manifolds in Metric Spaces

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Explore Riemannian manifold mappings, their applications in geometry, and the construction of canonical shapes. Gain insights into special mappings, stability problems, and geometric inequalities.
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12 Lesons
56 minutes
On-Demand
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Stony Brook Mathematics

The Formulation of the Navier-Stokes Equations on Riemannian Manifolds

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Explore advanced formulations of Navier-Stokes equations on Riemannian manifolds, focusing on Ebin and Marsden's approach and recent developments in this complex field of fluid dynamics.
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1 Lesons
1 hour
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Schmid College, Chapman University

Geometric Inequalities Between Intrinsic and Extrinsic Curvature Invariants

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Explore geometric inequalities between intrinsic and extrinsic curvature invariants in Riemannian manifolds, focusing on Nash's Theorem and recent developments in the field.
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1 Lesons
57 minutes
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Institut des Hautes Etudes Scientifiques (IHES)

Waists Measured via Urysohn Width in Riemannian Manifolds

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Explore Urysohn width's role in measuring approximate dimension of Riemannian manifolds and its connection to positive scalar curvature, with insights on slicing manifolds.
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1 Lesons
1 hour 2 minutes
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Institut des Hautes Etudes Scientifiques (IHES)

On the L^p Spectrum of the Laplacian on Riemannian Manifolds

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Explore the $L^p$ spectrum of the Laplacian on manifolds, including resolvent sets, Weyl criterion, and hyperbolic space, with insights on conformally compact manifolds.
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1 Lesons
59 minutes
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Centre de recherches mathématiques - CRM

Efficiently Chopping a Hyperbolic Surface in Two - Cheeger Constants and Spectral Geometry

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Explore the Cheeger constant of hyperbolic surfaces, its relation to spectral gaps, and recent findings on its upper bound for large genus surfaces. Gain insights into cutting Riemannian manifolds efficiently.
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10 Lesons
1 hour 7 minutes
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Centre de recherches mathématiques - CRM

Off-Diagonal Spectral Cluster Asymptotics on Zoll Manifolds

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Explore off-diagonal spectral cluster asymptotics on Zoll manifolds, examining universal asymptotic behavior of spectral cluster kernels and implications for monochromatic random waves in Riemannian geometry.
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1 Lesons
56 minutes
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Centre de recherches mathématiques - CRM

On the Critical Points of Steklov Eigenfunctions

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Explore critical points of Steklov eigenfunctions on Riemannian manifolds, examining relationships between eigenfunction indexes, boundary behavior, and Euler characteristics.
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1 Lesons
46 minutes
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Centre de recherches mathématiques - CRM

A Weighted Reilly Formula for Differential Forms and Sharp Steklov Eigenvalue Estimates - Lecture

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Explore weighted Reilly formula for differential forms and its applications in sharp Steklov eigenvalue estimates. Gain insights into spectral geometry and related open problems.
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1 Lesons
52 minutes
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BIMSA

Hyperbolic Manifolds in Dimension Higher Than 3

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Explore hyperbolic manifolds in dimensions 4 and higher, examining their properties, challenges in description, and current understanding in topology.
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1 Lesons
1 hour 7 minutes
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Centre de recherches mathématiques - CRM

Large Steklov Eigenvalues Under Geometric Constraints

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Explore large Steklov eigenvalues in compact Riemannian manifolds, examining geometric constraints and constructing metrics with fixed volume and boundary conditions.
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1 Lesons
50 minutes
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BIMSA

Minimal Surfaces and the Allen-Cahn Equation on 3-Manifolds

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Explore minimal surfaces and the Allen–Cahn equation on 3-manifolds, focusing on recent results and the multiplicity-one theorem in three dimensions.
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1 Lesons
52 minutes
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Free-Video
BIMSA

The Ricci Flow - Lecture by Richard Hamilton

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Explore the Ricci flow equation, its applications in geometry, and its role in understanding manifold curvature evolution. Gain insights into singularities and geometric analysis.
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1 Lesons
1 hour 6 minutes
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Free-Video
BIMSA

Generic and Random Behavior of Minimal Surfaces

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Explore minimal surfaces in Differential Geometry, focusing on recent quantitative findings under genericity and randomness conditions. Discover spatial equidistribution and hyperbolic properties.
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1 Lesons
46 minutes
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BIMSA

Ricci Limit Spaces are Semi-Locally Simply Connected

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Explore Ricci limit spaces and their semi-local simple connectivity, delving into fundamental groups and Gromov-Hausdorff convergence of Riemannian manifolds.
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1 Lesons
41 minutes
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HyperComplex Seminar

The Grad Div Operator in Symmetric Tensors on Riemannian Manifolds

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Explore the grad div operator in symmetric tensors on Riemannian manifolds, focusing on gradient and divergence definitions and their composition in differential geometry.
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1 Lesons
16 minutes
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Institut des Hautes Etudes Scientifiques (IHES)

Capacity in Low Regularity with Connections to General Relativity

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Explore capacity in metric spaces, its behavior under convergence, and connections to general relativity's total mass concept.
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1 Lesons
59 minutes
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Applied Algebraic Topology Network

Curvature Variation Based Sampling for Delaunay Triangulations of Manifolds

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Explore adaptive sampling for Delaunay triangulations of Riemannian manifolds, focusing on curvature variation and quality bounds for successful triangulation. Learn about geometric realizations and manifold triangulation techniques.
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10 Lesons
50 minutes
On-Demand
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Valence Labs

Manifold Diffusion Fields - Learning Generative Models of Continuous Functions on Riemannian Manifolds

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Explore Manifold Diffusion Fields for generating continuous functions on Riemannian manifolds. Learn about spectral geometry, intrinsic coordinate systems, and applications in AI for drug discovery.
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6 Lesons
27 minutes
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Institut des Hautes Etudes Scientifiques (IHES)

Stability of Spectra Under Riemannian Manifold Coverings

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Delve into advanced mathematical concepts exploring eigenfunction stability in Riemannian coverings, focusing on the relationship between manifold spectra and their pull-back properties.
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1 Lesons
1 hour 16 minutes
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Big Ideas In Dynamics

Flexibility Ideas for Geodesic Flow

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Explore innovative concepts in geodesic flow flexibility, uncovering dynamic approaches and mathematical insights for advanced understanding.
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1 Lesons
1 hour 3 minutes
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Dublin Institute for Advanced Studies DIAS

A Simple Axiom for Euclidean Quantum Field Theory

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Explore a concise mathematical definition of quantum field theory and its implications for physics through a categorical approach to Riemannian manifolds and Hilbert spaces.
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1 Lesons
1 hour 5 minutes
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Centre de recherches mathématiques - CRM

Graph Structure of the Nodal Set on Riemannian Manifolds

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Explore the geometric analysis of eigenfunction zero sets on Riemannian manifolds, examining connections between graph theory, nodal sets, and critical point estimation in spectral geometry.
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1 Lesons
40 minutes
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Centre de recherches mathématiques - CRM

Spectral Gap for Random Schottky Surfaces

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Delve into advanced mathematical concepts exploring spectral gaps in random Schottky surfaces, examining the behavior of Laplace eigenvalues and their relationship to hyperbolic geometry and probability theory.
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1 Lesons
1 hour
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Free-Video