Emanuel Milman: Functional Inequalities on sub-Riemannian manifolds via QCD
We are interested in obtaining Poincar ́e and log-Sobolev inequalities on domains in sub-Riemannian manifolds (equipped with their natural sub-Riemannian metric and volume measure). It is well-known that strictly sub-Riemannian manifolds do not satisfy any type of Curvature-Dimension condi
From playlist Workshop: High dimensional measures: geometric and probabilistic aspects
Ludovic Rifford: Geometric control and sub-Riemannian geodesics - Part I
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Geometry
MATH331: Riemann Surfaces - part 1
We define what a Riemann Surface is. We show that PP^1 is a Riemann surface an then interpret our crazy looking conditions from a previous video about "holomorphicity at infinity" as coming from the definition of a Riemann Surface.
From playlist The Riemann Sphere
Spectrum and abnormals in sub-Riemannian geometry: the 4D quasi-contact case - Nikhil Savale
Symplectic Dynamics/Geometry Seminar Topic: Spectrum and abnormals in sub-Riemannian geometry: the 4D quasi-contact case Speaker: Nikhil Savale Affiliation: University of Cologne Date: October 28, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Pierre Pansu: Differential forms and the Hölder equivalence problem - Part 1
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Geometry
Riemannian Geometry - Definition: Oxford Mathematics 4th Year Student Lecture
Riemannian Geometry is the study of curved spaces. It is a powerful tool for taking local information to deduce global results, with applications across diverse areas including topology, group theory, analysis, general relativity and string theory. In these two introductory lectures
From playlist Oxford Mathematics Student Lectures - Riemannian Geometry
Riemannian Geometry - Examples, pullback: Oxford Mathematics 4th Year Student Lecture
Riemannian Geometry is the study of curved spaces. It is a powerful tool for taking local information to deduce global results, with applications across diverse areas including topology, group theory, analysis, general relativity and string theory. In these two introductory lectures
From playlist Oxford Mathematics Student Lectures - Riemannian Geometry
Z. Badreddine - Optimal transportation problem and MCP property on sub-Riemannian structures
This presentation is devoted to the study of mass transportation on sub-Riemannian geometry. In order to obtain existence and uniqueness of optimal transport maps, the first relevant method to consider is the one used by Figalli and Rifford which is based on the local semiconcavity of the
From playlist Journées Sous-Riemanniennes 2018
Riemannian Exponential Map on the Group of Volume-Preserving Diffeomorphisms - Gerard Misiolek
Gerard Misiolek University of Notre Dame; Institute for Advanced Study October 19, 2011 In 1966 V. Arnold showed how solutions of the Euler equations of hydrodynamics can be viewed as geodesics in the group of volume-preserving diffeomorphisms. This provided a motivation to study the geome
From playlist Mathematics
Sachchidanand Prasad: Morse-Bott Flows and Cut Locus of Submanifolds
Sachchidanand Prasad, Indian Institute of Science Education and Research Kolkata Title: Morse-Bott Flows and Cut Locus of Submanifolds We will recall the notion of cut locus of closed submanifolds in a complete Riemannian manifold. Using Morse-Bott flows, it can be seen that the complement
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
This talk is about the Riemann-Roch theorem for genus 2 curves. We show that all genus 2 complex curves are hyperelliptic (meaning they are branched double covers of the projective line). We also describe the Weierstrass points and the holomorphic 1-forms explicitly. Finally we briefly su
From playlist Algebraic geometry: extra topics
Curvature of a Riemannian Manifold | Riemannian Geometry
In this lecture, we define the exponential mapping, the Riemannian curvature tensor, Ricci curvature tensor, and scalar curvature. The focus is on an intuitive explanation of the curvature tensors. The curvature tensor of a Riemannian metric is a very large stumbling block for many student
From playlist All Videos
Boundary regularity for area minimizing currents and a question of Almgren - Camillo De Lellis
Workshop on Mean Curvature and Regularity Topic: Boundary regularity for area minimizing currents and a question of Almgren Speaker: Camillo De Lellis Affiliation: Professor, School of Mathematics Date: November 6, 2018 For more video please visit http://video.ias.edu
From playlist Workshop on Mean Curvature and Regularity
C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 1 (version temporaire)
We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Entropy of manifolds and of their fundamental group - Gerard Besson
Workshop on Geometric Functionals: Analysis and Applications Topic: Entropy of manifolds and of their fundamental group Speaker: Gerard Besson Affiliation: Université de Grenoble Date: March 7, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Hodge theory and cycle theory of locally symmetric spaces – Nicolas Bergeron – ICM2018
Geometry Invited Lecture 5.1 Hodge theory and cycle theory of locally symmetric spaces Nicolas Bergeron Abstract: We discuss several results pertaining to the Hodge and cycle theories of locally symmetric spaces. The unity behind these results is motivated by a vague but fruitful analogy
From playlist Geometry
Riemann Roch: structure of genus 1 curves
This talk is about the Riemann Roch theorem in the spacial case of genus 1 curves or Riemann surface. We show that a compact Riemann surface satisfying the Riemann Roch theorem for g=1 is isomorphic to a nonsingular plane cubic. We show that this is topologically a torus, and use this to s
From playlist Algebraic geometry: extra topics