Theorems in Riemannian geometry | Differential geometry

Gromov's compactness theorem (geometry)

In the mathematical field of metric geometry, Mikhael Gromov proved a fundamental compactness theorem for sequences of metric spaces. In the special case of Riemannian manifolds, the key assumption of his compactness theorem is automatically satisfied under an assumption on Ricci curvature. These theorems have been widely used in the fields of geometric group theory and Riemannian geometry. (Wikipedia).

Video thumbnail

On the Gromov width of polygon spaces - Alessia Mandini

Alessia Mandini University of Pavia October 31, 2014 After Gromov's foundational work in 1985, problems of symplectic embeddings lie in the heart of symplectic geometry. The Gromov width of a symplectic manifold (M,ω)(M,ω) is a symplectic invariant that measures, roughly speaking, the siz

From playlist Mathematics

Video thumbnail

Mikhail Gromov - 3/4 Old, New and Unknown around Scalar Curvature

Geometry of scalar curvature, that is comparable in scope to symplectic geometry, mediates between two worlds: the domain of rigidity, one sees in convexity and the realm of softness, characteristic of topology, such as the cobordism theory. The aim of this course is threefold: 1. An ove

From playlist Mikhail Gromov - Old, New and Unknown around Scalar Curvature

Video thumbnail

Mikhail Gromov - 2/4 Old, New and Unknown around Scalar Curvature

Geometry of scalar curvature, that is comparable in scope to symplectic geometry, mediates between two worlds: the domain of rigidity, one sees in convexity and the realm of softness, characteristic of topology, such as the cobordism theory. The aim of this course is threefold: 1. An ove

From playlist Mikhail Gromov - Old, New and Unknown around Scalar Curvature

Video thumbnail

Math 131 Fall 2018 100318 Heine Borel Theorem

Definition of limit point compactness. Compact implies limit point compact. A nested sequence of closed intervals has a nonempty intersection. k-cells are compact. Heine-Borel Theorem: in Euclidean space, compactness, limit point compactness, and being closed and bounded are equivalent

From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)

Video thumbnail

An introduction to the Gromov-Hausdorff distance

Title: An introduction to the Gromov-Hausdorff distance Abstract: We give a brief introduction to the Hausdorff and Gromov-Hausdorff distances between metric spaces. The Hausdorff distance is defined on two subsets of a common metric space. The Gromov-Hausdorff distance is defined on any

From playlist Tutorials

Video thumbnail

Mikhail Gromov - 4/4 Old, New and Unknown around Scalar Curvature

Geometry of scalar curvature, that is comparable in scope to symplectic geometry, mediates between two worlds: the domain of rigidity, one sees in convexity and the realm of softness, characteristic of topology, such as the cobordism theory. The aim of this course is threefold: 1. An ove

From playlist Mikhail Gromov - Old, New and Unknown around Scalar Curvature

Video thumbnail

Mikhail Gromov - 1/4 Old, New and Unknown around Scalar Curvature

Geometry of scalar curvature, that is comparable in scope to symplectic geometry, mediates between two worlds: the domain of rigidity, one sees in convexity and the realm of softness, characteristic of topology, such as the cobordism theory. The aim of this course is threefold: 1. An ove

From playlist Mikhail Gromov - Old, New and Unknown around Scalar Curvature

Video thumbnail

Counting embedded curves in symplectic 6-manifolds - Aleksander Doan

Symplectic Dynamics/Geometry Seminar Topic: Counting embedded curves in symplectic 6-manifolds Speaker: Aleksander Doan Affiliation: Columbia University Date: February 03, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Open Gromov–Witten theory, skein modules, duality, and knot contact homology – T. Ekholm – ICM2018

Geometry | Topology Invited Lecture 5.7 | 6.3 Open Gromov–Witten theory, skein modules, large N duality, and knot contact homology Tobias Ekholm Abstract: Large N duality relates open Gromov–Witten invariants in the cotangent bundle of the 3-sphere with closed Gromov–Witten invariants in

From playlist Geometry

Video thumbnail

Transversality and super-rigidity in Gromov-Witten Theory by Chris Wendl

J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru

From playlist J-Holomorphic Curves and Gromov-Witten Invariants

Video thumbnail

Mikhael Gromov - 1/6 Probability, symmetry, linearity

I plan six lectures on possible directions of modification/generalization of the probability theory, both concerning mathematical foundations and applications within and without pure mathematics. Specifically, I will address two issues. 1. Enhancement of stochastic symmetry by linearizat

From playlist Mikhael Gromov - Probability, symmetry, linearity

Video thumbnail

Introduction to Contact Geometry by Dheeraj Kulkarni

DATE & TIME: 25 December 2017 to 04 January 2018 VENUE: Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex structure. The moduli space of these curves (

From playlist J-Holomorphic Curves and Gromov-Witten Invariants

Video thumbnail

Introduction to legendrian contact homology using pseudo-holomoprhic... by Michael G Sullivan

J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru

From playlist J-Holomorphic Curves and Gromov-Witten Invariants

Video thumbnail

Introduction to Gromov-Witten Invariants by Ritwik Mukherjee

J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru

From playlist J-Holomorphic Curves and Gromov-Witten Invariants

Video thumbnail

Quantum Cohomology and WDVV equation (Lecture 1) by Ritwik Mukherjee

Program : Integrable​ ​systems​ ​in​ ​Mathematics,​ ​Condensed​ ​Matter​ ​and​ ​Statistical​ ​Physics ORGANIZERS : Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE & TIME : 16 July 2018 to 10 August 2018 VENUE : Ramanujan L

From playlist Integrable​ ​systems​ ​in​ ​Mathematics,​ ​Condensed​ ​Matter​ ​and​ ​Statistical​ ​Physics

Video thumbnail

Moduli Space of Curves by Chitrabhanu Chaudhuri

J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru

From playlist J-Holomorphic Curves and Gromov-Witten Invariants

Video thumbnail

Symplectic homology, algebraic operations on (Lecture – 03) by Janko Latschev

J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru

From playlist J-Holomorphic Curves and Gromov-Witten Invariants

Video thumbnail

[BOURBAKI 2017] 21/10/2017 - 3/4 - Olivier GUICHARD

Groupes convexes-cocompacts en rang supérieur ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenriPoincare/ Twitter : https://twitter.com/InHenriPoincare Instagram : https://www

From playlist BOURBAKI - 2017

Video thumbnail

Transversality and super-rigidity in Gromov-Witten Theory (Lecture – 02) by Chris Wendl

J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru

From playlist J-Holomorphic Curves and Gromov-Witten Invariants

Video thumbnail

Introduction to h-principle by Mahuya Datta

DATE & TIME: 25 December 2017 to 04 January 2018 VENUE: Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex structure. The moduli space of these curves (

From playlist J-Holomorphic Curves and Gromov-Witten Invariants

Related pages

Gromov's compactness theorem (topology) | Geometric group theory | Gromov–Hausdorff convergence | Uniform convergence | Metric space | Ricci curvature | Natural number | Ultrafilter | Subsequence | Arzelà–Ascoli theorem | Riemannian manifold | Ultralimit | Bishop–Gromov inequality | Gromov's theorem on groups of polynomial growth | Riemannian geometry | Closed manifold