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
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
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
Sunhyuk Lim (9/24/21): The Gromov-Hausdorff distance between spheres
We provide general upper and lower bounds for the Gromov-Hausdorff distance d_GH(S^m,S^n) between spheres S^m and S^n (endowed with the round metric) for m less than n, with both integers between 0 and infinity, inclusive. Some of these lower bounds are based on certain topological ideas r
From playlist Vietoris-Rips Seminar
Dimitri Zvonkine - On two ELSV formulas
The ELSV formula (discovered by Ekedahl, Lando, Shapiro and Vainshtein) is an equality between two numbers. The first one is a Hurwitz number that can be defined as the number of factorizations of a given permutation into transpositions. The second is the integral of a characteristic class
From playlist 4th Itzykson Colloquium - Moduli Spaces and Quantum Curves
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
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
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
Riemann Sum Defined w/ 2 Limit of Sums Examples Calculus 1
I show how the Definition of Area of a Plane is a special case of the Riemann Sum. When finding the area of a plane bound by a function and an axis on a closed interval, the width of the partitions (probably rectangles) does not have to be equal. I work through two examples that are rela
From playlist Calculus
How Large is the Shadow of a Symplectic Ball? - Alberto Abbondandolo
Alberto Abbondandolo University of Pisa, Italy February 8, 2012 I will discuss a middle-dimensional generalization of Gromov's Non-Squeezing Theorem. For more videos, visit http://video.ias.edu
From playlist Mathematics
Lagrangian Floer theory (Lecture – 02) by Sushmita Venugopalan
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
Symplectic Dynamics Seminar: How Large is the Shadow of a Symplectic Ball? - Alberto Abbondandolo
Alberto Abbondandolo University of Pisa, Italy February 8, 2012 I will discuss a middle-dimensional generalization of Gromov's Non-Squeezing Theorem. For more videos, visit http://video.ias.edu
From playlist Mathematics
[BOURBAKI 2017] 14/01/2017 - 1/4 - Cédric VILLANI
Inégalités isopérimétriques dans les espaces métriques mesurés, d’après F. Cavalletti et A. Mondino La théorie synthétique de la courbure de Ricci dans les espaces métriques mesurés a remporté ses premiers succès il y a une dizaine d’années, et s’est rapidement développée depuis ; elle ac
From playlist BOURBAKI - 2017
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
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
Samplings and Observables. Limits of measured metric spaces - Gabor Elek
Conference on Graphs and Analysis Gabor Elek June 4, 2012 More videos on http://video.ias.edu
From playlist Mathematics
Séminaire Bourbaki 08/11/2014 - Rémi Coulon 1/4
"Théorie de la petite simplification : une approche géométrique" [d'après F. Dahmani, V. Guirardel, D. Osin et S. Cantat, S. Lamy] Une "bonne" action de groupe sur un espace hyperbolique (au sens de Gromov) permet de capturer les propriétés à large échelle du groupe. N'importe quelle ac
From playlist Bourbaki - 08 novembre 2014
Facundo Mémoli (5/2/21): The Gromov-Hausdorff distance between spheres
The Gromov-Hausdorff distance is a fundamental tool in Riemanian geometry, and also in applied geometry and topology. Whereas it is often easy to estimate the value of the distance between two given metric spaces, its precise value is rarely easy to determine. In this talk I will describe
From playlist TDA: Tutte Institute & Western University - 2021
L^2 methods, projective embeddings and Kahler-Einstein metrics (Lecture 1)by Ved Datar
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Youness Lamzouri: Large character sums
Abstract : For a non-principal Dirichlet character χ modulo q, the classical Pólya-Vinogradov inequality asserts that M(χ):=maxx|∑n≤xχ(n)|=O(q‾√log q). This was improved to q‾√log log q by Montgomery and Vaughan, assuming the Generalized Riemann hypothesis GRH. For quadratic characters, th
From playlist Number Theory