Metric geometry | Hyperbolic geometry | Hyperbolic metric space
In mathematics, a hyperbolic metric space is a metric space satisfying certain metric relations (depending quantitatively on a nonnegative real number δ) between points. The definition, introduced by Mikhael Gromov, generalizes the metric properties of classical hyperbolic geometry and of trees. Hyperbolicity is a large-scale property, and is very useful to the study of certain infinite groups called Gromov-hyperbolic groups. (Wikipedia).
Metric space definition and examples. Welcome to the beautiful world of topology and analysis! In this video, I present the important concept of a metric space, and give 10 examples. The idea of a metric space is to generalize the concept of absolute values and distances to sets more gener
From playlist Topology
The circle and projective homogeneous coordinates (cont.) | Universal Hyperbolic Geometry 7b
Universal hyperbolic geometry is based on projective geometry. This video introduces this important subject, which these days is sadly absent from most undergrad/college curriculums. We adopt the 19th century view of a projective space as the space of one-dimensional subspaces of an affine
From playlist Universal Hyperbolic Geometry
Hyperbolic Geometry is Projective Relativistic Geometry (full lecture)
This is the full lecture of a seminar on a new way of thinking about Hyperbolic Geometry, basically viewing it as relativistic geometry projectivized, that I gave a few years ago at UNSW. We discuss three dimensional relativistic space and its quadratic/bilinear form, particularly the uppe
From playlist MathSeminars
The circle and projective homogeneous coordinates | Universal Hyperbolic Geometry 7a | NJ Wildberger
Universal hyperbolic geometry is based on projective geometry. This video introduces this important subject, which these days is sadly absent from most undergrad/college curriculums. We adopt the 19th century view of a projective space as the space of one-dimensional subspaces of an affine
From playlist Universal Hyperbolic Geometry
Hyperbola 3D Animation | Objective conic hyperbola | Digital Learning
Hyperbola 3D Animation In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other an
From playlist Maths Topics
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
A handy three step guide to identifying hyperbolic geometry in the wild! #SoME1 e-mail: uadhi2@gmail.com
From playlist Summer of Math Exposition Youtube Videos
What is a metric space? An example
This is a basic introduction to the idea of a metric space. I introduce the idea of a metric and a metric space framed within the context of R^n. I show that a particular distance function satisfies the conditions of being a metric.
From playlist Mathematical analysis and applications
What are Hyperbolas? | Ch 1, Hyperbolic Trigonometry
This is the first chapter in a series about hyperbolas from first principles, reimagining trigonometry using hyperbolas instead of circles. This first chapter defines hyperbolas and hyperbolic relationships and sets some foreshadowings for later chapters This is my completed submission t
From playlist Summer of Math Exposition 2 videos
Urs Lang (2/3/23): Combinatorial dimension and higher-rank hyperbolicity
Dress characterized metric spaces of combinatorial dimension at most n in terms of a 2(n+1)-point inequality. We investigate a relaxed version of this inequality, which in the case n = 1 reduces to Gromov's quadruple definition of δ-hyperbolicity and which we experimentally call (n,δ)-hype
From playlist Vietoris-Rips Seminar
Anna Sakovich: On the mass of asymptotically hyperbolic manifolds and initial data set
HYBRID EVENT A complete Riemannian manifold is called asymptotically hyperbolic if its ends are modeled on neighborhoods of infinity in hyperbolic space. There is a notion of mass for this class of manifolds defined as a coordinate invariant computed in a fixed asymptotically hyperbolic en
From playlist Analysis and its Applications
Hyperbolic geometry, Fuchsian groups and moduli spaces (Lecture 1) by Subhojoy Gupta
ORGANIZERS : C. S. Aravinda and Rukmini Dey DATE & TIME: 16 June 2018 to 25 June 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore This workshop on geometry and topology for lecturers is aimed for participants who are lecturers in universities/institutes and colleges in India. This wi
From playlist Geometry and Topology for Lecturers
A. Zorich - Counting simple closed geodesics and volumes of moduli spaces (Part 1)
In the first two lectures I will try to tell (or, rather, to give an idea) of how Maryam Mirzakhani has counted simple closed geodesics on hyperbolic surfaces. I plan to briefly mention her count of Weil-Peterson volumes and her proof of Witten's conjecture, but only on the leve
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Jean-Pierre Demailly - Kobayashi pseudo-metrics, entire curves and hyperbolicity of ... (Part 2)
We will first introduce the basic concepts pertaining to Kobayashi pseudo-distances and hyperbolic complex spaces, including Brody’s theorem and the Ahlfors-Schwarz lemma. One of the main goals of the theory is to understand conditions under which a given algebraic variety is Kobayashi hyp
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
Anna Wienhard (7/29/22): Graph Embeddings in Symmetric Spaces
Abstract: Learning faithful graph representations has become a fundamental intermediary step in a wide range of machine learning applications. We propose the systematic use of symmetric spaces as embedding targets. We use Finsler metrics integrated in a Riemannian optimization scheme, that
From playlist Applied Geometry for Data Sciences 2022
A. Zorich - Counting simple closed geodesics and volumes of moduli spaces (Part 2)
In the first two lectures I will try to tell (or, rather, to give an idea) of how Maryam Mirzakhani has counted simple closed geodesics on hyperbolic surfaces. I plan to briefly mention her count of Weil-Peterson volumes and her proof of Witten's conjecture, but only on the leve
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Constructing group actions on quasi-trees – Koji Fujiwara – ICM2018
Topology Invited Lecture 6.12 Constructing group actions on quasi-trees Koji Fujiwara Abstract: A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general construction of many actions of groups on quasi-trees. The groups we can handle include non-elementary hype
From playlist Topology
What is the definition of a hyperbola
Learn all about hyperbolas. A hyperbola is a conic section with two fixed points called the foci such that the difference between the distances of any point on the hyperbola from the two foci is equal to the distance between the two foci. Some of the characteristics of a hyperbola includ
From playlist The Hyperbola in Conic Sections
Antoine Song - Spherical Plateau problem and applications
I will discuss an area minimization problem in certain quotients of the Hilbert sphere by countable groups. An early version of that setting appears in Besson-Courtois-Gallot’s work on the entropy inequality. As an application of this minimization problem, we obtain some stability results.
From playlist Not Only Scalar Curvature Seminar