Geometric group theory | Properties of groups | Metric geometry | Combinatorics on words | Hyperbolic metric space | Hyperbolic geometry
In group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group equipped with a word metric satisfying certain properties abstracted from classical hyperbolic geometry. The notion of a hyperbolic group was introduced and developed by Mikhail Gromov. The inspiration came from various existing mathematical theories: hyperbolic geometry but also low-dimensional topology (in particular the results of Max Dehn concerning the fundamental group of a hyperbolic Riemann surface, and more complex phenomena in three-dimensional topology), and combinatorial group theory. In a very influential (over 1000 citations ) chapter from 1987, Gromov proposed a wide-ranging research program. Ideas and foundational material in the theory of hyperbolic groups also stem from the work of George Mostow, William Thurston, James W. Cannon, Eliyahu Rips, and many others. (Wikipedia).
Groups acting acylindrically on hyperbolic spaces – Denis Osin – ICM2018
Geometry Invited Lecture 5.3 Groups acting acylindrically on hyperbolic spaces Denis Osin Abstract: The goal of this article is to survey some recent developments in the study of groups acting on hyperbolic spaces. We focus on the class of ‘acylindrically hyperbolic groups’; it is broad
From playlist Geometry
Denis Osin: Acylindrically hyperbolic groups (part 3)
The lecture was held within the framework of Follow-up Workshop TP Rigidity. 1.5.2015
From playlist HIM Lectures 2015
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
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
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
Denis Osin: Acylindrically hyperbolic groups (part 1)
The lecture was held within the framework of Follow-up Workshop TP Rigidity. 28.4.2015
From playlist HIM Lectures 2015
Introduction to Hyperbolic Functions
This video provides a basic overview of hyperbolic function. The lesson defines the hyperbolic functions, shows the graphs of the hyperbolic functions, and gives the properties of hyperbolic functions. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Differentiation of Hyperbolic Functions
Camille Horbez: Automorphisms of hyperbolic groups and growth
Abstract: Let G be a torsion-free hyperbolic group, let S be a finite generating set of G, and let f be an automorphism of G. We want to understand the possible growth types for the word length of fn(g), where g is an element of G. Growth was completely described by Thurston when G is the
From playlist Topology
Calculus 2: Hyperbolic Functions (1 of 57) What is a Hyperbolic Function? Part 1
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what are hyperbolic functions and how it compares to trig functions. Next video in the series can be seen at: https://youtu.be/c8OR8iJ-aUo
From playlist CALCULUS 2 CH 16 HYPERBOLIC FUNCTIONS
Denis Osin: Acylindrically hyperbolic groups (part 2)
The lecture was held within the framework of Follow-up Workshop TP Rigidity. 30.4.2015
From playlist HIM Lectures 2015
Ariyan Javanpeykar: Arithmetic and algebraic hyperbolicity
Abstract: The Green-Griffiths-Lang-Vojta conjectures relate the hyperbolicity of an algebraic variety to the finiteness of sets of “rational points”. For instance, it suggests a striking answer to the fundamental question “Why do some polynomial equations with integer coefficients have onl
From playlist Algebraic and Complex Geometry
Prayagdeep Parija: Random Quotients of Hyperbolic Groups and Property (T)
Prayagdeep Parija, University of Wisconsin Milwaukee Title: Random Quotients of Hyperbolic Groups and Property (T) What does a typical quotient of a group look like? Gromov had looked at density model of quotients of free groups. The density parameter d measures the rate of exponential gro
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Denis Osin: Invariant random subgroups of acylindrically hyperbolic groups
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 Algebra
Hyperbolic surfaces and their Teichmüller spaces (Lecture - 02) by Subhojoy Gupta
Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b
From playlist Geometry, Groups and Dynamics (GGD) - 2017
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
Boris Apanasov: Non-rigidity for Hyperbolic Lattices and Geometric Analysis
Boris Apanasov, University of Oklahoma Title: Non-rigidity for Hyperbolic Lattices and Geometric Analysis We create a conformal analogue of the M. Gromov-I. Piatetski-Shapiro interbreeding construction to obtain non-faithful representations of uniform hyperbolic 3-lattices with arbitrarily
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022