Trigonometry in elliptic geometry | Universal Hyperbolic Geometry 41 | NJ Wildberger
We here introduce new laws for spherical and elliptic trigonometry. These are natural consequences of applying Rational Trigonometry to the three dimensional projective setting. Remarkably, the main laws end up being exactly the same as those in Universal Hyperbolic Geometry! It means ther
From playlist Universal Hyperbolic Geometry
Is there a difference between a donut and a cup of coffee? It turns out the answer is no! In this video, we'll define the notion of homeomorphism and see why those two objects are homeomorphic. Enjoy! Topology Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHGGBXRMV32
From playlist Topology
Divine Proportions: Rational Trigonometry to Universal Geometry
I discuss my book Divine Proportions: Rational Trigonometry to Universal Geometry, which gives a novel way of thinking not only about trigonometry, but also Euclidean geometry. It also lays the ground work for a more rational and logical approach to other geometries, including hyperbolic g
From playlist MathSeminars
Spherical and elliptic geometries: an introduction | Universal Hyperbolic Geometry 33
We introduce PART II of this course on universal hyperbolic geometry: Bringin geometries together. This lecture introduces the very basic definitions of spherical geometry; lines as great circles, antipodal points, spherical triangles, circles, and some related notions on points, lines and
From playlist Universal Hyperbolic Geometry
Applications of rational spherical trigonometry I | Universal Hyperbolic Geometry 43 | NJ Wildberger
We review the basics of rational spherical/elliptic trigonometry, a cleaner more logical view of classical spherical trigonometry which is intimately linked with hyperbolic geometry. We illustrate the basic laws by having an in-depth look at a specific example of a spherical triangle, fo
From playlist Universal Hyperbolic Geometry
Apollonius and polarity | Universal Hyperbolic Geometry 1 | NJ Wildberger
This is the start of a new course on hyperbolic geometry that features a revolutionary simplifed approach to the subject, framing it in terms of classical projective geometry and the study of a distinguished circle. This subject will be called Universal Hyperbolic Geometry, as it extends t
From playlist Universal Hyperbolic Geometry
Rational trigonometry: an overview | Universal Hyperbolic Geometry 39 | NJ Wildberger
This important video introduces Rational Trigonometry from first principles using a vector approach. The main notions of quadrance and spread replace distance and angle, and are introduced purely algebraically. The scalar/inner/dot product plays an important role, and allows us to introduc
From playlist Universal Hyperbolic Geometry
Emily Stark: The visual boundary of hyperbolic free-by-cyclic groups
Abstract: Given an automorphism of the free group, we consider the mapping torus defined with respect to the automorphism. If the automorphism is atoroidal, then the resulting free-by-cyclic group is hyperbolic by work of Brinkmann. In addition, if the automorphism is fully irreducible, th
From playlist Topology
Barcodes for Hamiltonian homeomorphisms of surfaces -Benoît Joly
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Barcodes for Hamiltonian homeomorphisms of surfaces Speaker: Benoît Joly Affiliation: Ruhr-Universität Bochum Date: March 25, 2022 In this talk, we will study the Floer Homology barcodes from a dynamical poin
From playlist Mathematics
Parallel session 9 by Jean-Francois Lafont
Geometry Topology and Dynamics in Negative Curvature URL: https://www.icts.res.in/program/gtdnc DATES: Monday 02 Aug, 2010 - Saturday 07 Aug, 2010 VENUE : Raman Research Institute, Bangalore DESCRIPTION: This is An ICM Satellite Conference. The conference intends to bring together ma
From playlist Geometry Topology and Dynamics in Negative Curvature
Canonical forms for free group automorphisms - Jean Pierre Mutanguha
Arithmetic Groups Topic: Canonical forms for free group automorphisms Speaker: Jean Pierre Mutanguha Affiliation: Member, School of Mathematics Date: March 23, 2022 The Nielsen-Thurston theory of surface homeomorphism can be thought of as a surface analogue to the Jordan Canonical Form.
From playlist Mathematics
The remarkable Platonic solids I | Universal Hyperbolic Geometry 47 | NJ Wildberger
The Platonic solids have fascinated mankind for thousands of years. These regular solids embody some kind of fundamental symmetry and their analogues in the hyperbolic setting will open up a whole new domain of discourse. Here we give an introduction to these fascinating objects: the tetra
From playlist Universal Hyperbolic Geometry
Flows, planes, and circles - Steven Frankel
Short Talks by Postdoctoral Members Steven Frankel - September 21, 2015 http://www.math.ias.edu/calendar/event/87724/1442865600/1442866500 More videos on http://video.ias.edu
From playlist Short Talks by Postdoctoral Members
Jens Hemelaer: Toposes in arithmetic noncommutative geometry
Talk by Jens Hemelaer in Global Noncommutative Geometry Seminar (Americas) on February 5, 2021
From playlist Global Noncommutative Geometry Seminar (Americas)
Diffeomorphism Groups of Critical Regularity (Lecture 4) by Sang-hyun Kim
PROGRAM: PROBABILISTIC METHODS IN NEGATIVE CURVATURE ORGANIZERS: Riddhipratim Basu (ICTS - TIFR, India), Anish Ghosh (TIFR, Mumbai, India), Subhajit Goswami (TIFR, Mumbai, India) and Mahan M J (TIFR, Mumbai, India) DATE & TIME: 27 February 2023 to 10 March 2023 VENUE: Madhava Lecture Hall
From playlist PROBABILISTIC METHODS IN NEGATIVE CURVATURE - 2023
Lie Groups and Lie Algebras: Lesson 40: SU(2) as Universal Covering Group
Lie Groups and Lie Algebras: Lesson 40: SU(2) as Universal Covering Group In this lesson we walk through the example of SO(3), SL(1,Q), and SU(2). This will prepare us for a more complex example: u(2)! Please consider supporting this channel on Patreon: https://www.patreon.com/XYLYXYLYX
From playlist Lie Groups and Lie Algebras
Graham ELLIS - Computational group theory, cohomology of groups and topological methods 3
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Set Theory (Part 2b): The Bogus Universal Set
Please feel free to leave comments/questions on the video below! In this video, I argue against the existence of the set of all sets and show that this claim is provable in ZFC. This theorem is very much tied to the Russell Paradox, besides being one of the problematic ideas in mathematic
From playlist Set Theory by Mathoma
Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group
Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group We are finally in position to understand the nature of the Universal Covering Group and its connection to all the Lie groups which share a single Lie algebra. This is a critical lecture! In this lecture we simply state
From playlist Lie Groups and Lie Algebras