Relativity 8 - the yardstick of spacetime
The final piece of the puzzle falls in place. Herman Minkowski showed that Special Relativity defines a spacetime invariant - the "proper time" - between two events. Einstein's insight into the equivalence between falling and floating allowed him to realize that this also applied to Genera
From playlist Relativity
Giovanni Sambin: Pointfree topology is real and pointwise is ideal
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Both competing visions of mathematics in the past century, the thesis of formal- ism and the antithesis intuitionism, assume a notion of truth in which the quality of in
From playlist Workshop: "Constructive Mathematics"
Null points and null lines | Universal Hyperbolic Geometry 12 | NJ Wildberger
Null points and null lines are central in universal hyperbolic geometry. By definition a null point is just a point which lies on its dual line, and dually a null line is just a line which passes through its dual point. We extend the rational parametrization of the unit circle to the proj
From playlist Universal Hyperbolic Geometry
Hausdorff Example 1: Cofinite Topology
Point Set Topology: We recall the notion of a Hausdorff space and consider the cofinite topology as a source of non-Hausdorff examples. We also note that this topology is always compact.
From playlist Point Set Topology
Marston Morse - An Isoperimetric Concept for the Mass in General Relativity - Gerhard Huisken
Gerhard Huisken Max-Planck Institute for Gravitational Physics March 20, 2009 For more videos, visit http://video.ias.edu
From playlist Mathematics
Why it took 379 pages to prove 1+1=2
Sign up to Brilliant to receive a 20% discount with this link! https://brilliant.org/upandatom/ Hi! I'm Jade. If you'd like to consider supporting Up and Atom, head over to my Patreon page :) https://www.patreon.com/upandatom Visit the Up and Atom store https://store.nebula.app/collecti
From playlist Math
Discrete groups in complex hyperbolic geometry (Lecture - 2) by Pierre Will
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
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
Gérard Besson: Some open 3-manifolds
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 Algebraic and Complex Geometry
Hausdorff Example 3: Function Spaces
Point Set Topology: For a third example, we consider function spaces. We begin with the space of continuous functions on [0,1]. As a metric space, this example is Hausdorff, but not complete. We consider Cauchy sequences and a possible completion.
From playlist Point Set Topology
Karen Vogtmann - On the cohomological dimension of automorphism groups of RAAGs
The class of right-angled Artin groups (RAAGs) includes free groups and free abelian groups, Both of these have extremely interesting automorphism groups, which share some properties and not others. We are interested in automorphism groups of general RAAGs, and in particular
From playlist Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette
The circle and Cartesian coordinates | Universal Hyperbolic Geometry 5 | NJ Wildberger
This video introduces basic facts about points, lines and the unit circle in terms of Cartesian coordinates. A point is an ordered pair of (rational) numbers, a line is a proportion (a:b:c) representing the equation ax+by=c, and the unit circle is x^2+y^2=1. With this notation we determine
From playlist Universal Hyperbolic Geometry
A. Wright - Mirzakhani's work on Earthquakes (Part 2)
We will give the proof of Mirzakhani's theorem that the earthquake flow and Teichmuller unipotent flow are measurably isomorphic. We will assume some familiarity with quadratic differentials, but no familiarity with earthquakes, and the first lecture will be devoted to preliminaries. The s
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Rational Homotopy Groups (Lecture 3) By Somnath Basu
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Projective view of conics and quadrics | Differential Geometry 9 | NJ Wildberger
In this video we introduce projective geometry into the study of conics and quadrics. Our point of view follows Mobius and Plucker: the projective plane is considered as the space of one-dimensional subspaces of a three dimensional vector space, or in other words lines through the origin.
From playlist Differential Geometry
Lie Algebras and Homotopy Theory - Jacob Lurie
Members' Seminar Topic: Lie Algebras and Homotopy Theory Speaker: Jacob Lurie Affiliation: Professor, School of Mathematics Date: November 11, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Spectra and stable homotopy theory (Remote Talk) by Samik Basui
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
Giles Gardam: Kaplansky's conjectures
Talk by Giles Gardam in the Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/3580/ on September 17, 2021.
From playlist Global Noncommutative Geometry Seminar (Americas)
Stable Homotopy Seminar, 15: Dualizable and invertible spectra
I present the useful fact that spectra are generated by finite complexes under filtered homotopy colimits. I then define Spanier-Whitehead duality, which is a special case of a notion of duality that exists in any closed symmetric monoidal category. Two natural classes of spectra rise from
From playlist Stable Homotopy Seminar
Classical spherical trigonometry | Universal Hyperbolic Geometry 36 | NJ Wildberger
This video presents a summary of classical spherical trigonometry. First we define spherical distance between two points on a sphere, then the angle between two lines on a sphere (i.e. great circles). After a quick reminder of the circular functions cos,sin and tan, we present the main la
From playlist Universal Hyperbolic Geometry