Independence results | Mathematical problems | Group theory

Whitehead problem

In group theory, a branch of abstract algebra, the Whitehead problem is the following question: Is every abelian group A with Ext1(A, Z) = 0 a free abelian group? Saharon Shelah proved that Whitehead's problem is independent of ZFC, the standard axioms of set theory. (Wikipedia).

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What is General Relativity? Lesson 69: The Einstein Equation

What is General Relativity? Lesson 69: The Einstein Equation Having done so much work with the Einstein tensor, the interpretation of the Einstein equation is almost anti-climatic! The hard part is finding the Newtonian limit in order to understand the constant of proportionality between

From playlist What is General Relativity?

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Problems with the Calculus | Math History | NJ Wildberger

We discuss some of the controversy and debate generated by the 17th century work on Calculus. Newton and Leibniz's ideas were not universally accepted as making sense, despite the impressive, even spectacular achievements that the new theory was able to demonstrate. In this lecture we di

From playlist MathHistory: A course in the History of Mathematics

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Separation of variables and the Schrodinger equation

A brief explanation of separation of variables, application to the time-dependent Schrodinger equation, and the solution to the time part. (This lecture is part of a series for a course based on Griffiths' Introduction to Quantum Mechanics. The Full playlist is at http://www.youtube.com/

From playlist Mathematical Physics II - Youtube

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What is General Relativity? Lesson 68: The Einstein Tensor

What is General Relativity? Lesson 68: The Einstein Tensor The Einstein tensor defined! Using the Ricci tensor and the curvature scalar we can calculate the curvature scalar of a slice of a manifold using the Einstein tensor. Please consider supporting this channel via Patreon: https:/

From playlist What is General Relativity?

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What is the Riemann Hypothesis?

This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation

From playlist Mathematics

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19/11/2015 - Demetrios Christodoulou - The Formulation of the Two-Body Problem in General Relativity

Abstract. In my talk I shall discuss the formulation of the two-body problem in general relativity. The setup is to represent two stars coming in from infinity with asymptotically uniform velocities and with no incoming radiation. In electromagnetic theory, where the field equations are li

From playlist 2015-T3 - Mathematical general relativity - CEB Trimester

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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

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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

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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

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Gravity and its impact explained

Did you know that gravity is weaker than the pull of a fridge magnet? Despite this, it’s responsible for everything from ocean tides to the formation of stars. Learn more about this intriguing force in our video. Find out more information at https://bit.ly/34OwJmR To get the latest sc

From playlist Engineering Wonders

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Barber & Russell Paradoxes (History of Undecidability Part 2) - Computerphile

$20 off your 1st purchase at www.LittleBits.com use the code “COMPUTERPHILE” The Barber Paradox: Professor Brailsford continues the history of undecidability. History of Undecidability Part1: http://youtu.be/nsZsd5qtbo4 Turing & The Halting Problem: http://youtu.be/macM_MtS_w4 http://

From playlist The History of Undecidability

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Mark Feighn: The conjugacy problem for polynomially growing elements of Out(F_n)

(joint work with Michael Handel) $Out(F_{n}) := Aut(F_{n})/Inn(F_{n})$ denotes the outer automorphism group of the rank n free group $F_{n}$. An element $f$ of $Out(F_{n})$ is polynomially growing if the word lengths of conjugacy classes in Fn grow at most polynomially under iteration by $

From playlist Topology

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Lars Andersson - Geometry and analysis in black hole spacetimes (Part 4)

Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity. Following a brief i

From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale

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Mark Grant (10/22/20): Bredon cohomology and LS-categorical invariants

Title: Bredon cohomology and LS-categorical invariants Abstract: Farber posed the problem of describing the topological complexity of aspherical spaces in terms of algebraic invariants of their fundamental groups. In Part One of this talk, I’ll discuss joint work with Farber, Lupton and O

From playlist Topological Complexity Seminar

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Christoph Winges: On the isomorphism conjecture for Waldhausen's algebraic K-theory of spaces

The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "The Farrell-Jones conjecture" I will survey recent progress on the isomorphism conjecture for Waldhausen's "algebraic K-theory of spaces" functor, and how this relates to the original isomorp

From playlist HIM Lectures: Junior Trimester Program "Topology"

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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

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Frege, Russell, & Modern Logic - A. J. Ayer & Bryan Magee (1987)

In this program, A. J. Ayer discusses the work of Gottlob Frege, Bertrand Russell, and modern logic with Bryan Magee. This is from the 1987 series on great philosophers. #Philosophy #Bryanmagee #BertrandRussell

From playlist Bryan Magee Interviews - The Great Philosophers (1987)

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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

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Lars Andersson - Geometry and analysis in black hole spacetimes (Part 2)

Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity. Following a brief i

From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale

Related pages

Exact sequence | Ext functor | Whitehead torsion | Axiom of constructibility | Set theory | Abstract algebra | Free abelian group | Constructible universe | Continuum hypothesis | Group theory | Consistency | Independence (mathematical logic) | Abelian group | Martin's axiom