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
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?
Albert Einstein, Holograms and Quantum Gravity
In the latest campaign to reconcile Einstein’s theory of gravity with quantum mechanics, many physicists are studying how a higher dimensional space that includes gravity arises like a hologram from a lower dimensional particle theory. Read about the second episode of the new season here:
From playlist In Theory
The big mathematics divide: between "exact" and "approximate" | Sociology and Pure Maths | NJW
Modern pure mathematics suffers from a major schism that largely goes unacknowledged: that many aspects of the subject are parading as "exact theories" when in fact they are really only "approximate theories". In this sense they can be viewed either as belonging more properly to applied ma
From playlist Sociology and Pure Mathematics
Einstein Field Equations - for beginners!
Einstein's Field Equations for General Relativity - including the Metric Tensor, Christoffel symbols, Ricci Cuvature Tensor, Curvature Scalar, Stress Energy Momentum Tensor and Cosmological Constant.
From playlist Gravity
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"
Christoph Winges: Automorphisms of manifolds and the Farrell Jones conjectures
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Building on previous work of Bartels, Lück, Reich and others studying the algebraic K-theory and L-theory of discrete group rings, the validity of the Farrell-Jones Conjecture has be
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
A (compelling?) reason for the Riemann Hypothesis to be true #SOME2
A visual walkthrough of the Riemann Zeta function and a claim of a good reason for the truth of the Riemann Hypothesis. This is not a formal proof but I believe the line of argument could lead to a formal proof.
From playlist Summer of Math Exposition 2 videos
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
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
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?
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
Michael Farber: Topology of large random spaces
The lecture was held within the framework of the Hausdorff Trimester Program : Applied and Computational Algebraic Topology I will discuss various models producing large random spaces (simplicial complexes and closed manifolds). The main goal is to analyse properties which hold with proba
From playlist HIM Lectures: Special Program "Applied and Computational Algebraic Topology"
Dale Rolfsen: Braids, Orderings and Minimal Volume Cusped Hyperbolic 3-Manifolds
Dale Rolfsen, University of British Columbia Title: Braids, Orderings and Minimal Volume Cusped Hyperbolic 3-Manifolds The orderability properties of fundamental groups of minimal volume cusped hyperbolic 3-manifolds will be explored using the theory of braids and automorphisms of free gro
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Differential Equations | Abel's Theorem
We present Abel's Theorem with a proof. http://www.michael-penn.net
From playlist Differential Equations
Retract rationality of some (exceptional) group varieties by Maneesh Thakur
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Mohammed Abouzaid: Nearby Lagrangians are simply homotopic
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 Jean-Morlet Chair - Lalonde/Teleman
General Relativity & Mathematical Reality
Yet another anecdote that (in my opinion) suggest that mathematics is the basis of our reality: Inside Einstein's Mind — PBS Nova In this brief clip explaining the beauty of Einstein's equation for General Relativity, Professor Robbert Dijkgraaf of Princeton's Institute for Advanced Study
From playlist Gravity
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)