Theorems in functional analysis | Articles containing proofs | Operator theory
The Sz.-Nagy dilation theorem (proved by Béla Szőkefalvi-Nagy) states that every contraction T on a Hilbert space H has a unitary dilation U to a Hilbert space K, containing H, with Moreover, such a dilation is unique (up to unitary equivalence) when one assumes K is minimal, in the sense that the linear span of ∪nUnH is dense in K. When this minimality condition holds, U is called the minimal unitary dilation of T. (Wikipedia).
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This class introduces recent research on flattening fixed-angle chains and addresses flipping of pockets in a polygon. Flaws and o
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
Dimitri Zvonkine - On two ELSV formulas
The ELSV formula (discovered by Ekedahl, Lando, Shapiro and Vainshtein) is an equality between two numbers. The first one is a Hurwitz number that can be defined as the number of factorizations of a given permutation into transpositions. The second is the integral of a characteristic class
From playlist 4th Itzykson Colloquium - Moduli Spaces and Quantum Curves
Dimitri Zvonkine - Hurwitz numbers, the ELSV formula, and the topological recursion
We will use the example of Hurwitz numbers to make an introduction into the intersection theory of moduli spaces of curves and into the subject of topological recursion.
From playlist Physique mathématique des nombres de Hurwitz pour débutants
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
Yuri Kifer: Nonconventional limit theorems in probability and dynamical systems
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 Probability and Statistics
L6.2 Weak-field Zeeman effect; general structure
MIT 8.06 Quantum Physics III, Spring 2018 Instructor: Barton Zwiebach View the complete course: https://ocw.mit.edu/8-06S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L L6.2 Weak-field Zeeman effect; general structure License: Creative Common
From playlist MIT 8.06 Quantum Physics III, Spring 2018
We learned from the central limit theorem that a mean of a sample or difference between means of samples are just one of many, many others. All of these means or differences in means follow a distribution pattern.
From playlist Learning medical statistics with python and Jupyter notebooks
Digression: THH of the integers (corrected)
In this video, we explain how to compute THH of the integers. In order to do this we compute it first relative to the element p and then use a spectral sequence to deduce the final result. This is a corrected version of the old video, in which I got the Hasse-squares at 13:10 and 24:20 w
From playlist Topological Cyclic Homology
"Order-by-Disorder" in the Hilbert Space and Anomalous Thermalization in Rokhsar....by Arnab Sen
PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In
From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)
Chapter13_The_central_limit_theorem_vignette
In this lesson we take a look at what lies at the heart of inferential statistics: the central limit theorem. It describes the distribution of possible study means.
From playlist Learning medical statistics with python and Jupyter notebooks
Number Theory 1.1 : Product Formula for the Zeta Function
In this video, I prove Euler's product formula for the Riemann Zeta function. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Number Theory
Differential Equations | Abel's Theorem
We present Abel's Theorem with a proof. http://www.michael-penn.net
From playlist Differential Equations
Lecture 8 | New Revolutions in Particle Physics: Basic Concepts
(November 16, 2009) Leonard Susskind discusses the theory and mathematics of particle spin and half spin, the Dirac equation, and isotopic spin. Leonard Susskind, Felix Bloch Professor of Physics, received a PhD from Cornell University and has taught at Stanford since 1979. He has won b
From playlist Lecture Collection | Particle Physics: Basic Concepts
Alessandra Sarti: Topics on K3 surfaces - Lecture 3: Basic properties of K3 surfaces
Abstract: Aim of the lecture is to give an introduction to K3 surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space. The name K3 was given by André Weil in 1958 in hono
From playlist Algebraic and Complex Geometry
From playlist Courses and Series
Weil conjectures 1 Introduction
This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie
From playlist Algebraic geometry: extra topics
Homotopical effects of k-dilation - Larry Guth
Variational Methods in Geometry Seminar Topic: Homotopical effects of k-dilation Speaker: Larry Guth Affiliation: Massachusetts Institute of Technology Date: November 27, 2018 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
The Hungarian Revolution of 1956: History Matters (Short Animated Documentary)
Twitter: https://twitter.com/Tenminhistory Patreon: https://www.patreon.com/user?u=4973164 Merch: https://teespring.com/stores/history-matters-store-2 Special Thanks to the following Patrons for their support on Patreon: Franco La Bruna James Baker Daniel Lambert Richard Wolfe Chris Fatt
From playlist Playlist: The Cold War (1945-1991)
Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
László Moholy-Nagy, Composition A.XX, 1924, oil on canvas, 135.5 x 115cm (Musée national d'art moderne, Centre Georges Pompidou, Paris) Speakers: Dr. Beth Harris and Dr. Steven Zucker. Created by Beth Harris and Steven Zucker.
From playlist Expressionism to Pop Art | Art History | Khan Academy