Theorems in functional analysis
In functional analysis, the Dixmier-Ng Theorem is a characterization of when a normed space is in fact a dual Banach space. Dixmier-Ng Theorem. Let be a normed space. The following are equivalent: 1. * There exists a Hausdorff locally convex topology on so that the closed unit ball, , of is -compact. 2. * There exists a Banach space so that is isometrically isomorphic to the dual of . That 2. implies 1. is an application of the Banach–Alaoglu theorem, setting to the Weak-* topology. That 1. implies 2. is an application of the Bipolar theorem. (Wikipedia).
A Complete Dichotomy Rises from the Capture of Vanishing Signatures - Jin-Yi Cai
Jin-Yi Cai University of Wisconsin November 19, 2012 Holant Problems are a broad framework to describe counting problems. The framework generalizes counting Constraint Satisfaction Problems and partition functions of Graph Homomorphisms. We prove a complexity dichotomy theorem for Holant
From playlist Mathematics
Differential Isomorphism and Equivalence of Algebraic Varieties Board at 49:35 Sum_i=1^N 2/(x-phi_i(y,t))^2
From playlist Fall 2017
Ulrich Pennig: "Fell bundles, Dixmier-Douady theory and higher twists"
Actions of Tensor Categories on C*-algebras 2021 "Fell bundles, Dixmier-Douady theory and higher twists" Ulrich Pennig - Cardiff University, School of Mathematics Abstract: Classical Dixmier-Douady theory gives a full classification of C*-algebra bundles with compact operators as fibres
From playlist Actions of Tensor Categories on C*-algebras 2021
D-varieties and the Dixmier-Moeglin equivalence - R. Moosa - Workshop 3 - CEB T1 2018
Rahim Moosa (Waterloo) / 28.03.2018 D-varieties and the Dixmier-Moeglin Equivalence About four years ago, a new application of the model theory of differentially closed fields arose. The target was the Dixmier-Moeglin equivalence problem (DME) in noncommutative affine algebras, as well a
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Jean Pierre Labesse - L’héritage de Roger Godement
J’évoquerai tout d’abord la carrière scientifique de Roger Godement, ses goûts et son influence via ses exposés, ses cours et ses élèves. Dans une seconde partie j’exposerai l’état du travail avec Bertrand Lemaire sur la formule des traces en caractéristique positive. Ce se
From playlist Reductive groups and automorphic forms. Dedicated to the French school of automorphic forms and in memory of Roger Godement.
Definably simple groups in valued fields - D. Macpherson - Workshop 3 - CEB T1 2018
Dugald Macpherson (Leeds) / 29.03.2018 D-varieties and the Dixmier-Moeglin Equivalence About four years ago, a new application of the model theory of differentially closed fields arose. The target was the Dixmier-Moeglin equivalence problem (DME) in noncommutative affine algebras, as wel
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Number Theory | Linear Diophantine Equations
We explore the solvability of the linear Diophantine equation ax+by=c
From playlist Divisibility and the Euclidean Algorithm
Easiest Way to Multiply Two Trinomials by Each Other - Math Tutorial
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply a Trinomial by a Trinomial
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
The Distributive Property (L2.4)
This video defines the distributive property and provides several examples of how to multiply using the distributive property. Video content created Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)
From playlist The Distributive Property and Simplifying Algebraic Expressions
Invariant hypersurfaces We study an extension of a theorem of Cantat, which says that if $\phi:X \rightarrow X$ is adominant rational self-map then the number of totally invariant hypersurfaces $C$ (that is, hyper-surfaces for which $\phi^{-1}(C)=C$) is finite unless $\phi\circ f=\phi$ f
From playlist DART X
Diophantine properties of Markoff numbers - Jean Bourgain
Using available results on the strong approximation property for the set of Markoff triples together with an extension of Zagier’s counting result, we show that most Markoff numbers are composite. For more videos, visit http://video.ias.edu
From playlist Mathematics
A nonabelian Brunn-Minkowski inequality - Ruixiang Zhang
Members’ Seminar Topic: A nonabelian Brunn-Minkowski inequality Speaker: Ruixiang Zhang Affiliation: University of Wisconsin-Madison; Member, School of Mathematics Date: January 25, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
How to Simplify an Expression Using Distributive Property - Math Tutorial
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
#shorts This video reviews the divisibility rule for 3.
From playlist Math Shorts
[BOURBAKI 2019] La C*-simplicité - Raum - 19/01/19 - 2/4
Sven RAUM / 19.01.19 La C∗-simplicité, d’après Kalantar-Kennedy, Breuillard-Kalantar-Kennedy-Ozawa, Kennedy et Haagerup Un groupe est dit C∗-simple si sa C∗-algèbre réduite est simple. Cet exposé commence par un résumé d’his- toire de la C∗-simplicité avant 2014, l’année de la découverte
From playlist BOURBAKI - 2019
Applications of additive combinatorics to Diophantine equations - Alexei Skorobogatov
Alexei Skorobogatov Imperial College London April 10, 2014 The work of Green, Tao and Ziegler can be used to prove existence and approximation properties for rational solutions of the Diophantine equations that describe representations of a product of norm forms by a product of linear poly
From playlist Mathematics
Visual Group Thoery, Lecture 5.5: p-groups
Visual Group Thoery, Lecture 5.5: p-groups Before we can introduce the Sylow theorems, we need to develop some theory about groups of prime power order, which we call p-groups. In this lecture, we show that the number of fixed point of a p-group acting on a set S is congruent modulo p to
From playlist Visual Group Theory
Alain Connes: The Music of Shapes
19th Wright Colloquium, Geneva, Nov 5, 2020 https://colloquewright.ch/en/public-talks/the-music-of-shapes/ Title: The Music of Shapes Abstract: Quantum physics, especially matrix mechanics, has had a profound influence on mathematical notions of geometric space. This lecture will explain t
From playlist Noncommutative Geometry
Using the Box Method to Multiply a Trinomial by a Trinomial - Math Tutorial
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply a Trinomial by a Trinomial