Unsolved problems in mathematics | Abstract algebra | Conjectures

Dixmier conjecture

In algebra the Dixmier conjecture, asked by Jacques Dixmier in 1968, is the conjecture that any endomorphism of a Weyl algebra is an automorphism. in 2005, and independently and Kontsevich in 2007, showed that the Dixmier conjecture is stably equivalent to the Jacobian conjecture. (Wikipedia).

Video thumbnail

10/13/17 Yuri Berest

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

Video thumbnail

Number Theory | Linear Diophantine Equations

We explore the solvability of the linear Diophantine equation ax+by=c

From playlist Divisibility and the Euclidean Algorithm

Video thumbnail

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

Video thumbnail

Divisibility, Prime Numbers, and Prime Factorization

Now that we understand division, we can talk about divisibility. A number is divisible by another if their quotient is a whole number. The smaller number is a factor of the larger one, but are there numbers with no factors at all? There's some pretty surprising stuff in this one! Watch th

From playlist Mathematics (All Of It)

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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.

Video thumbnail

Introduction to Solving Linear Diophantine Equations Using Congruence

This video defines a linear Diophantine equation and explains how to solve a linear Diophantine equation using congruence. mathispower4u.com

From playlist Additional Topics: Generating Functions and Intro to Number Theory (Discrete Math)

Video thumbnail

[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

Video thumbnail

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

Video thumbnail

Divisibility Rules

This video covers the divisibility rules for 2,3,4,5,6,8,9,and 10. http://mathispower4u.yolasite.com/

From playlist Factors, Prime Factors, and Least Common Factors

Video thumbnail

Rahim Moosa 5/13/16 Part 2

Title: The Dixmier-Moeglin Problem for D-Varieties May 2016 Kolchin Seminar Workshop

From playlist May 2016 Kolchin Seminar Workshop

Video thumbnail

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

Video thumbnail

Yuri Matiyasevich - On Hilbert's 10th Problem [2000]

On Hilbert's 10th Problem - Part 1 of 4 Speaker: Yuri Matiyasevich Date: Wed, Mar 1, 2000 Location: PIMS, University of Calgary Abstract: A Diophantine equation is an equation of the form $ D(x_1,...,x_m) $ = 0, where D is a polynomial with integer coefficients. These equations were n

From playlist Number Theory

Video thumbnail

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

Video thumbnail

Jason Bell

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

Video thumbnail

Bourbaki, les années 1945-75 - Jean-Pierre Serre, Pierre Cartier, Jacques Dixmier & Alain Connes

Jean-Pierre Serre, Pierre Cartier et Jacques Dixmier reviennent sur l'âge d'or du groupe Bourbaki. Discussion animée par Alain Connes.

From playlist Math History

Video thumbnail

Number Theory | Divisibility Basics

We present some basics of divisibility from elementary number theory.

From playlist Divisibility and the Euclidean Algorithm

Related pages

Weyl algebra | Uniformly bounded representation | Algebra | Automorphism | Endomorphism | Jacobian conjecture