Differential structures | Lie groups
Hilbert's fifth problem is the fifth mathematical problem from the problem list publicized in 1900 by mathematician David Hilbert, and concerns the characterization of Lie groups. The theory of Lie groups describes continuous symmetry in mathematics; its importance there and in theoretical physics (for example quark theory) grew steadily in the twentieth century. In rough terms, Lie group theory is the common ground of group theory and the theory of topological manifolds. The question Hilbert asked was an acute one of making this precise: is there any difference if a restriction to smooth manifolds is imposed? The expected answer was in the negative (the classical groups, the most central examples in Lie group theory, are smooth manifolds). This was eventually confirmed in the early 1950s. Since the precise notion of "manifold" was not available to Hilbert, there is room for some debate about the formulation of the problem in contemporary mathematical language. (Wikipedia).
Space-Filling Curves (2 of 4: Hilbert Curve)
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From playlist Exploring Mathematics: Fractals
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From playlist Elementary Number Theory
Mathematica Tutorial 5 - Countability of the rational numbers
In this Mathematica tutorial you will learn the meaning of the statement that the rational numbers are countable and learn to construct a Mathematica function that outputs the nth rational number.
From playlist Mathematica Tutorials
Algebraic geometry 49: Hilbert polynomials
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives a review of the Hilbert polynomial of a graded module over a graded ring, and classifies integer-valued polynomials.
From playlist Algebraic geometry I: Varieties
John Pardon: Totally disconnected groups (not) acting on three-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 Geometry
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From playlist Abstract Algebra 2
General Relativity and Gravity | What Einstein Discovered
Shortly after publishing his special theory of relativity, Einstein began to work toward creating an even more complete and far-reaching theory of space and time. It took him another decade, but eventually Einstein came up with an expanded and completely general form of his theory. The gen
From playlist Science
Math Major Examples -- Number Theory #4
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From playlist Number Theory
Ex: Linear Equation Application with One Variable - Number Problem
This video provides and example of how to solve a number problem using a linear equation with one variable. One number is a multiple of the other. The difference is a constant. Find the two numbers. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com
From playlist Whole Number Applications
M. Kisin - Hilbert's thirteenth problem and the moduli space of abelian varieties
The (multi-valued) solution of a general polynomial of degree n is a priori a function of n-1 variables. Hilbert's thirteenth problem and its variants ask when such functions can be written as a composite of functions in a smaller number of variables. I will explain some progress on this q
From playlist Arithmetic and Algebraic Geometry: A conference in honor of Ofer Gabber on the occasion of his 60th birthday
Hans G. Feichtinger: Mathematical and numerical aspects of frame theory - Part 2
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 Analysis and its Applications
Nonlinear algebra, Lecture 10: "Invariant Theory", by Bernd Sturmfels
This is the tenth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Miles Reid: Graded rings and Fano 3-Folds - an introduction to Tom and Jerry
It is known that there are about 60000 possibilities for the Hilbert series of anticanonical rings of Q-Fano 3-folds in the Mori category. Graded ring methods allow the construction of Q-smooth Q-Fano 3-folds corresponding to many hundreds of these Hilbert series. One expects the methods t
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Infinity: The Science of Endless
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From playlist Explore the World Science Festival
Turing Machines & The Halting Problem (Part 1)
In the year 1900, David Hilbert gave a list of 23 mathematics problems for the mathematicians of the new generation. His tenth problem proved to be an enigma for many years until Alan Turing solved it while simultaneously creating the modern computer. Watch the video to see how Alan Turi
From playlist Math
David Krejčiřík: Spectrum of the Möbius strip: true, fake and not-so-fake
CIRM VIRTUAL EVENT Recorded during the meeting "Shape Optimization, Spectral Geometry and Calculus of Variations" the March 30, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worl
From playlist Virtual Conference
Zero to Infinity | Full Documentary | NOVA | PBS
Discover how the concepts of zero and infinity revolutionized mathematics. Official Website: https://to.pbs.org/3tkPFTx | #novapbs Zero and infinity. These seemingly opposite, obvious, and indispensable concepts are relatively recent human inventions. Discover the surprising story of h
From playlist Full episodes I NOVA
The Palais-Smale Theorem and the Solution of Hilbert’s 23 Problem - Karen Uhlenbeck
Members' Seminar Topic: The Palais-Smale Theorem and the Solution of Hilbert’s 23 Problem Speaker: Karen Uhlenbeck Affiliation: The University of Texas at Austin; Distinguished Visiting Professor, School of Mathematics Date: April 6, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
The Frobenius Problem - Method for Finding the Frobenius Number of Two Numbers
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From playlist ℕumber Theory