Differential structures | Lie groups

Hilbert's fifth problem

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).

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From playlist Exploring Mathematics: Fractals

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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

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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

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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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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

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From playlist Number Theory

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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

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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

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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

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From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"

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From playlist Explore the World Science Festival

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From playlist Math

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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

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Zero to Infinity | Full Documentary | NOVA | PBS

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From playlist Full episodes I NOVA

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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

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From playlist ℕumber Theory

Related pages

Continuous symmetry | Group action | Topological manifold | Locally compact abelian group | Lie group | No small subgroup | Classical group | Topological group | Up to | David Hilbert | Hidehiko Yamabe | Hilbert–Smith conjecture | Closed manifold | Leo Zippin | John von Neumann | Connected space | Totally disconnected group | Group theory | Euclidean space | Circle group | Compact group | Abelian group | Locally compact group