Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
The complexification of a real vector space. The complexification of an operator on a real vector space. Every operator on a nonzero finite-dimensional real vector space has an invariant subspace of dimension 1 or 2. Every operator on an odd-dimensional real vector space has an eigenvalue.
From playlist Linear Algebra Done Right
Now that we have defined and understand quotient groups, we need to look at product groups. In this video I define the product of two groups as well as the group operation, proving that it is indeed a group.
From playlist Abstract algebra
Introduction to Homotopy Theory- PART 1: UNIVERSAL CONSTRUCTIONS
The goal of this series is to develop homotopy theory from a categorical perspective, alongside the theory of model categories. We do this with the hope of eventually developing stable homotopy theory, a personal goal a passion of mine. I'm going to follow nLab's notes, but I hope to add t
From playlist Introduction to Homotopy Theory
Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.
From playlist Abstract algebra
Stabilizer in abstract algebra
In the previous video we looked at the orbit of a set. To work towards the orbit stabilizer theorem, we take a look at what a stabilizer is in this video.
From playlist Abstract algebra
Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-
From playlist Abstract Algebra
Ana Balibanu: The partial compactification of the universal centralizer
Abstract: Let G be a semisimple algebraic group of adjoint type. The universal centralizer is the family of centralizers in G of regular elements in Lie(G), parametrized by their conjugacy classes. It has a natural symplectic structure, obtained by Hamiltonian reduction from the cotangent
From playlist Algebra
Math 101 Introduction to Analysis 120415: Compactness and Continuity
Compactness and Continuity: recall continuous image of compact set is compact; alternate (third) proof of extreme value theorem; motivation for uniform continuity; definition of uniform continuity; continuous on a compact set implies uniformly continuous
From playlist Course 6: Introduction to Analysis
In this video, I define a cool operation called the symmetrization, which turns any matrix into a symmetric matrix. Along the way, I also explain how to show that an (abstract) linear transformation is one-to-one and onto. Finally, I show how to decompose and matrix in a nice way, sort of
From playlist Linear Transformations
Mirko Mauri : The essential skeletons of pairs and the geometric P=W conjecture
The geometric P=W conjecture is a conjectural description of the asymptotic behavior of a celebrated correspondence in non-abelian Hodge theory. In particular, it is expected that the dual boundary complex of the compactification of character varieties is a sphere. In a joint work with Enr
From playlist Algebraic and Complex Geometry
Thibaut Delcroix : Kähler-Einstein metrics on group compactifications
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 Algebraic and Complex Geometry
Tropical Geometry - Lecture 2 - Curve Counting | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
Stéphane Fischler: Between interpolation and multiplicity estimates on commutative algebraic groups
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 Algebraic and Complex Geometry
George Boxer: Construction of torsion Galois representations
Find 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, bibliographies,
From playlist Algebraic and Complex Geometry
String Theory and the Real World - S. Schafer-Nameki - 2/24/2015
Introduction by John Schwarz. Learn more about the Inaugural Celebration and Symposium of the Walter Burke Institute for Theoretical Physics: https://burkeinstitute.caltech.edu/workshops/Inaugural_Symposium Produced in association with Caltech Academic Media Technologies. ©2015 Californi
From playlist Walter Burke Institute for Theoretical Physics - Dedication and Inaugural Symposium - Feb. 23-24, 2015
John Pardon: Virtual fundamental cycles and contact homology
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 Jean-Morlet Chair - Lalonde/Teleman
Tony Yue Yu - 1/4 The Frobenius Structure Conjecture for Log Calabi-Yau Varieties
Notes: https://nextcloud.ihes.fr/index.php/s/GwJbsQ8xMW2ifb8 1/4 - Motivation and ideas from mirror symmetry, main results. --- We show that the naive counts of rational curves in an affine log Calabi-Yau variety U, containing an open algebraic torus, determine in a surprisingly simple wa
From playlist Tony Yue Yu - The Frobenius Structure Conjecture for Log Calabi-Yau Varieties
Lecture 9 | String Theory and M-Theory
(November 23, 2010) Leonard Susskind gives a lecture on the constraints of string theory and gives a few examples that show how these work. String theory (with its close relative, M-theory) is the basis for the most ambitious theories of the physical world. It has profoundly influenced
From playlist Lecture Collection | String Theory and M-Theory
Free ebook http://tinyurl.com/EngMathYT A basic introduction to the curl of a vector field - one of the basic operations of vector calculus. I show how to calculate the curl and discuss its relationship with rotation and circulation density. Many examples are presented.
From playlist Engineering Mathematics