A Concrete Introduction to Tensor Products
The tensor product of vector spaces (or modules over a ring) can be difficult to understand at first because it's not obvious how calculations can be done with the elements of a tensor product. In this video we give an explanation of an explicit construction of the tensor product and work
From playlist Tensor Products
Lecture 27. Properties of tensor products
0:00 Use properties of tensor products to effectively think about them! 0:50 Tensor product is symmetric 1:17 Tensor product is associative 1:42 Tensor product is additive 21:40 Corollaries 24:03 Generators in a tensor product 25:30 Tensor product of f.g. modules is itself f.g. 32:05 Tenso
From playlist Abstract Algebra 2
What is a Tensor 5: Tensor Products
What is a Tensor 5: Tensor Products Errata: At 22:00 I write down "T_00 e^0 @ e^1" and the correct expression is "T_00 e^0 @ e^0"
From playlist What is a Tensor?
Proof: Uniqueness of the Tensor Product
Universal property introduction: https://youtu.be/vZzZhdLC_YQ This video proves the uniqueness of the tensor product of vector spaces (or modules over a commutative ring). This uses the universal property of the tensor product to prove the existence of an isomorphism (linear bijection) be
From playlist Tensor Products
What is a Tensor 6: Tensor Product Spaces
What is a Tensor 6: Tensor Product Spaces There is an error at 15:00 which is annotated but annotations can not be seen on mobile devices. It is a somewhat obvious error! Can you spot it? :)
From playlist What is a Tensor?
What is a Tensor? Lesson 29: Transformations of tensors and p-forms (part review)
What is a Tensor? Lesson 29: Tensor and N-form Transformations This long lesson begins with a review of tensor product spaces and the relationship between coordinate transformations on spacetime and basis transformations of tensor fields. Then we do a full example to introduce the idea th
From playlist What is a Tensor?
Hilbert Space Techniques in Complex Analysis and Geometry (Lecture - 2) by Dror Varolin
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
R. Lazarsfeld: The Equations Defining Projective Varieties part 4
The lecture was held within the framework of the Junior Hausdorff Trimester Program Algebraic Geometry. (6.-22.1.2014)
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
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
The TRUTH about TENSORS, Part 9: Vector Bundles
In this video we define vector bundles in full abstraction, of which tangent bundles are a special case.
From playlist The TRUTH about TENSORS
What Is A Tensor Lesson #1: Elementary vector spaces
We define a vector space and lay the foundation of a solid understanding of tensors.
From playlist What is a Tensor?
Oliver Gabriel: Functorial Rieffel deformations and (periodic) cyclic cohomology
Inspired by previous work by S. Brain, G. Landi and W. van Suijlekom, we study functorial deformations of algebras and modules based on actions of Abelian locally compact groups. We consider the case of G = S^1 \times \mathbb Z, provide an explicit form for the deformation and show how fun
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Hilbert Space Techniques in Complex Analysis and Geometry (Lecture - 3) by Dror Varolin
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Zhaoting Wei: Determinant line bundles and cohesive modules
Talk by Zhaoting Wei in Global Noncommutative Geometry Seminar (Americas) https://www.math.wustl.edu/~xtang/NCG-Seminar on December 16, 2020
From playlist Global Noncommutative Geometry Seminar (Americas)
The TRUTH about tensors (Part 1 ???)
Following Michael Penn's recent and wonderful video, some people had questions about what this has to do with tensors in physics. In this off-the-cuff video, I outline some of what goes into connecting these ideas. Michael's video: https://www.youtube.com/watch?v=K7f2pCQ3p3U&t=205s&ab_
From playlist The TRUTH about TENSORS
Differential geometry of the Torelli map (Lecture 3) by Alessandro Ghigi and Paola Frediani
DISCUSSION MEETING TOPICS IN HODGE THEORY (HYBRID) ORGANIZERS: Indranil Biswas (TIFR, Mumbai, India) and Mahan Mj (TIFR, Mumbai, India) DATE: 20 February 2023 to 25 February 2023 VENUE: Ramanujan Lecture Hall and Online This is a followup discussion meeting on complex and algebraic ge
From playlist Topics in Hodge Theory - 2023
Transversality and super-rigidity in Gromov-Witten Theory (Lecture - 04) by Chris Wendl
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
Complete Derivation: Universal Property of the Tensor Product
Previous tensor product video: https://youtu.be/KnSZBjnd_74 The universal property of the tensor product is one of the most important tools for handling tensor products. It gives us a way to define functions on the tensor product using bilinear maps. However, the statement of the universa
From playlist Tensor Products
Noah Arbesfeld: A geometric R-matrix for the Hilbert scheme of points on a general surface
Abstract: We explain how to use a Virasoro algebra to construct a solution to the Yang-Baxter equation acting in the tensor square of the cohomology of the Hilbert scheme of points on a generalsurface S. In the special case where the surface S is C2, the construction appears in work of Mau
From playlist Algebraic and Complex Geometry