Euler's Formula for the Quaternions
In this video, we will derive Euler's formula using a quaternion power, instead of a complex power, which will allow us to calculate quaternion exponentials such as e^(i+j+k). If you like quaternions, this is a pretty neat formula and a simple generalization of Euler's formula for complex
From playlist Math
Euler's formulas, Rodrigues' formula
In this video I proof various generalizations of Euler's formula, including Rodrigues' formula and explain their 3 dimensional readings. Here's the text used in this video: https://gist.github.com/Nikolaj-K/eaaa80861d902a0bbdd7827036c48af5
From playlist Algebra
Proof synthesis and differential linear logic
Linear logic is a refinement of intuitionistic logic which, viewed as a functional programming language in the sense of the Curry-Howard correspondence, has an explicit mechanism for copying and discarding information. It turns out that, due to these mechanisms, linear logic is naturally r
From playlist Talks
The Campbell-Baker-Hausdorff and Dynkin formula and its finite nature
In this video explain, implement and numerically validate all the nice formulas popping up from math behind the theorem of Campbell, Baker, Hausdorff and Dynkin, usually a.k.a. Baker-Campbell-Hausdorff formula. Here's the TeX and python code: https://gist.github.com/Nikolaj-K/8e9a345e4c932
From playlist Algebra
The Weyl algebra and the Heisenberg Lie algebra
In this video we give a simple teaser into the world of operator algebras. In particular, we talk about the Weyl algebra and compute some expressions that fulfill the property which defines the Heisenberg Lie algebra http://math.uchicago.edu/~may/REU2012/REUPapers/Lingle.pdf https://en.w
From playlist Algebra
Commutative algebra 40 The Eilenberg Mazur swindle
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We describe the Eilenberg-Mazur swindle, a technique making using of "paradoxical" properties of infinite sets. As examples we
From playlist Commutative algebra
Example of Gram-Schmidt Orthogonalization
Linear Algebra: Construct an orthonormal basis of R^3 by applying the Gram-Schmidt orthogonalization process to (1, 1, 1), (1, 0, 1), and (1, 1, 0). In addition, we show how the Gram-Schmidt equations allow one to factor an invertible matrix into an orthogonal matrix times an upper tria
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul
From playlist Linear Algebra
By Differential Algebra we mean rings with extra operations. In this video we show how to encode rings with extra operations using birings/affine ring schemes. This video was hacked together. Let me know if you have no idea what I'm talking about. I plan to use this later.
From playlist Birings
Lie groups: Baker Campbell Hausdorff formula
This lecture is part of an online graduate course on Lie groups. We state the Baker Campbell Hausdorff formula for exp(A)exp(B). As applications we show that a Lie group is determined up to local isomorphism by its Lie algebra, and homomorphisms from a simply connected Lie group are deter
From playlist Lie groups
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
Yinhuo Zhang: Braided autoequivalences, quantum commutative Galois objects and the Brauer 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 Algebra
Claudia Pinzari: "Weak quasi-Hopf algebras associated to Verlinde fusion categories"
Actions of Tensor Categories on C*-algebras 2021 "Weak quasi-Hopf algebras associated to Verlinde fusion categories" Claudia Pinzari - Sapienza Università di Roma Abstract: Unitary modular fusion categories arise in various frameworks. After a general overview on unitarity, we discuss th
From playlist Actions of Tensor Categories on C*-algebras 2021
Ralph Kaufmann: Graph Hopf algebras and their framework
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: I will discuss recent results linking the Hopf algebras of Goncharov for multiple zetas, the Hopf algebra of Connes and Kreimer for renormalis
From playlist Workshop: "Amplitudes and Periods"
Guangyu Zhu: The Galois group of the category of mixed Hodge Tate structures
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: The category of mixed Hodge-Tate structures over Q is a mixed Tate category of homological dimension one. By Tannakian formalism, it is equiva
From playlist Workshop: "Periods and Regulators"
The Hopf Fibration via Higher Inductive Types - Peter Lumsdaine
Peter Lumsdaine Dalhousie University; Member, School of Mathematics February 13, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
Matt SZCZESNY - Toric Hall Algebras and infinite-dimentional Lie algebras
The process of counting extensions in categories yields an associative (and sometimes Hopf) algebra called a Hall algebra. Applied to the category of Feynman graphs, this process recovers the Connes-Kreimer Hopf algebra. Other examples abound, yielding various combinatorial Hopf algebras.
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Introduction to quantized enveloping algebras - Leonardo Maltoni
Quantum Groups Seminar Topic: Introduction to quantized enveloping algebras Speaker: Leonardo Maltoni Affiliation: Sorbonne University Date: January 21, 2021 For more video please visit http://video.ias.edu
From playlist Quantum Groups Seminar
The Lie-algebra of Quaternion algebras and their Lie-subalgebras
In this video we discuss the Lie-algebras of general quaternion algebras over general fields, especially as the Lie-algebra is naturally given for 2x2 representations. The video follows a longer video I previously did on quaternions, but this time I focus on the Lie-algebra operation. I st
From playlist Algebra