Schemes 46: Differential operators
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we define differential operators on rings, and calculate the universal (normalized) differential operator of order n. As a special case we fin
From playlist Algebraic geometry II: Schemes
This lecture is part of an online graduate course on Lie groups. We define the Lie algebra of a Lie group in two ways, and show that it satisfied the Jacobi identity. The we calculate the Lie algebras of a few Lie groups. For the other lectures in the course see https://www.youtube.co
From playlist Lie groups
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
Lie groups: Lie groups and Lie algebras
This lecture is part of an online graduate course on Lie groups. We discuss the relation between Lie groups and Lie algebras, and give several examples showing how they behave differently. Lie algebras turn out to correspond more closely to the simply connected Lie groups. We then explain
From playlist Lie groups
Infinitesimals in Synthetic Differential Geometry
In this video I describe the logic of Synthetic Differential Geometry. This is a non-constructive theory collapsing in the presence of the law of excluded middle. As a logic al theory, it can be realized in a topos and it has sheave models giving a nice representation of tangent bundles.
From playlist Algebra
Linear Algebra 5.4 Differential Equations
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 A. Roberts is supported in part by the grants NSF CAREER 1653602 and NSF DMS 2153803.
From playlist Linear Algebra
In this video I write down the axioms of Lie algebras and then discuss the defining anti-symmetric bilinear map (the Lie bracket) which is zero on the diagonal and fulfills the Jacobi identity. I'm following the compact book "Introduction to Lie Algebras" by Erdmann and Wildon. https://gi
From playlist Algebra
(0.3.101) Exercise 0.3.101: Classifying Differential Equations
This video explains how to classify differential equations based upon their properties https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined
Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined In this lecture we define a "continuous groups" and show the connection between the algebraic properties of a group with topological properties. Please consider supporting this channel via Patreon: https://www.patreon.co
From playlist Lie Groups and Lie Algebras
Nero Budur: Cohomology jump loci and singularities
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
Lie Algebras and Homotopy Theory - Jacob Lurie
Members' Seminar Topic: Lie Algebras and Homotopy Theory Speaker: Jacob Lurie Affiliation: Professor, School of Mathematics Date: November 11, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Lie groups: Poincare-Birkhoff-Witt theorem
This lecture is part of an online graduate course on Lie groups. We state the Poincare-Birkhoff Witt theorem, which shows that the universal enveloping algebra (UEA) of a Lie algebra is the same size as a polynomial algebra. We prove it for Lie algebras of Lie groups and sketch a proof of
From playlist Lie groups
Michel Dubois-Violette: The Weil algebra of a Hopf algebra
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
Haldun Özgür Bayindir : Adjoining roots to ring spectra and algebraic 𝐾-theory
CONFERENCE Recording during the thematic meeting : « Chromatic Homotopy, K-Theory and Functors» the January 24, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIR
From playlist Topology
Twisted matrix factorizations and loop groups - Daniel Freed
Daniel Freed University of Texas, Austin; Member, School of Mathematics and Natural Sciences February 9, 2015 The data of a compact Lie group GG and a degree 4 cohomology class on its classifying space leads to invariants in low-dimensional topology as well as important representations of
From playlist Mathematics
Rafael Díaz: Deformations of N-differential graded algebras
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
https://www.math.ias.edu/files/media/agenda.pdf More videos on http://video.ias.edu
From playlist Mathematics
Pablo Linares & Markus Tempelmayr - A tree-free construction of the structure group
We present a new approach to regularity structures, and in particular to the construction of the structure group, which replaces the tree-based framework of Hairer by a more Lie-geometric setting. We consider the space of pairs (a,p), where a is a placeholder for the nonlinearity and p is
From playlist Research Spotlight
A Gentle Approach to Crystalline Cohomology - Jacob Lurie
Members’ Colloquium Topic: A Gentle Approach to Crystalline Cohomology Speaker: Jacob Lurie Affiliation: Professor, School of Mathematics Date: February 28, 2022 Let X be a smooth affine algebraic variety over the field C of complex numbers (that is, a smooth submanifold of C^n which can
From playlist Mathematics
Using the general and vector forms of the equation of a plane from the normal and a point, or two points on the plane.
From playlist Linear Algebra