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
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
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
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
Galilean group cohomology in classical mechanics
In this video we discuss how the second group cohomology relates to classical mechanics. We discuss Galilean invariance in the Lagrangian formalism and its quantum mechanics analog. You find the used text and all the links mentioned here: https://gist.github.com/Nikolaj-K/deb54c9127b6f0f3f
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
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 Groups and Lie Algebras: Lesson 32: Parameters Space and Compactness
Lie Groups and Lie Algebras: Lesson 32: Parameters Space and Compactness I this lecture we prepare ourselves for the study of the homology of SO(3) and SU(2). Homology will be our way of beginning to understand the difference between these groups. This lecture ends abruptly, but it was
From playlist Lie Groups and Lie Algebras
Lie Groups and Lie Algebras: Lesson 25 - the commutator and the Lie Algebra
Lie Groups and Lie Algebras: Lesson 25 - the commutator In this lecture we discover how to represent an infinitesimal commutator of the Lie group using a member of the Lie algebra. We promote the vector space spawned by the group generators to an algebra. Please consider supporting this
From playlist Lie Groups and Lie Algebras
David Corwin, Kim's conjecture and effective Faltings
VaNTAGe seminar, on Nov 24, 2020 License: CC-BY-NC-SA.
From playlist ICERM/AGNTC workshop updates
Ben Davison: Kac Moody Lie algebras as BPS Lie algebras
The lecture was held within the framework of the Hausdorff Trimester Program: Symplectic Geometry and Representation Theory. Abstract: In this talk I will explain how a surprising perverse filtration on the Kontsevich-Soibelman cohomological Hall algebra for a quiver with potential (Q,W)
From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"
This lecture is part of an online graduate course on Lie groups. This lecture is about Lie's theorem, which implies that a complex solvable Lie algebra is isomorphic to a subalgebra of the upper triangular matrices. . For the other lectures in the course see https://www.youtube.com/playl
From playlist Lie groups
Cup Products in Automorphic Cohomology - Matthew Kerr
Matthew Kerr Washington University in St. Louis March 30, 2012 In three very interesting and suggestive papers, H. Carayol introduced new aspects of complex geometry and Hodge theory into the study of non-classical automorphic representations -- in particular, those involving the totally d
From playlist Mathematics
Laurent Manivel - The Satake correspondence in quantum cohomology
The Satake isomorphism identi es the irreducible representations of a semisimple algebraic group with the intersection cohomologies of the Schubert varieties in the ane Grassmannian of the Langlands dual group. In the very special case where the Schubert varieties are smooth, one gets an i
From playlist École d’été 2011 - Modules de courbes et théorie de Gromov-Witten
Calabi-Yau mirror symmetry: from categories to curve-counts - Tim Perutz
Tim Perutz University of Texas at Austin November 15, 2013 I will report on joint work with Nick Sheridan concerning structural aspects of mirror symmetry for Calabi-Yau manifolds. We show (i) that Kontsevich's homological mirror symmetry (HMS) conjecture is a consequence of a fragment of
From playlist Mathematics
Alexander HULPKE - Computational group theory, cohomology of groups and topological methods 2
The lecture series will give an introduction to the computer algebra system GAP, focussing on calculations involving cohomology. We will describe the mathematics underlying the algorithms, and how to use them within GAP. Alexander Hulpke's lectures will being with some general computation
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Title: Rational Matrix Differential Operators and Integral Systems of PDEs
From playlist Fall 2017
Automorphic Cohomology II (Carayol's Work and an Application) - Phillip Griffiths
Automorphic Cohomology II (Carayol's Work and an Application) Phillip Griffiths Institute for Advanced Study February 17, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Lie Groups and Lie Algebras: Lesson 22 - Lie Group Generators
Lie Groups and Lie Algebras: Lesson 22 - Lie Group Generators A Lie group can always be considered as a group of transformations because any group can transform itself! In this lecture we replace the "geometric space" with the Lie group itself to create a new collection of generators. P
From playlist Lie Groups and Lie Algebras
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