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
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
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 and Lie Algebras: Lesson 16 - representations, connectedness, definition of Lie Group
Lie Groups and Lie Algebras: Lesson 16 - representations, connectedness, definition of Lie Group We cover a few concepts in this lecture: 1) we introduce the idea of a matrix representation using our super-simple example of a continuous group, 2) we discuss "connectedness" and explain tha
From playlist Lie Groups and Lie Algebras
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
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 and Lie Algebras: Lesson 18- Group Generators
Lie Groups and Lie Algebras: Lesson 18- Generators This is an important lecture! We work through the calculus of *group generators* and walk step-by-step through the exploitation of analyticity. That is, we use the Taylor expansion of the continuous functions associated with a Lie group o
From playlist Lie Groups and Lie Algebras
This lecture is part of an online graduate course on Lie groups. We give an introductory survey of Lie groups theory by describing some examples of Lie groups in low dimensions. Some recommended books: Lie algebras and Lie groups by Serre (anything by Serre is well worth reading) Repre
From playlist Lie groups
In this clip I casually give a roundup of some of my current interests and also recommend you some literature. Get into Lie algebras, Lie groups and algebraic groups. Do it now! https://en.wikipedia.org/wiki/Lie_algebra http://www.jmilne.org/math/index.html
From playlist Algebra
Hong Wang: The restriction problem and the polynomial method, Lecture IV
Stein’s restriction conjecture is about estimating functions with Fourier transform supported on a hypersurface, for example, a sphere in Rn. These functions can be decomposed into a sum over wave packets supported on long thin tubes. Guth introduced the polynomial method in restriction th
From playlist Harmonic Analysis and Analytic Number Theory
Julien Grivaux - The Lie algebra attached to a tame closed embedding
Abstract: If X is a smooth closed subscheme of an ambient smooth scheme Y, Calaque, Caldararu and Tu have endowed the shifted normal bundle NX/Y[−1] with a derived Lie algebroid structure. This structure generalizes the Lie algebra structure on the shifted tangent bundle TX[−1] on a smoot
From playlist Algebraic Analysis in honor of Masaki Kashiwara's 70th birthday
Differential Isomorphism and Equivalence of Algebraic Varieties Board at 49:35 Sum_i=1^N 2/(x-phi_i(y,t))^2
From playlist Fall 2017
Jean Michel BISMUT - Fokker-Planck Operators and the Center of the Enveloping Algebra
The heat equation method in index theory gives an explicit local formula for the index of a Dirac operator. Its Lagrangian counterpart involves supersymmetric path integrals. Similar methods can be developed to give a geometric formula for semi simple orbital integrals associated with the
From playlist Integrability, Anomalies and Quantum Field Theory
Tony Yue Yu - 3/4 The Frobenius Structure Conjecture for Log Calabi-Yau Varieties
Notes: https://nextcloud.ihes.fr/index.php/s/pSQnsgx72a4S5zj 3/4 - Naive counts, tail conditions and deformation invariance. --- 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 w
From playlist Tony Yue Yu - The Frobenius Structure Conjecture for Log Calabi-Yau Varieties
Bjorn Poonen - Cohomological Obstructions to Rational Points [2008]
Cohomological Obstructions to Rational Points. CMI/MSRI Workshop: Modular Forms And Arithmetic June 28, 2008 - July 02, 2008 June 30, 2008 (10:30 AM PDT - 11:30 AM PDT) Speaker(s): Bjorn Poonen (Massachusetts Institute of Technology) Location: MSRI: Simons Auditorium http://www.msri.org
From playlist Number Theory
Hong Wang: The restriction problem and the polynomial method, Lecture 2
Stein’s restriction conjecture is about estimating functions with Fourier transform sup- ported on a hypersurface, for example, a sphere in Rn. These functions can be decomposed into a sum over wave packets supported on long thin tubes. Guth introduced the polynomial method in restriction
From playlist Harmonic Analysis and Analytic Number Theory
Tony Yue Yu - 2/4 The Frobenius Structure Conjecture for Log Calabi-Yau Varieties
Notes: https://nextcloud.ihes.fr/index.php/s/8KTr2Mfdk22rpqX 2/4 - Skeletal curves: a key notion in the theory. --- 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 way, a family
From playlist Tony Yue Yu - The Frobenius Structure Conjecture for Log Calabi-Yau Varieties
Perverse sheaves on configuration spaces, Hopf algebras and parabolic induction - Mikhail Kapranov
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Perverse sheaves on configuration spaces, Hopf algebras and parabolic induction Speaker: Mikhail Kapranov Affiliation: Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo Dat
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
15 Properties of partially ordered sets
When a relation induces a partial ordering of a set, that set has certain properties with respect to the reflexive, (anti)-symmetric, and transitive properties.
From playlist Abstract algebra
Moduli of p-divisible groups (Lecture 4) by Ehud De Shalit
PROGRAM PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France
From playlist Perfectoid Spaces 2019