Birkhoff's representation theorem

RT6. Representations on Function Spaces

Representation Theory: We note how to transfer a group action of a group G on a set X to a group action on F(X), the functions on X. Because F(X) is a vector space, we obtain a representation of the group, and we can apply previous techniques. In particular, the group acts on itself in

From playlist Representation Theory

Representation theory: Introduction

This lecture is an introduction to representation theory of finite groups. We define linear and permutation representations, and give some examples for the icosahedral group. We then discuss the problem of writing a representation as a sum of smaller ones, which leads to the concept of irr

From playlist Representation theory

Representation theory: Frobenius groups

We recall the definition of a Frobenius group as a transitive permutation group such that any element fixing two points is the identity. Then we prove Frobenius's theorem that the identity together with the elements fixing no points is a normal subgroup. The proof uses induced representati

From playlist Representation theory

Ch7Pr38: Matrix Representation Theorem

This video answers four questions regarding properties of a linear transformation, its image, rank and nullity. This is Chapter 7 Problem 38 from the MATH1231/1241 Algebra notes. Presented by Dr Thomas Britz from the UNSW School of Mathematics and Statistics.

From playlist Mathematics 1B (Algebra)

Number Theory - The Basis Representation Theorem

From playlist ℕumber Theory

RT4.2. Schur's Lemma (Expanded)

Representation Theory: We introduce Schur's Lemma for irreducible representations and apply it to our previous constructions. In particular, we identify Hom(V,V) with invariant sesquilinear forms on V when (pi, V) is unitary. Course materials, including problem sets and solutions, availa

From playlist Representation Theory

Philip Boalch - Topology of the Stokes Phenomenon

From playlist Resurgence in Mathematics and Physics

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

A quantum Sinai billiard, phase evolution

Simulation of Schrödinger's equation for a quantum particle in a Sinai billiard. Luminosity corresponds to the probability of finding the quantum particle (modulus of the wave function squared), and the color's hue represents the phase (argument) of the wave function. The initial state is

From playlist Schrödinger's equation

The SL (2, R) action on spaces of differentials (Lecture 01) by Jayadev Athreya

DISCUSSION MEETING SURFACE GROUP REPRESENTATIONS AND PROJECTIVE STRUCTURES ORGANIZERS: Krishnendu Gongopadhyay, Subhojoy Gupta, Francois Labourie, Mahan Mj and Pranab Sardar DATE: 10 December 2018 to 21 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore The study of spaces o

From playlist Surface group representations and Projective Structures (2018)

Ergodicity of the Weil-Petersson geodesic flow (Lecture - 1) Keith Burns

Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b

From playlist Geometry, Groups and Dynamics (GGD) - 2017

Koopman Spectral Analysis (Overview)

In this video, we introduce Koopman operator theory for dynamical systems. The Koopman operator was introduced in 1931, but has experienced renewed interest recently because of the increasing availability of measurement data and advanced regression algorithm. https://www.eigensteve.com

From playlist Koopman Analysis

Lecture 5 | Topics in String Theory

(February 7, 2011) Leonard Susskind gives a lecture on string theory and particle physics that focuses again on black holes and how light behaves around a black hole. He uses his own theories to mathematically explain the behavior of a black hole and the area around it. In the last of cou

From playlist Lecture Collection | Topics in String Theory (Winter 2011)

[BOURBAKI 2019] Infinité d’hypersurfaces minimales en basses dimensions - Rivière - 15/06/19

Tristan RIVIÈRE Infinité d’hypersurfaces minimales en basses dimensions, d’après Fernando Codá Marques, André Neves et Antoine Song Une conjecture de Shing Tung Yau du début des années 80 pose le problème de l’existence d’une infinité de surfaces minimales (points critiques de la foncti

From playlist BOURBAKI - 2019

10/18/18 Konstantin Mischaikow

A Combinatorial/Algebraic Topological Approach to Nonlinear Dynamics

From playlist Fall 2018 Symbolic-Numeric Computing

Maxim Kazarian - 1/3 Mathematical Physics of Hurwitz numbers

Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge num

From playlist ­­­­Physique mathématique des nombres de Hurwitz pour débutants

A gentle introduction to group representation theory -Peter Buergisser

Optimization, Complexity and Invariant Theory Topic: A gentle introduction to group representation theory Speaker: Peter Buergisser Affiliation: Technical University of Berlin Date: June 4, 2018 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Yves Benoist - Random walk on p-adic flag varieties

Yves Benoist (Université Paris Sud, France) According to a theorem of Furstenberg, a Zariski dense probability measure on a real semisimple Lie group admits a unique stationary probability measure on the flag variety. In this talk we will see that a Zariski dense probability measure on a

From playlist T1-2014 : Random walks and asymptopic geometry of groups.

Ellipses of small eccentricity are determined by their Dirichlet... - Steven Morris Zelditch

Analysis Seminar Topic: Ellipses of small eccentricity are determined by their Dirichlet (or, Neumann) spectra Speaker: Steven Morris Zelditch Affiliation: Northwestern University Date: April 28, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

How to find the position function given the acceleration function

👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the

From playlist Riemann Sum Approximation