Theorems in representation theory | Theorems in group theory | Representation theory of finite groups
In mathematics, Maschke's theorem, named after Heinrich Maschke, is a theorem in group representation theory that concerns the decomposition of representations of a finite group into irreducible pieces. Maschke's theorem allows one to make general conclusions about representations of a finite group G without actually computing them. It reduces the task of classifying all representations to a more manageable task of classifying irreducible representations, since when the theorem applies, any representation is a direct sum of irreducible pieces (constituents). Moreover, it follows from the Jordan–Hölder theorem that, while the decomposition into a direct sum of irreducible subrepresentations may not be unique, the irreducible pieces have well-defined multiplicities. In particular, a representation of a finite group over a field of characteristic zero is determined up to isomorphism by its character. (Wikipedia).
This talk is the first of two talks that give a proof of the Riemann Roch theorem, in the spacial case of nonsingular complex plane curves. We divide the Riemann-Roch theorem into 3 pieces: Riemann's theorem, a topological theorem identifying the three definitions of the genus, and Roch'
From playlist Algebraic geometry: extra topics
The Schrodinger Equation is (Almost) Impossible to Solve.
Sure, the equation is easily solvable for perfect / idealized systems, but almost impossible for any real systems. The Schrodinger equation is the governing equation of quantum mechanics, and determines the relationship between a system, its surroundings, and a system's wave function. Th
From playlist Quantum Physics by Parth G
Separation of variables and the Schrodinger equation
A brief explanation of separation of variables, application to the time-dependent Schrodinger equation, and the solution to the time part. (This lecture is part of a series for a course based on Griffiths' Introduction to Quantum Mechanics. The Full playlist is at http://www.youtube.com/
From playlist Mathematical Physics II - Youtube
History of representation theory in quantum mechanics
In this video I speak about the early history of group representation theory in quantum mechanics using the rather recent history book by Schneider on van der Waerden, called "Zwischen Zwei Disziplinen". Other names dropped are Frobenius, Burnside, Schur, Killing, Study, Cartan, Weyl, Brau
From playlist Physics
How the Schrodinger Equation Predicts Real Life (and Why It's So Difficult) - Quantum Mech Parth G
Understanding the Schrodinger Equation theoretically is very useful... but the main aim of the equation is to predict what happens in real life! In this video, we'll be looking at how the Schrodinger Equation can be used to predict the behaviour of a hydrogen atom. To do this, we'll first
From playlist Quantum Physics by Parth G
Bernhard Maschke : Hamiltonian control systems for open Irreversible Thermodynamic systems
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 30, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
The Schrodinger equation made simple | Linearity
We've talked about the quantum state plenty- but what happens to it over time? That's exactly the question the Schrodinger equation solves. This video we talk about 'Linearity'. In the next video we discuss the equation itself and its derivation. Click here fore that: https://youtu.be/DEgW
From playlist Quantum Mechanics (all the videos)
A quantum particle in a periodic egg carton potential
This simulation of a quantum particle in a periodic particle explores a new visualization, in which the z-coordinate is the sum of the potential, and another quantity related to the wave function (either its real part, or its modulus squared). There is a detailed theory on Schrödinger's eq
From playlist Schrödinger's equation
Physicist Explains Wikipedia Page: The Schrodinger Equation
Why are Wikipedia Physics pages so difficult to understand? Hey guys, I'm back with a new video! This time, I'm looking at how certain Wikipedia pages can be so complicated to understand, and so here's a Wikipedia page made easy! Now I can totally understand that a wiki page is meant to p
From playlist Quantum Physics by Parth G
This lecture is part of an online course on algebraic geometry, following the book "Algebraic geometry" by Hartshorne. It is the first of a few elementary lectures on the Riemann-Roch theorem, mostly for compact complex curves. In this lecture we state the Riemann Roch theorem and explain
From playlist Algebraic geometry: extra topics
Calculus 1 (Stewart) Ep 22, Mean Value Theorem (Oct 28, 2021)
This is a recording of a live class for Math 1171, Calculus 1, an undergraduate course for math majors (and others) at Fairfield University, Fall 2021. The textbook is Stewart. PDF of the written notes, and a list of all episodes is at the class website. Class website: http://cstaecker.f
From playlist Math 1171 (Calculus 1) Fall 2021
Equidistribution of Unipotent Random Walks on Homogeneous spaces by Emmanuel Breuillard
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
What is Green's theorem? Chris Tisdell UNSW
This lecture discusses Green's theorem in the plane. Green's theorem not only gives a relationship between double integrals and line integrals, but it also gives a relationship between "curl" and "circulation". In addition, Gauss' divergence theorem in the plane is also discussed, whic
From playlist Vector Calculus @ UNSW Sydney. Dr Chris Tisdell
Real Analysis Ep 32: The Mean Value Theorem
Episode 32 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is more about the mean value theorem and related ideas. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/courses/2020f3371/ Chris Staecker
From playlist Math 3371 (Real analysis) Fall 2020
Pythagorean theorem - What is it?
► My Geometry course: https://www.kristakingmath.com/geometry-course Pythagorean theorem is super important in math. You will probably learn about it for the first time in Algebra, but you will literally use it in Algebra, Geometry, Trigonometry, Precalculus, Calculus, and beyond! That’s
From playlist Geometry
Wolfram Physics Project: Working Session Sept. 15, 2020 [Physicalization of Metamathematics]
This is a Wolfram Physics Project working session on metamathematics and its physicalization in the Wolfram Model. Begins at 10:15 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the
From playlist Wolfram Physics Project Livestream Archive
Johnathan Bush (7/8/2020): Borsuk–Ulam theorems for maps into higher-dimensional codomains
Title: Borsuk–Ulam theorems for maps into higher-dimensional codomains Abstract: I will describe Borsuk-Ulam theorems for maps of spheres into higher-dimensional codomains. Given a continuous map from a sphere to Euclidean space, we say the map is odd if it respects the standard antipodal
From playlist AATRN 2020
Worldwide Calculus: Extrema and the Mean Value Theorem
Lecture on 'Extrema and the Mean Value Theorem' from 'Worldwide Differential Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Worldwide Single-Variable Calculus for AP®
Physics - Ch 66 Ch 4 Quantum Mechanics: Schrodinger Eqn (12 of 92) Time & Position Dependencies 1/3
Visit http://ilectureonline.com for more math and science lectures! In this video I will separate the time and position dependencies of the Schrodinger's equation, part 1/3. Next video in this series can be seen at: https://youtu.be/djlpmDUtIZY
From playlist PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION