Algebraic combinatorics | Lie algebras | Representation theory
In mathematics, the Littelmann path model is a combinatorial device due to Peter Littelmann for computing multiplicities without overcounting in the representation theory of symmetrisable Kac–Moody algebras. Its most important application is to complex semisimple Lie algebras or equivalently compact semisimple Lie groups, the case described in this article. Multiplicities in irreducible representations, tensor products and branching rules can be calculated using a coloured directed graph, with labels given by the simple roots of the Lie algebra. Developed as a bridge between the theory of crystal bases arising from the work of Kashiwara and Lusztig on quantum groups and the standard monomial theory of C. S. Seshadri and Lakshmibai, Littelmann's path model associates to each irreducible representation a rational vector space with basis given by paths from the origin to a weight as well as a pair of root operators acting on paths for each simple root. This gives a direct way of recovering the algebraic and combinatorial structures previously discovered by Kashiwara and Lusztig using quantum groups. (Wikipedia).
Petra Schwer: Studying affine Deligne Lusztig varieties via folded galleries in buildings
Abstract: We present a new approach to affine Deligne Lusztig varieties which allows us to study the so called "non-basic" case in a type free manner. The central idea is to translate the question of non-emptiness and the computation of the dimensions of these varieties into geometric ques
From playlist Algebra
Gauss, normals and fundamental forms | Differential Geometry 34 | NJ Wildberger
We introduce the approach of C. F. Gauss to differential geometry, which relies on a parametric description of a surface, and the Gauss - Rodrigues map from an oriented surface S to the unit sphere S^2, which describes how a unit normal moves along the surface. The first fundamental form
From playlist Differential Geometry
Here I evaluate the Gaussian Integral in under a minute. This is a must-see for calculus lovers! Gaussian Integral: https://youtu.be/kpmRS4s6ZR4 Gaussian Integral Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCgLyHWMXGZnioRHLqOk2bW Subscribe to my channel: https://youtube.co
From playlist Gaussian Integral
Abonniert den Kanal oder unterstützt ihn auf Steady: https://steadyhq.com/en/brightsideofmaths Ihr werdet direkt informiert, wenn ich einen Livestream anbiete. Hier erkläre ich kurz das Riemann-Integral mit Ober- und Untersumme. Die Definition ist übliche, die im 1. Semester eingeführt w
From playlist Analysis
Parametric equations on one Cartesian path (1 of 2: Introduction)
More resources available at www.misterwootube.com
From playlist Mathematical Exploration
Cartesian to parametric form of line
How to transform a Cartesian form of a line to a parametric form of a line. An example is discussed. Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Test your understanding via a short quiz http://goo.gl/forms/OsY1rkt1al
From playlist Introduction to Vectors
Quantum Integral. Gauss would be proud! I calculate the integral of x^2n e^-x^2 from -infinity to infinity, using Feynman's technique, as well as the Gaussian integral and differentiation. This integral appears over and over again in quantum mechanics and is useful for calculus and physics
From playlist Integrals
Lines: Cartesian to parametric form
How to convert a Cartesian form of a line to a parametric form. An example is discussed. Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link)
From playlist Introduction to Vectors
This shows an small game that illustrates the concept of a vector. The clip is from the book "Immersive Linear Algebra" at http://www.immersivemath.com
From playlist Chapter 2 - Vectors
Second SIAM Activity Group on FME Virtual Talk
This is the second in a series of online talks on topics related to mathematical finance and engineering. The series is organized by the SIAM Activity Group on Financial Mathematics and Engineering. Title: A Data-driven Market Simulator for Small Data Environments Abstract: In this talk w
From playlist SIAM Activity Group on FME Virtual Talk Series
Statistical Rethinking 2023 - 06 - Good & Bad Controls
Course details: https://github.com/rmcelreath/stat_rethinking_2023 Intro music: https://www.youtube.com/watch?v=PDohhCaNf98 Outline 00:00 Introduction 01:43 Causal implications 14:28 do-calculus 16:59 Backdoor criterion 40:48 Pause 41:22 Good and bad controls 1:09:34 Summary 1:26:27 Bonu
From playlist Statistical Rethinking 2023
Mark Rychnovsky (Columbia) -- GUE corners process inboundary-weighted six vertex models
The stochastic six vertex model is a measure on up-right paths in a quadrant of the integer lattice. It is also an exactly solvable model in the Kardar-Parisi-Zhang universality class. For a particular weighted boundary, previous simulations have suggested that the model exhibits novel lim
From playlist Northeastern Probability Seminar 2020
Fractal properties, noise-sensitivity and chaos in models of random geometry - Shirshendu Ganguly
Probability Seminar Topic: Fractal properties, noise-sensitivity and chaos in models of random geometry. Speaker: Shirshendu Ganguly Affiliation: University of California, Berkeley Date: March 31, 2023 Planar last passage percolation models are canonical examples of stochastic growth, po
From playlist Mathematics
Statistical Rethinking 2022 Lecture 06 - Good & Bad Controls
Slides and other course materials: https://github.com/rmcelreath/stat_rethinking_2022 Intro video: https://www.youtube.com/watch?v=6erBpdV-fi0 Intro music: https://www.youtube.com/watch?v=Pc0AhpjbV58 Chapters: 00:00 Introduction 01:23 Parent collider 08:13 DAG thinking 27:48 Backdoor cri
From playlist Statistical Rethinking 2022
Noise Sensitivity and Chaos in Random Planar Geometry by Shirshendu Ganguly
PROGRAM : FIRST-PASSAGE PERCOLATION AND RELATED MODELS (HYBRID) ORGANIZERS : Riddhipratim Basu (ICTS-TIFR, India), Jack Hanson (City University of New York, US) and Arjun Krishnan (University of Rochester, US) DATE : 11 July 2022 to 29 July 2022 VENUE : Ramanujan Lecture Hall and online T
From playlist First-Passage Percolation and Related Models 2022 Edited
Amol Aggarwal: "Arctic Curves for Ice Models"
Asymptotic Algebraic Combinatorics 2020 "Arctic Curves for Ice Models" Amol Aggarwal - Harvard University Abstract: Certain two-dimensional models in statistical mechanics have long been widely known or believed to exhibit arctic boundaries, which are sharp transitions from ordered (froz
From playlist Asymptotic Algebraic Combinatorics 2020
Ernesto Estrada - Network bypasses sustain complexity - IPAM at UCLA
Recorded 31 August 2022. Ernesto Estrada of the University of the Balearic Islands (Illes Balears) presents "Network bypasses sustain complexity" at IPAM's Reconstructing Network Dynamics from Data: Applications to Neuroscience and Beyond. Abstract: Real-world networks are neither regular
From playlist 2022 Reconstructing Network Dynamics from Data: Applications to Neuroscience and Beyond
Planes: Cartesian to parametric form
How to transform the Cartesian form of a plane into a parametric vector form. An example is discussed. Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Test your understanding via a short quiz http://goo.gl/forms/Snbj3dFShj
From playlist Introduction to Vectors
R - SEM - Path Analysis Class Assignment 1
Recorded: Summer 2015 Lecturer: Dr. Erin M. Buchanan Packages needed: lavaan, semPlot Class assignment for structural equation modeling. Topic covers how to put in correlation/covariance tables, create path models, run path models, create a picture of the model with semPaths, mediation in
From playlist Structural Equation Modeling