Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
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
Projection Theorem | Special Case of the Wigner–Eckart Theorem
The projection theorem is a special case of the Wigner–Eckart theorem, which generally involves spherical tensor operators. If we consider one example of a spherical tensor operator, a rank-1 spherical tensor, we can derive a powerful theorem, which states that expectation values of vector
From playlist Quantum Mechanics, Quantum Field Theory
Maxim Kazarian - 2/3 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
Maxim Kazarian - 3/3 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
What is General Relativity? Lesson 68: The Einstein Tensor
What is General Relativity? Lesson 68: The Einstein Tensor The Einstein tensor defined! Using the Ricci tensor and the curvature scalar we can calculate the curvature scalar of a slice of a manifold using the Einstein tensor. Please consider supporting this channel via Patreon: https:/
From playlist What is General Relativity?
Theory of numbers: Congruences: Euler's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim
From playlist Theory of numbers
Lecture 4 | Modern Physics: Statistical Mechanics
April 20, 2009 - Leonard Susskind explains how to calculate and define pressure, explores the formulas some of applications of Helm-Holtz free energy, and discusses the importance of the partition function. Stanford University: http://www.stanford.edu/ Stanford Continuing Studies P
From playlist Lecture Collection | Modern Physics: Statistical Mechanics
Entropy: Origin of the Second Law of Thermodynamics
How did Clausius create entropy and why? I read his original papers to follow how possibly the most confusing concept in Classical Physics was created. My Patreon Page (thanks!): https://www.patreon.com/user?u=15291200 The music is from the awesome Kim Nalley of course www.KimNalley.
From playlist Laws of Thermodynamics: History
The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg
In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t
From playlist Algebraic Calculus One
Statistical Mechanics Lecture 5
(April 29, 2013) Leonard Susskind presents the mathematical definition of pressure using the Helmholtz free energy, and then derives the famous equation of state for an ideal gas: pV = NkT. Originally presented in the Stanford Continuing Studies Program. Stanford University: http://www.s
From playlist Course | Statistical Mechanics
Field Equations Helmholz Decomposition [Redux]
[Redux: Errata fixed from previous version of this lecture. I corrected the expression for the Laplacian and gradient in spherical coordinates and repaired my execution of the delta function's volume integral.] In this lesson we prove the theorem which tells us that any vector field can b
From playlist QED- Prerequisite Topics
Diffusive limits for random walks and diffusions with long memory – B. Tóth – ICM2018
Probability and Statistics Invited Lecture 12.3 Diffusive and super-diffusive limits for random walks and diffusions with long memory Bálint Tóth Abstract: We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ℝ^d or ℤ^d. The first
From playlist Probability and Statistics
Konrad Polthier (7/27/22): Boundary-sensitive Hodge decompositions
Abstract: We provide a theoretical framework for discrete Hodge-type decomposition theorems of piecewise constant vector fields on simplicial surfaces with boundary that is structurally consistent with decomposition results for differential forms on smooth manifolds with boundary. In parti
From playlist Applied Geometry for Data Sciences 2022
The Equation of State for Water IAPWS-95 Programmed in Mathematica 11.1
To learn more about Wolfram Technology Conference, please visit: https://www.wolfram.com/events/technology-conference/ Speaker: Mario-Cesar Suarez-Arriaga Wolfram developers and colleagues discussed the latest in innovative technologies for cloud computing, interactive deployment, mobile
From playlist Wolfram Technology Conference 2017
21st Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series Talk
Date: Wednesday, April 14, 2021, 10:00am Eastern Time Zone (US & Canada) Speaker: Fioralba Cakoni, Rutgers University Title: On some old and new spectral problems in inverse scattering theory Abstract: Scattering poles, non-scattering frequencies and transmission eigenvalues are intrins
From playlist Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series
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
Numerical Homogenization Approaches for Nonlinear Problems by Barbara Verfürth
DISCUSSION MEETING Multi-Scale Analysis: Thematic Lectures and Meeting (MATHLEC-2021, ONLINE) ORGANIZERS: Patrizia Donato (University of Rouen Normandie, France), Antonio Gaudiello (Università degli Studi di Napoli Federico II, Italy), Editha Jose (University of the Philippines Los Baño
From playlist Multi-scale Analysis: Thematic Lectures And Meeting (MATHLEC-2021) (ONLINE)
Topics in Combinatorics lecture 11.6 --- Two applications of Shearer's lemma
In the previous video I stated and proved Shearer's entropy lemma. Here I give two applications. The first provides an upper bound for the number of triangles a graph with m edges can have. The second is an upper bound for the size of a family of graphs with vertex set {1,2,...,n} if the i
From playlist Topics in Combinatorics (Cambridge Part III course)
Max Planck Biography with Depth and Humor
Max Planck was loved by the people who knew him, learn about this influential scientist and why he was so admired. My Patreon Page (thanks!): https://www.patreon.com/user?u=15291200 The music is from the awesome Kim Nalley of course www.KimNalley.com
From playlist Max Planck Biographies