Berge's lemma, an animated proof
Berge's lemma is a mathematical theorem in graph theory which states that a matching in a graph is of maximum cardinality if and only if it has no augmenting paths. But what do those terms even mean? And how do we prove Berge's lemma to be true? == CORRECTION: at 7:50, the red text should
From playlist Summer of Math Exposition Youtube Videos
Proof of Lemma and Lagrange's Theorem
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div
From playlist Abstract Algebra
This lecture is part of an online course on rings and modules. We continue the previous lecture on complete rings by discussing Hensel's lemma for finding roots of polynomials over p-adic rings or over power series rings. We sketch two proofs, by slowly improving a root one digit at a tim
From playlist Rings and modules
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers
Commutative algebra 51: Hensel's lemma continued
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. This lecture continues the discussion of Hensel's lemma. We first use it to find the structure of the group of units of the p-
From playlist Commutative algebra
Bryna Kra : Multiple ergodic theorems: old and new - lecture 2
Abstract : The classic mean ergodic theorem has been extended in numerous ways: multiple averages, polynomial iterates, weighted averages, along with combinations of these extensions. I will give an overview of these advances and the different techniques that have been used, focusing on co
From playlist Dynamical Systems and Ordinary Differential Equations
Commutative algebra 50: Hensel's lemma
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We describe Hensel's lemma for finding roots of polynomials over complete rings, and give some examples of using it to find wh
From playlist Commutative algebra
Burnside's Lemma (Part 2) - combining math, science and music
Part 1 (previous video): https://youtu.be/6kfbotHL0fs Orbit-stabilizer theorem: https://youtu.be/BfgMdi0OkPU Burnside's lemma is an interesting result in group theory that helps us count things with symmetries considered, e.g. in some situations, we don't want to count things that can be
From playlist Traditional topics, explained in a new way
Asymptotic spectra and their applications II - Jeroen Zuiddam
Computer Science/Discrete Mathematics Seminar II Topic: Asymptotic spectra and their applications II Speaker: Jeroen Zuiddam Affiliation: Member, School of Mathematics Date: October 16, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Joseph Bengeloun - Quantum Mechanics of Bipartite Ribbon Graphs...
Quantum Mechanics of Bipartite Ribbon Graphs: A Combinatorial Interpretation of the Kronecker Coefficient. The action of subgroups on a product of symmetric groups allows one to enumerate different families of graphs. In particular, bipartite ribbon graphs (with at most edges) enumerate
From playlist Combinatorics and Arithmetic for Physics: 02-03 December 2020
Introduction to additive combinatorics lecture 5.8 --- Freiman homomorphisms and isomorphisms.
The notion of a Freiman homomorphism and the closely related notion of a Freiman isomorphism are fundamental concepts in additive combinatorics. Here I explain what they are and prove a lemma that states that a subset A of F_p^N such that kA - kA is not too large is "k-isomorphic" to a sub
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Geometry of the symmetric space SL(n,R)/SO(n,R) (Lecture - 02) by Pranab Sardar
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
Asymptotic spectra and Applications I - Jeroen Zuiddam
Computer Science/Discrete Mathematics Seminar I Topic: Asymptotic spectra and Applications I Speaker: Jeroen Zuiddam Affiliation: Member, School of Mathematics Date: October 8, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Non-commutative rank - Visu Makam
Computer Science/Discrete Mathematics Seminar II Topic: Non-commutative rank Speaker: Visu Makam Affiliation: University of Michigan; Member, School of Mathematics Date: February 5, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Dmitryi Bilyk: Uniform distribution, lacunary Fourier series, and Riesz products
Uniform distribution theory, which originated from a famous paper of H. Weyl, from the very start has been closely connected to Fourier analysis. One of the most interesting examples of such relations is an intricate similarity between the behavior of discrepancy (a quantitative measure of
From playlist HIM Lectures: Trimester Program "Harmonic Analysis and Partial Differential Equations"
Ryomei Iwasa: Chern classes with modulus
The lecture was held within the framework of the Hausdorff Trimester Program : Workshop "K-theory in algebraic geometry and number theory"
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
MAST30026 Lecture 21: Coordinates in Hilbert space (Part 2)
I completed the proof that the complex exponential functions e^{in\theta} form an orthonormal family spanning a dense subspace of the L^2 space of the circle, and then developed enough of the abstract theory of orthonormal bases to prove that every vector in that L^2 space can be written a
From playlist MAST30026 Metric and Hilbert spaces
Number Theory - Euclid's Division Lemma
From playlist ℕumber Theory
Karlheinz Gröchenig: Gabor Analysis and its Mysteries (Lecture 2)
Due to technical problems the blackboard is not visible. The lecture was held within the framework of the Hausdorff Trimester Program Mathematics of Signal Processing. In Gabor analysis one studies the construction and properties of series expansions of functions with respect to a set of
From playlist HIM Lectures: Trimester Program "Mathematics of Signal Processing"
Proof & Explanation: Gauss's Lemma in Number Theory
Euler's criterion: https://youtu.be/2IBPOI43jek One common proof of quadratic reciprocity uses Gauss's lemma. To understand Gauss's lemma, here we prove how it works using Euler's criterion and the Legendre symbol. Quadratic Residues playlist: https://www.youtube.com/playlist?list=PLug5Z
From playlist Quadratic Residues