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
From playlist Week 1 2015 Shorts
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)
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
Regularity lemma and its applications Part I - Fan Wei
Computer Science/Discrete Mathematics Seminar II Topic: Regularity lemma and its applications Part I Speaker: Fan Wei Affiliation: Member, School of Mathematics Dater: December 3, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Ramla Abdellatif - Iwahori - Hecke algebras and hovels for split Kac - Moody groups
Let F be a non-archimedean local field and G be the group of F-rational points of a connected reductive group defined over F. The study of (complex smooth) representations of G imply various tools coming from different nature. These include in particular induction functors, Hecke al
From playlist Reductive groups and automorphic forms. Dedicated to the French school of automorphic forms and in memory of Roger Godement.
P. Scholze - p-adic K-theory of p-adic rings
The original proof of Grothendieck's purity conjecture in étale cohomology (the Thomason-Gabber theorem) relies on results on l-adic K-theory and its relation to étale cohomology when l is invertible. Using recent advances of Clausen-Mathew-Morrow and joint work with Bhatt and Morrow, our
From playlist Arithmetic and Algebraic Geometry: A conference in honor of Ofer Gabber on the occasion of his 60th birthday
Srinivasa Varadhan - The Abel Prize interview 2007
0:00 Abel Prize Ceremonies (Norwegian) 01:00 Interview with Skau and Raussen starts 02:30 Why so long for probability or statistics to be recognised? 04:35 Born and raised on Chennai, studied at Madras; mathematical influences 05:52 Excellent math. teacher, math. for enjoyment 07:30 Why gr
From playlist The Abel Prize Interviews
Hagop Tossounian: On Kac’s model, ideal Thermostats, and finite Reservoirs
The lecture was held within the framework of the Hausdorff Trimester Program: Kinetic Theory Abstract: In 1956, Mark Kac introduced a stochastic model to derive a Boltzmann-like equation. Like the space-homogeneous Boltzmann’s equation, Kac’s equation is ergodic with centered Gaussians as
From playlist Workshop: Probabilistic and variational methods in kinetic theory
One cannot (always) hear the shape of a drum
The question "Can One Hear the Shape of a Drum?" was asked by Marc Kac in a 1966 article in the American Mathematical Monthly. The vibrations of a drum are governed by its resonant frequencies, which are related to what mathematicians call the "eigenvalues of the Laplace operator with Diri
From playlist Billiards in polygons
Wave amplitude in two isospectral drums
Like the video https://youtu.be/RaQZ11ydBZo this simulation shows two drums that have exactly the same resonant frequencies. It is based on the same construction involving 7 triangles obtained by reflecting an initial triangle. The initial triangle has a different shape than before, and th
From playlist Billiards in polygons
Wave amplitude and average energy in homophonic drums
This is another visualization of waves in two homophonic drums, showing the wave height and the average energy from the beginning of the simulation, instead of the wave energy at a given time, like the video https://youtu.be/fEA1KpYA07A Wave height: 0:00 Average wave energy: 2:25 The two d
From playlist Billiards in polygons
Homophonic drums: two different drums that should sound the same
Like the video https://youtu.be/RaQZ11ydBZo this simulation shows two drums that have exactly the same resonant frequencies. In addition, their resonant modes (eigenfunctions) have the same value at two specific points, namely the inner points where 6 triangles meet. Therefore, the drums m
From playlist Wave equation
One cannot always hear the shape of a drum: Isospectral billiards in 3D
This is a remake of the video https://youtu.be/RaQZ11ydBZo showing isospectral drums, this time in 3D. The question "Can One Hear the Shape of a Drum?" was asked by Marc Kac in a 1966 article in the American Mathematical Monthly. The vibrations of a drum are governed by its resonant frequ
From playlist Wave equation
3D rendering of the Buser-Conway-Doyle-Semmler homophonic drums
I said homophonic, not homophobic: these drums have no issue whatsoever with the LGBT community. Homophonic means the drums should sound the same when hit in the same way. This is a remake of the video https://youtu.be/fEA1KpYA07A showing homophonic and isospectral drums, this time rendre
From playlist Wave equation
What is the formula for the rule for the nth term of a arithmetic sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
The Schwarz Lemma -- Complex Analysis
Part 1 -- The Maximum Principle: https://youtu.be/T_Msrljdtm4 Part 3 -- Liouville's theorem: https://www.youtube.com/watch?v=fLnRDhhzWKQ In today's video, we want to take a look at the Schwarz lemma — this is a monumental result in the subject of one complex variable, and has lead to many
From playlist Complex Analysis
Martina Lanini, Introduction - 9 December 2014
Minicourses of the session "Vertex algebras, W-algebras, and applications" (2014) http://www.crm.sns.it/event/321/speakers.html?page=1#title INdAM Intensive research period Perspectives in Lie Theory Session 1: Vertex algebras, W-algebras, and applications Mini-courses Tomoyuki Arakawa
From playlist Vertex algebras, W-algebras, and applications - 2014-2015
This video explains the Handshake lemma and how it can be used to help answer questions about graph theory. mathispower4u.com
From playlist Graph Theory (Discrete Math)