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
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
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
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
Sum of Polynomial Coefficients Challenge
Solution on Lemma: https://www.lem.ma/-K (and additional challenges) Tangentially related good read: http://bit.ly/PascalsTri Twitter: https://twitter.com/PavelGrinfeld
From playlist Problems, Paradoxes, and Sophisms
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
In this video, I prove the famous Riemann-Lebesgue lemma, which states that the Fourier transform of an integrable function must go to 0 as |z| goes to infinity. This is one of the results where the proof is more important than the theorem, because it's a very classical Lebesgue integral
From playlist Real Analysis
László Lovász: The many facets of the Regularity Lemma
Abstract: The Regularity Lemma of Szemerédi, first obtained in the context of his theorem on arithmetic progressions in dense sequences, has become one of the most important and most powerful tools in graph theory. It is basic in extremal graph theory and in the theory of property testing.
From playlist Abel Lectures
Haluk SENGUN - Cohomology of arithmetic groups and number theory: geometric, ... 1
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Quadrature domains in higher dimensions by Pranav Haridas
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Introduction to quadrature domains (Lecture – 2) by Kaushal Verma
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Chandrashekhar Khare, Serre's conjecture and computational aspects of the Langlands program
VaNTAGe Seminar, April 5, 2022 License: CC-BY-NC-SA Some relevant links: Edixhoven-Couveignes-de Jong-Merkl-Bosman: https://arxiv.org/abs/math/0605244 Ramanujan's 1916 paper: http://ramanujan.sirinudi.org/Volumes/published/ram18.pdf Delta's home page in the LMFDB: https://www.lmfdb.org/
From playlist Modularity and Serre's conjecture (in memory of Bas Edixhoven)
Adam Piggott & Murray Elder Double Header: Geodesics in Groups
Double header seminar by two SMRI domestic visitors: Adam Piggott (Australian National University) ‘Stubborn conjectures concerning rewriting systems, geodesic normal forms and geodetic graphs’ & Murray Elder (University of Technology Sydney) ‘Which groups have polynomial geodesic growth
From playlist SMRI Seminars
Amir Mohammadi: Finitary analysis in homogeneous spaces and applications
Abstract: Rigidity phenomena in homogeneous dynamics have been extensively studied over the past few decades with several striking results and applications. In this talk, we will give an overview of recent activities related to quantitative aspect of the analysis in this context; we will a
From playlist Number Theory Down Under 9
Burnside's Lemma (Part 1) - combining group theory and combinatorics
A result often used in math competitions, 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 transformed into one another by rotation different, like in this cas
From playlist Traditional topics, explained in a new way
A Tight Bound for Hypergraph Regularity - Guy Moshkovitz
Computer Science/Discrete Mathematics Seminar I Topic: A Tight Bound for Hypergraph Regularity Speaker: Guy Moshkovitz Affiliation: Harvard University Date: Febuary 27, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
on the Brumer-Stark Conjecture (Lecture 3) by Mahesh Kakde
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
[BOURBAKI 2018] 13/01/2018 - 2/4 - Raphaël BEUZART-PLESSIS
Progrès récents sur les conjectures de Gan-Gross-Prasad [d'après Jacquet-Rallis, Waldspurger, W. Zhang, etc.] Les conjectures de Gan-Gross-Prasad ont deux aspects: localement elles décrivent de façon explicite certaines lois de branchements entre représentations de groupes de Lie réels ou
From playlist BOURBAKI - 2018
Linear Algebra 2q: Summary of Terms Encountered so Far
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications