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
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
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
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
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
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
The Campbell-Baker-Hausdorff and Dynkin formula and its finite nature
In this video explain, implement and numerically validate all the nice formulas popping up from math behind the theorem of Campbell, Baker, Hausdorff and Dynkin, usually a.k.a. Baker-Campbell-Hausdorff formula. Here's the TeX and python code: https://gist.github.com/Nikolaj-K/8e9a345e4c932
From playlist 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
Giovanni Peccati: Some applications of variational techniques in stochastic geometry III
Second-order Poincaré inequalities and related convergence results I will describe a new collection of probabilistic bounds on the Poisson space, allowing one to mea- sure the distance to Gaussianity for (possibly multidimensional) random elements displaying a form of ’two-scale stabiliza
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
Domains of holomorphy and Dolbeault cohomology
Domains of holomorphy can be characterized by vanishing of Dolbeault cohomology. We prove one direction of this characterization. For more detais see Gunning's "Introduction to holomorphic functions of several variables, Vol 1", Section G. Please point out any imprecisions in the comments
From playlist Several Complex Variables
Franc Forstnerič - Non singular holomorphic foliations on Stein manifolds (Part 3)
Non singular holomorphic foliations on Stein manifolds (Part 3)
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Problems, Paradoxes, and Sophisms
Kai Cieliebak - Stein and Weinstein manifolds
Stein manifolds arise naturally in the theory of several complex variables. This talk will give an informal introduction to some of their topological and symplectic aspects such as: handlebody construction of Stein manifolds; their symplectic counterparts; Weinstein manifolds; flexibility
From playlist Not Only Scalar Curvature Seminar
Math 131 Spring 2022 050422 Riemann-Lebesgue lemma; Classical Fourier Series.
Recall definition of orthonormal systems. Results about General Fourier Series: Proof of "Best Mean Square Approximation" (that the partial sum of the Fourier series of a (Riemann integrable) function is the best linear combination approximating the function in the L2 sense). Consequence
From playlist Math 131 Spring 2022 Principles of Mathematical Analysis (Rudin)
Hilbert Space Techniques in Complex Analysis and Geometry (Lecture 10) by Dror Varolin
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
Kähler–Einstein metrics on Fano manifolds: variational and algebro-geometric – S. Boucksom – ICM2018
Algebraic and Complex Geometry | Analysis and Operator Algebras Invited Lecture 4.1 | 8.1 Kähler–Einstein metrics on Fano manifolds: variational and algebro-geometric aspects Sébastien Boucksom Abstract: I will describe a variational approach to the existence of Kähler–Einstein metrics o
From playlist Algebraic & Complex Geometry
Workshop 1 "Operator Algebras and Quantum Information Theory" - CEB T3 2017 - N.LaRacuente
Nicholas LaRacuente (UIUC) / 14.09.17 Title: Non-commutative L_p Spaces and Asymmetry Measures Abstract: We relate a common class of entropic asymmetry measures to non-commutative L_p space norms. These asymmetry measures have operational meanings related to the resource theory of asymme
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Linear Algebra 6g: Linear Dependence Example 3 - Geometric Vectors
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