In this video, I state and prove Chebyshev's inequality, and its cousin Markov's inequality. Those inequalities tell us how big an integrable function can really be. Enjoy!
From playlist Real Analysis
Introduction to Differential Inequalities
What is a differential inequality and how are they useful? Inequalities are a very practical part of mathematics: They give us an idea of the size of things -- an estimate. They can give us a location for things. It is usually far easier to satisfy assumptions involving inequalities t
From playlist Advanced Studies in Ordinary Differential Equations
x plus 1/x is greater than or equal to 2 when x is positive IV (visual proof via calculus)
This is a short, animated visual proof demonstrating that sum of a positive real number and its reciprocal is always greater than or equal to 2. #math #manim #visualproof #mathvideo #geometry #mathshorts #algebra #mtbos #animation #theorem #pww #proofwithoutwords #proof #ite
From playlist Inequalities
Introduction to additive combinatorics lecture 2.7 --- Khovanskii's theorem
Khovanskii's theorem states that if A is a finite subset of an Abelian group and nA = A+A+...+A, where there are n A's in the sum, then the size of nA is a polynomial function of n when n is sufficiently large. The proof given here is due to Melvyn Nathanson and Imre Ruzsa. 0:00 Introduct
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Gilles Pisier : On the non-commutative Khintchine inequalities
Abstract: This is joint work with Éric Ricard. We give a proof of the Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the
From playlist Analysis and its Applications
Homological generalizations of trace - Dmitry Vaintrob
Topic: Homological generalizations of trace Speaker: Dmitry Vaintrob, Member, School of Mathematics Time/Room: 4:15pm - 4:30pm/S-101 More videos on http://video.ias.edu
From playlist Mathematics
Bo’az Klartag: On Yuansi Chen’s work on the KLS conjecture II
The Kannan-Lovasz-Simonovits (KLS) conjecture is concerned with the isoperimetric problem in high-dimensional convex bodies. The problem asks for the optimal way to partition a convex body into two pieces of equal volume so as to minimize their interface. The conjecture suggests that up to
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
8ECM Invited Lecture: Rupert Frank
From playlist 8ECM Invited Lectures
Radek Adamczak: Functional inequalities and concentration of measure II
Concentration inequalities are one of the basic tools of probability and asymptotic geo- metric analysis, underlying the proofs of limit theorems and existential results in high dimensions. Original arguments leading to concentration estimates were based on isoperimetric inequalities, whic
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
An isoperimetric inequality for the Hamming cube and some consequences - Jinyoung Park
Computer Science/Discrete Mathematics Seminar I Topic: An isoperimetric inequality for the Hamming cube and some consequences Speaker: Jinyoung Park Affiliation: Rutgers University Date: November 18, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem
In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Galyna Livshyts: On some tight convexity inequalities for symmetric convex sets
We conjecture an inequality which strengthens the Ehrhard inequality for symmetric convex sets, in the case of the standard Gaussian measure. We explain its relation to other questions, such as the isoperimetric problem, and (if time permits), to the tight bound in a version of the Dirichl
From playlist Workshop: High dimensional measures: geometric and probabilistic aspects
Galyna Livshyts - On a conjectural symmetric version of the Ehrhard inequality
Recorded 08 February 2022. Galyna Livshyts of the Georgia Institute of Technology presents "On a conjectural symmetric version of the Ehrhard inequality" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: Ehrhard’s inequality is a sharp inequality about the Ga
From playlist Workshop: Calculus of Variations in Probability and Geometry
Bo'az Klartag - Convexity in High Dimensions I
October 28, 2022 This is the first talk in the Minerva Mini-course of Bo'az Klartag, Weizmann Institute of Science and Princeton's Fall 2022 Minerva Distinguished Visitor We will discuss recent progress in the understanding of the isoperimetric problem for high-dimensional convex sets, an
From playlist Minerva Mini Course - Bo'az Klartag
Proof of a 35 Year Old Conjecture for Entropy of Coherent States and Generalization - Elliot Lieb
Elliot Lieb Princeton University November 12, 2012 35 years ago Wehrl defined a classical entropy of a quantum density matrix using Gaussian (Schr\"odinger, Bargmann, ...) coherent states. This entropy, unlike other classical approximations, has the virtue of being positive. He conjectured
From playlist Mathematics
Local Dissipation of Energy for Continuous Incompressible Euler Flows - Philip Isett
Workshop on Recent developments in incompressible fluid dynamics Topic: Local Dissipation of Energy for Continuous Incompressible Euler Flows Speaker: Philip Isett Affiliation: University of Texas, Austin Date: April 04, 2022 I will discuss the construction of continuous solutions to th
From playlist Mathematics
Terence Tao (UCLA): Pseudorandomness of the Liouville function
The Liouville pseudorandomness principle (a close cousin of the Mobius pseudorandomness principle) asserts that the Liouville function λ(n), which is the completely multiplicative function that equals −1 at every prime, should be "pseudorandom" in the sense that it behaves statistically li
From playlist TP Harmonic Analysis and Analytic Number Theory: Opening Day
Bo'az Klartag - Convexity in High Dimensions IV
November 18, 2022 This is the fourth talk in the Minerva Mini-course of Bo'az Klartag, Weizmann Institute of Science and Princeton's Fall 2022 Minerva Distinguished Visitor We will discuss recent progress in the understanding of the isoperimetric problem for high-dimensional convex sets,
From playlist Minerva Mini Course - Bo'az Klartag
I. Uriarte-Tuero: Two weight norm inequalities for singular and fractional integral operators in R^N
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Harmonic Analysis and Partial Differential Equations.
From playlist HIM Lectures: Trimester Program "Harmonic Analysis and Partial Differential Equations"
Dimitris Koukoulopoulos: Approximating reals by rationals
Abstract: Given any irrational number α, Dirichlet proved that there are infinitely many reduced fractions a/q such that |α − a/q| ≤ 1/q^2. A natural question that arises is whether the fractions a/q can get even closer to α. For certain ”quadratic irrationals” such as α = √2 the answer is
From playlist Number Theory Down Under 9