Functional Analysis Lecture 26 2014 05 01 Closed Graph Theorem, Besicovitch Sets
Does every sequence of complex numbers (of vanishing modulus) arise as Fourier coefficients? No. Closed graph theorem. Besicovitch sets: definition, power sets, distance from a point to a set; delta-neighborhood of a set; Hausdorff distance between two sets.
From playlist Course 9: Basic Functional and Harmonic Analysis
Math 135 Complex Analysis Lecture 04 012915: Basic Topological Concepts part 2
Closed sets; closed sets and set operations; topological continuity (inverse image of open set is open); sequences; Cauchy sequence; closedness in terms of convergent sequences; continuity in terms of sequences; connected and path-connected sets; compact sets; Heine-Borel theorem (statemen
From playlist Course 8: Complex Analysis
Galois theory: Algebraic closure
This lecture is part of an online graduate course on Galois theory. We define the algebraic closure of a field as a sort of splitting field of all polynomials, and check that it is algebraically closed. We hen give a topological proof that the field C of complex numbers is algebraically
From playlist Galois theory
Limit Theories and Higher Order Fourier Analysis - Balazs Szegedy
Balazs Szegedy University of Toronto; Member, School of Mathematics October 4, 2011 We present a unified approach to various topics in mathematics including: Ergodic theory, graph limit theory, hypergraph regularity, and Higher order Fourier analysis. The main theme is that very large comp
From playlist Mathematics
The Definition of a Graph (Graph Theory)
The Definition of a Graph (Graph Theory) mathispower4u.com
From playlist Graph Theory (Discrete Math)
Graph Theory FAQs: 01. More General Graph Definition
In video 02: Definition of a Graph, we defined a (simple) graph as a set of vertices together with a set of edges where the edges are 2-subsets of the vertex set. Notice that this definition does not allow for multiple edges or loops. In general on this channel, we have been discussing o
From playlist Graph Theory FAQs
What are Connected Graphs? | Graph Theory
What is a connected graph in graph theory? That is the subject of today's math lesson! A connected graph is a graph in which every pair of vertices is connected, which means there exists a path in the graph with those vertices as endpoints. We can think of it this way: if, by traveling acr
From playlist Graph Theory
Limit Theories and Higher Order Fourier Analysis - Balazs Szegedy
Balazs Szegedy University of Toronto; Member, School of Mathematics October 11, 2011 We present a unified approach to various topics in mathematics including: Ergodic theory, graph limit theory, hypergraph regularity, and Higher order Fourier analysis. The main theme is that very large com
From playlist Mathematics
All About Closed Sets and Closures of Sets (and Clopen Sets) | Real Analysis
We introduced closed sets and clopen sets. We'll visit two definitions of closed sets. First, a set is closed if it is the complement of some open set, and second, a set is closed if it contains all of its limit points. We see examples of sets both closed and open (called "clopen sets") an
From playlist Real Analysis
From graph limits to higher order Fourier analysis – Balázs Szegedy – ICM2018
Combinatorics Invited Lecture 13.8 From graph limits to higher order Fourier analysis Balázs Szegedy Abstract: The so-called graph limit theory is an emerging diverse subject at the meeting point of many different areas of mathematics. It enables us to view finite graphs as approximation
From playlist Combinatorics
Boolean function analysis: beyond the Boolean cube - Yuval Filums
http://www.math.ias.edu/seminars/abstract?event=128828 More videos on http://video.ias.edu
From playlist Mathematics
Boolean function analysis: beyond the Boolean cube (continued) - Yuval Filmus
http://www.math.ias.edu/seminars/abstract?event=129061 More videos on http://video.ias.edu
From playlist Mathematics
Knots, three-manifolds and instantons – Peter Kronheimer & Tomasz Mrowka – ICM2018
Plenary Lecture 11 Knots, three-manifolds and instantons Peter Kronheimer & Tomasz Mrowka Abstract: Over the past four decades, input from geometry and analysis has been central to progress in the field of low-dimensional topology. This talk will focus on one aspect of these developments
From playlist Plenary Lectures
Introduction to quadrature domains (Lecture 5) 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
Terence Tao - Long arithmetic progressions in the primes [ICM 2006]
slides for this talk: https://drive.google.com/open?id=1CkB1KiNe5T3YXH8mBimrWDAN0t4HQrfL ICM Madrid Videos 23.08.2006 Long arithmetic progressions in the primes Terence Tao University of California, Los Angeles, USA https://www.mathunion.org/icm/icm-videos/icm-2006-videos-madrid-spain/i
From playlist Number Theory
The PCP theorem, locally testable codes, and property testing - Irit Dinur
Stability and Testability Topic: The PCP theorem, locally testable codes, and property testing Speaker: Irit Dinur Affiliation: Weizmann Institute of Science Date: January 13, 2021 For more video please visit http://video.ias.edu
From playlist Stability and Testability
18. Roth's theorem I: Fourier analytic proof over finite field
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX The finite field model is a nice sandbox for methods and
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Background material on the Cauchy-Riemann equations (Lecture 1) by Debraj Chakrabarti
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
Graph Theory: 42. Degree Sequences and Graphical Sequences
Here I describe what a degree sequence is and what makes a sequence graphical. Using some examples I'll describe some obvious necessary conditions (which are not sufficient). Then I explain how a Theorem by Havel and Hakimi gives a necessary and sufficient condition for a sequence of non
From playlist Graph Theory part-8
A Deterministic Sample of Bourgain’s Work - Peter Sarnak and Avi Wigderson
Honoring the Life and Work of Jean Bourgain Topic: A Deterministic Sample of Bourgain’s Work Speakers: Peter Sarnak, Avi Wigderson Date: May 31, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics