The Homework Problem That Started as a Phd Thesis: 14 set theorem
In a handful of introductory topology textbooks, Kuratowski's 14 set theorem is given as an exercise despite it being one of the results proven as a part of his phd thesis in 1922. This homework problem that started out as a phd thesis is not an easy exercise if you don't know how to think
From playlist The New CHALKboard
MATH1081 Discrete Maths: Chapter 5 Question 27 a
This problem is about planar graphs. The theorem mentioned is Fáry's Theorem (1948); see http://bit.ly/1gmUrXT . Presented by Thomas Britz of the School of Mathematics and Statistics, Faculty of Science, UNSW.
From playlist MATH1081 Discrete Mathematics
Graph Theory: 61. Characterization of Planar Graphs
We have seen in a previous video that K5 and K3,3 are non-planar. In this video we define an elementary subdivision of a graph, as well as a subdivision of a graph. We then discuss the fact that if a graph G contains a subgraph which is a subdivision of a non-planar graph, then G is non-
From playlist Graph Theory part-10
Vitaly Bergelson: Mutually enriching connections between ergodic theory and combinatorics - part 7
Abstract : * The early results of Ramsey theory : Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres. * Three main principles of Ramsey theory : First principl
From playlist Jean-Morlet Chair - Lemanczyk/Ferenczi
Vitaly Bergelson: Mutually enriching connections between ergodic theory and combinatorics - part 8
Abstract : * The early results of Ramsey theory : Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres. * Three main principles of Ramsey theory : First principl
From playlist Jean-Morlet Chair - Lemanczyk/Ferenczi
Vitaly Bergelson: Mutually enriching connections between ergodic theory and combinatorics - part 5
Abstract : * The early results of Ramsey theory : Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres. * Three main principles of Ramsey theory : First principl
From playlist Jean-Morlet Chair - Lemanczyk/Ferenczi
Rade Zivaljevic (6/27/17) Bedlewo: Topological methods in discrete geometry; new developments
Some new applications of the configurations space/test map scheme can be found in Chapter 21 of the latest (third) edition of the Handbook of Discrete and Computational Geometry [2]. In this lecture we focus on some of the new developments which, due to the limitations of space, may have b
From playlist Applied Topology in Będlewo 2017
Vitaly Bergelson: Mutually enriching connections between ergodic theory and combinatorics- part 4
Abstract : * The early results of Ramsey theory : Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres. * Three main principles of Ramsey theory : First principl
From playlist Jean-Morlet Chair - Lemanczyk/Ferenczi
A Classification of Planar Graphs - A Proof of Kuratowski's Theorem
A visually explained proof of Kuratowski's theorem, an interesting, important and useful result classifying "planar" graphs. Proof adapted from: http://math.uchicago.edu/~may/REU2017/REUPapers/Xu,Yifan.pdf and: https://www.math.cmu.edu/~mradclif/teaching/228F16/Kuratowski.pdf Also check
From playlist Summer of Math Exposition Youtube Videos
MATH1081 Discrete Maths: Chapter 5 Question 33 - Kuratowski's Theorem (part 1)
MATH1081 "Discrete Mathematics" Topic 5 Question 33a
From playlist MATH1081 Discrete Mathematics
Graph Theory: 62. Graph Minors and Wagner's Theorem
In this video, we begin with a visualisation of an edge contraction and discuss the fact that an edge contraction may be thought of as resulting in a multigraph or simple graph, depending on the application. We then state the definition a contraction of edge e in a graph G resulting in a
From playlist Graph Theory part-10
Vitaly Bergelson: Mutually enriching connections between ergodic theory and combinatorics - part 3
Abstract : * The early results of Ramsey theory : Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres. * Three main principles of Ramsey theory : First principl
From playlist Jean-Morlet Chair - Lemanczyk/Ferenczi
[BOURBAKI 2019] Homology of Hurwitz spaces and the Cohen–Lenstra (...)- Randal-Williams - 15/06/19
Oscar RANDAL-WILLIAMS Homology of Hurwitz spaces and the Cohen–Lenstra heuristic for function fields, after Ellenberg, Venkatesh, and Westerland Ellenberg, Venkatesh, and Westerland have established a weak form of the function field analogue of the Cohen–Lenstra heuristic, on the distrib
From playlist BOURBAKI - 2019
MATH1081 Discrete Maths: Chapter 5 Question 33 - Kuratowski's Theorem (part 2)
MATH1081 "Discrete Mathematics" Topic 5 Question 33c
From playlist MATH1081 Discrete Mathematics
Vitaly Bergelson: Mutually enriching connections between ergodic theory and combinatorics - part 2
Abstract : * The early results of Ramsey theory : Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres. * Three main principles of Ramsey theory : First principl
From playlist Jean-Morlet Chair - Lemanczyk/Ferenczi
Vitaly Bergelson: Mutually enriching connections between ergodic theory and combinatorics - part 6
Abstract : * The early results of Ramsey theory : Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres. * Three main principles of Ramsey theory : First principl
From playlist Jean-Morlet Chair - Lemanczyk/Ferenczi
Featuring Professor Maria Chudnovsky from Princeton University - see part two about her work on Perfect Graphs - https://youtu.be/C4Zr4cOVm9g More links & stuff in full description below ↓↓↓ Correction at 13:58 - remove the word "not". Professor Chudnovsky's webpage: https://web.math.pri
From playlist Women in Mathematics - Numberphile
Vitaly Bergelson: Mutually enriching connections between ergodic theory and combinatorics - part 1
Abstract : * The early results of Ramsey theory : Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres. * Three main principles of Ramsey theory : First principl
From playlist Jean-Morlet Chair - Lemanczyk/Ferenczi
Wormholes Explained – Breaking Spacetime
Are wormholes real or are they just magic disguised as physics and maths? And if they are real how do they work and where can we find them? Sources and further reading: https://authors.library.caltech.edu/9262/1/MORprl88.pdf http://www.cmp.caltech.edu/refael/league/thorne-morris.pdf OUR
From playlist Our Best Stuff
Andrea D'Agnolo : On the Riemann-Hilbert correspondence for irregular holonomic D-modules
Abstract: The classical Riemann-Hilbert correspondence establishes an equivalence between the triangulated categories of regular holonomic D-modules and of constructible sheaves. In a joint work with Masaki Kashiwara, we proved a Riemann-Hilbert correspondence for holonomic D-modules which
From playlist Analysis and its Applications