Ramsey theory is based on Ramsey's theorem, because without it, there would be no Ramsey numbers, since they are not well-defined. This is part 2 of the trilogy of the Ramsey numbers. Useful link: https://en.wikipedia.org/wiki/Ramsey%27s_theorem#2-colour_case Other than commenting on the
From playlist Ramsey trilogy
Advances on Ramsey numbers - Jacob Fox
https://www.math.ias.edu/seminars/abstract?event=83564
From playlist Computer Science/Discrete Mathematics
This video is about some of the basic properties of Ramsey numbers.
From playlist Basics: Graph Theory
Rhapsody on Ramsey numbers (and aliens?)
Why are aliens involved in this graph theory problem? This video trilogy will investigate deep into Ramsey's theory, ultimately showing R(4,4)=18. Although this field of graph theory is pretty famous and possibly covered by many Youtube channels, this more-than-20-minute journey Other th
From playlist Ramsey trilogy
Metrizable universal minimal flows and Ramsey theory - T. Tsankov - Workshop 1 - CEB T1 2018
Todor Tsankov (Université Paris Diderot) / 01.02.2018 The connection between Ramsey theory and topological dynamics goes back at least to Furstenberg who used dynamical systems of the group of integers to derive a new proof of Van Der Waerden’s theorem. More recently, Kechris, Pestov, and
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Using nonstandard natural numbers in Ramsey Theory - M. Di Nasso - Workshop 1 - CEB T1 2018
Mauro Di Nasso (Pisa) / 01.02.2018 In Ramsey Theory, ultrafilters often play an instrumental role. By means of nonstandard models, one can reduce those third-order objects (ultrafilters are sets of sets of natural numbers) to simple points. In this talk we present a nonstandard technique
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Ramsey numbers and Game of Thrones || #VeritasiumContest #shorts
"Suppose aliens invade the earth and threaten to obliterate it in a year's time unless human beings can find the Ramsey number R(5). We could marshal the world's best minds and fastest computers, and within a year we could probably calculate the value. If the aliens demanded the Ramsey num
From playlist Summer of Math Exposition Youtube Videos
The absorption method, and an application to an old Ramsey problem - Matija Bucic
Computer Science/Discrete Mathematics Seminar II Topic: The absorption method, and an application to an old Ramsey problem Speaker: Matija Bucic Affiliation: Veblen Research Instructor, School of Mathematics Date: March 29, 2022 The absorption method is a very simple yet surprisingly pow
From playlist Mathematics
Ramsey theorems for classes of structures with (...) - J. Hubička - Workshop 1 - CEB T1 2018
Jan Hubička (Charles U) / 02.02.2018 Ramsey theorems for classes of structures with functions and relations We discuss a generalization of Nešetřil-Rődl theorem for free amalgamation classes of structures in a language containing both relations and partial functions. Then we further stre
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
New Developments in Hypergraph Ramsey Theory - D. Mubayi - Workshop 1 - CEB T1 2018
Dhruv Mubayi (UI Chicago) / 30.01.2018 I will describe lower bounds (i.e. constructions) for several hypergraph Ramsey problems. These constructions settle old conjectures of Erd˝os–Hajnal on classical Ramsey numbers as well as more recent questions due to Conlon–Fox–Lee–Sudakov and othe
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Natasha Dobrinen: Borel sets of Rado graphs are Ramsey
The Galvin-Prikry theorem states that Borel partitions of the Baire space are Ramsey. Thus, given any Borel subset $\chi$ of the Baire space and an infinite set $N$, there is an infinite subset $M$ of $N$ such that $\left [M \right ]^{\omega }$ is either contained in $\chi$ or disjoint fr
From playlist Combinatorics
Ramsey classes and sparsity for finite models - J. Nešetřil - Workshop 1 - CEB T1 2018
Jaroslav Nešetřil (Prague) / 31.01.2018 In the talk we relate two notions in the title particularly in the context of sparse dense dichotomy (nowhere and somewhere dense classes and stability) and Ramsey classes of finite models in the context of the characterisation programme. A joint wo
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Dependent random choice - Jacob Fox
Marston Morse Lectures Topic: Dependent random choice Speaker: Jacob Fox, Stanford University Date: October 26, 2016 For more videos, visit http://video.ias.edu
From playlist Mathematics
Extremal Combinatorics with Po-Shen Loh 03/30 Mon
Carnegie Mellon University is protecting the community from the COVID-19 pandemic by running courses online for the Spring 2020 semester. This is the video stream for Po-Shen Loh’s PhD-level course 21-738 Extremal Combinatorics. Professor Loh will not be able to respond to questions or com
From playlist CMU PhD-Level Course 21-738 Extremal Combinatorics
Lecture 18 - Probability G. F.
This is Lecture 18 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2018.pdf More information may
From playlist CSE547 - Discrete Mathematics - 1999 SBU
Amanda Montejano: Zero-sum squares in bounded discrepancy {-1,1}-matrices
A square in a matrix $\mathcal M =(a_{ij})$ is a 2X2 sub-matrix of $\mathcal M$ with entries $a_{ij}, a_{i+s,j}, ai,j+s, a_{i+s,j+s}$s for some $s\geq 1$. An Erickson matrix is a square binary matrix that contains no squares with constant entries. In [Eri96], Erickson asked for the maximum
From playlist Virtual Conference
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics