Kakeya set

Set Game

SET is an awesome game that really gets your brain working. Play it! Read more about SET here: http://theothermath.com/index.php/2020/03/27/set/

From playlist Games and puzzles

What is a Set Complement?

What is the complement of a set? Sets in mathematics are very cool, and one of my favorite thins in set theory is the complement and the universal set. In this video we will define complement in set theory, and in order to do so you will also need to know the meaning of universal set. I go

From playlist Set Theory

What is Set Subtraction?

What is set subtraction? In this video we go over that, the set minus set operation, and an example of subtraction in set theory. This is a handy concept to grasp to understand the complement of a set and universal sets, which I also have videos on. Links below. I hope you find this vide

From playlist Set Theory

Set Theory (Part 2b): The Bogus Universal Set

Please feel free to leave comments/questions on the video below! In this video, I argue against the existence of the set of all sets and show that this claim is provable in ZFC. This theorem is very much tied to the Russell Paradox, besides being one of the problematic ideas in mathematic

From playlist Set Theory by Mathoma

Set Theory (Part 2): ZFC Axioms

Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their

From playlist Set Theory by Mathoma

Set Theory (Part 1): Notation and Operations

Please feel free to leave comments/questions on the video and practice problems below! In this video series, we'll explore the basics of set theory. I assume no experience with set theory in the video series and anyone who's "been around town" in math should understand the videos. To make

From playlist Set Theory by Mathoma

algebraic geometry 4 Kakeya sets

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It continues with more examples from algebraic geometry, in particular Kakeya sets over finite fields and the 27 lines on a cubic surface.

From playlist Algebraic geometry I: Varieties

Set Theory (Part 3): Ordered Pairs and Cartesian Products

Please feel free to leave comments/questions on the video and practice problems below! In this video, I cover the Kuratowski definition of ordered pairs in terms of sets. This will allow us to speak of relations and functions in terms of sets as the basic mathematical objects and will ser

From playlist Set Theory by Mathoma

Power Set of the Power Set of the Power Set of the Empty Set | Set Theory

The power set of the power set of the power set of the empty set, we'll go over how to find just that in today's set theory video lesson! We'll also go over the power set of the empty set, the power set of the power set of the empty set, and we'll se the power set of the power set of the p

From playlist Set Theory

Kakeya's Needle Problem - Numberphile

The famed Kakeya Needle Problem, discussed by Charles Fefferman from Princeton University. More links & stuff in full description below ↓↓↓ Edit and animation by Pete McPartlan Film and interview by Brady Haran 17-gon: https://youtu.be/87uo2TPrsl8 Support us on Patreon: http://www.patre

From playlist Fields Medallists on Numberphile

Bourgain’s Work on Restriction and Decoupling - Larry Guth

Honoring the Life and Work of Jean Bourgain Topic: Bourgain’s Work on Restriction and Decoupling Speaker: Larry Guth Date: June 1, 2019 For more video please visit http://video.ias.edu

From playlist Mathematics

Chris SOGGE - Toponogov's theorem and improved Kakeya-Nikodym estimates...

Toponogov's theorem and improved Kakeya-Nikodym estimates for eigenfunctions on manifolds of nonpositive curvature This is joint work with Matthew Blair. Using wave equation techniques and elementary facts from Riemannian geometry, we show that, on negatively curved manifolds, eigenfuncti

From playlist Trimestre "Ondes Non linéaires" - June Conference

The Kakeya needle problem (the squeegee approach)

The Mathologer attacks the hundred-year-old Kakeya needle problem with his trusty squeegee: What is the smallest amount of area required to continuously rotate a (mathematical) needle in the plane by 180 degrees? The surprising answer is the starting point for a huge amount of very deep ma

From playlist Recent videos

Search games and Optimal Kakeya Sets - Yuval Peres

Yuval Peres Microsoft Research April 28, 2014 A planar set that contains a unit segment in every direction is called a Kakeya set. These sets have been studied intensively in geometric measure theory and harmonic analysis since the work of Besicovich (1919); we find a new connection to gam

From playlist Mathematics

Topics in Combinatorics lecture 12.2 --- Dvir's solution to the finite-field Kakeya problem

A line in F_p^n is a set of the form {x+ty: t=0,1,...,p-1}. We call y the direction of the line. How small can a subset A of F_p^n be if it contains at least one line in every direction? This question can be regarded as a combinatorial version of the famous Kakeya problem (https://en.wikip

From playlist Topics in Combinatorics (Cambridge Part III course)

What is a closed set ?

I define closed sets, an important notion in topology and analysis. It is defined in terms of limit points, and has a priori nothing to do with open sets. Yet I show the important result that a set is closed if and only if its complement is open. More topology videos can be found on my pla

From playlist Topology

Characteristic subsets and the polynomial method – Miguel Walsh – ICM2018

Dynamical Systems and Ordinary Differential Equations | Number Theory Invited Lecture 9.14 | 3.9 Characteristic subsets and the polynomial method Miguel Walsh Abstract: We provide an informal discussion of the polynomial method. This is a tool of general applicability that can be used to

From playlist Number Theory

The Kakeya Set conjecture over Z mod N for general N - Manik Dhar

Computer Science/Discrete Mathematics Seminar I Topic: The Kakeya Set conjecture over Z mod N for general N Speaker: Manik Dhar Affiliation: Princeton University Date: November 08, 2021 A Kakeya Set in (Z/N Z)^n is a set that contains a line in every direction. It has been known for ove

From playlist Mathematics

The perfect number of axioms | Axiomatic Set Theory, Section 1.1

In this video we introduce 6 of the axioms of ZFC set theory. My Twitter: https://twitter.com/KristapsBalodi3 Intro: (0:00) The Axiom of Existence: (2:39) The Axiom of Extensionality: (4:20) The Axiom Schema of Comprehension: (6:15) The Axiom of Pair (12:16) The Axiom of Union (15:15) T

From playlist Axiomatic Set Theory

Ciprian Demeter: Decoupling theorems and their applications

We explain how a certain decoupling theorem from Fourier analysis finds sharp applications in PDEs, incidence geometry and analytic number theory. This is joint work with Jean Bourgain. The lecture was held within the framework of the Hausdorff Trimester Program Harmonic Analysis and Part

From playlist HIM Lectures: Trimester Program "Harmonic Analysis and Partial Differential Equations"