Paul Shafer:Reverse mathematics of Caristi's fixed point theorem and Ekeland's variational principle
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Caristi's fixed point theorem is a fixed point theorem for functions that are controlled by continuous functions but are necessarily continuous themselves. Let a 'Caristi
From playlist Workshop: "Proofs and Computation"
Mark Sapir - The Tarski numbers of groups.
Mark Sapir (Vanderbilt University, USA) The Tarski number of a non-amenable group is the minimal number of pieces in a paradoxical decomposition of the group. It is known that a group has Tarski number 4 if and only if it contains a free non-cyclic subgroup, and the Tarski numbers of tors
From playlist T1-2014 : Random walks and asymptopic geometry of groups.
Silvia Steila: An overview over least fixed points in weak set theories
Given a monotone function on a complete lattice the least fixed point is defined as the minimum among the fixed points. Tarski Knaster Theorem states that every monotone function on a complete lattice has a least fixed point. There are two standard proofs of Tarski Knaster Theorem. The f
From playlist Workshop: "Proofs and Computation"
In this video, I prove a very neat result about fixed points and give some cool applications. This is a must-see for calculus lovers, enjoy! Old Fixed Point Video: https://youtu.be/zEe5J3X6ISE Banach Fixed Point Theorem: https://youtu.be/9jL8iHw0ans Continuity Playlist: https://www.youtu
From playlist Calculus
This Math Theorem Proves that 1=1+1 | The Banach-Tarskis Paradox
Mathematicians are in nearly universal agreement that the strangest paradox in math is the Banach-Tarski paradox, in which you can split one ball into a finite number of pieces, then rearrange the pieces to get two balls of the same size. Interestingly, only a minority of mathematicians ha
From playlist Math and Statistics
The Lawvere fixed point theorem
In this video we prove a version of Lawveres fixed point theorem that holds in Cartesian closed categories. It's a nice construction that specializes to results such as Cantors diagonal argument and prove the the power set of a set is classically always larger than the set itself. https:/
From playlist Logic
Fixed and Periodic Points | Nathan Dalaklis
Fixed Points and Periodic points are two mathematical objects that come up all over the place in Dynamical systems, Differential equations, and surprisingly in Topology as well. In these videos, I introduce the concepts of fixed points and periodic points and gradually build to a proof of
From playlist The New CHALKboard
The Banach Tarski paradox - is it nonsense? | Sociology and Pure Mathematics | N J Wildberger
One of the famous "paradoxes" of 20th century pure mathematics is the assertion that it is possible to subdivide a solid ball of radius 1 in three dimensional space into 5 disjoint pieces, take those five pieces and subject them to rigid motions, that is rotations and translations, to obta
From playlist Sociology and Pure Mathematics
Measurable equidecompositions – András Máthé – ICM2018
Analysis and Operator Algebras Invited Lecture 8.8 Measurable equidecompositions András Máthé Abstract: The famous Banach–Tarski paradox and Hilbert’s third problem are part of story of paradoxical equidecompositions and invariant finitely additive measures. We review some of the classic
From playlist Analysis & Operator Algebras
Robert Ghrist (8/29/21): Laplacians and Network Sheaves
This talk will begin with a simple introduction to cellular sheaves as a generalized notion of a network of algebraic objects. With a little bit of geometry, one can often define a Laplacian for such sheaves. The resulting Hodge theory relates the geometry of the Laplacian to the algebraic
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Joel David Hamkins : The hierarchy of second-order set theories between GBC and KM and beyond
Abstract: Recent work has clarified how various natural second-order set-theoretic principles, such as those concerned with class forcing or with proper class games, fit into a new robust hierarchy of second-order set theories between Gödel-Bernays GBC set theory and Kelley-Morse KM set th
From playlist Logic and Foundations
Infinity shapeshifter vs. Banach-Tarski paradox
Take on solid ball, cut it into a couple of pieces and rearrange those pieces back together into two solid balls of exactly the same size as the original ball. Impossible? Not in mathematics! Recently Vsauce did a brilliant video on this so-called Banach-Tarski paradox: https://youtu.be/s
From playlist Recent videos
What is the max and min of a horizontal line on a closed interval
👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We dicuss the axiom of chice, and sketch why it is independent of the other axioms of set theory. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52EKVgPi-p50f
From playlist Zermelo Fraenkel axioms
Model Theory - part 08 - Syntactic Catgories
These are the categories where functors from these dudes are models... these take forever to define. On top of it, these end up just being friggin' definable sets and definable morphisms!! I remember being a place in here where there is a diagram which i say commutes but I need to actually
From playlist Model Theory
Kurt Gödel Centenary - Part III
John W. Dawson, Jr. Pennsylvania State University November 17, 2006 More videos on http://video.ias.edu
From playlist Kurt Gödel Centenary
Matthew Foreman: Welch games to Laver ideals
Recorded during the meeting "XVI International Luminy Workshop in Set Theory" the September 16, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Au
From playlist Logic and Foundations
Fixed points and stability: one dimension
Shows how to determine the fixed points and their linear stability of a first-order nonlinear differential equation. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: https://www.coursera.org
From playlist Differential Equations