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
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
Applications of analysis to fractional differential equations
I show how to apply theorems from analysis to fractional differential equations. The ideas feature the Arzela-Ascoli theorem and Weierstrass' approximation theorem, leading to a new approach for solvability of certain fractional differential equations. When do fractional differential equ
From playlist Mathematical analysis and applications
Loose the screw for moving the stopper to new position and then tighten it. The stopper is kept immobile by wedge mechnism.
From playlist Mechanisms
Étale cohomology 9/10/2020 Part 2
Čech cohomology
From playlist Étale cohomology and the Weil conjectures
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
On some questions about minimal log discrepancies - Mircea Mustata
Mircea Mustata University of Michigan March 3, 2015 The minimal log discrepancy is a measure of singularities of pairs. While akin to the log canonical threshold, it turns out to be much more difficult to study, with many questions still open. I will discuss a question about the boundedne
From playlist Mathematics
Lecture with Ole Christensen. Kapitler: 00:00 - Def.: Closure Of A Subset; 06:45 - Dense Vs. Closure; 19:00 - Extension Of Operators On Dense Subspaces; 24:15 - Proof;
From playlist DTU: Mathematics 4 Real Analysis | CosmoLearning.org Math
Yoshihiro Ohnita: Minimal Maslov number of R-spaces canonically embedded in Einstein-Kähler C-spaces
An R-space is a compact homogeneous space obtained as an orbit of the isotropy representation of a Riemannian symmetric space. It is known that each R-space has the canonical embedding into a Kähler C-space as a real form which is a compact embedded totally geodesic Lagrangian submanifold.
From playlist Geometry
When do fractional differential equations have maximal solutions?
When do fractional differential equations have maximal solutions? This video discusses this question in the following way. Firstly, a comparison theorem is formulated that involves fractional differential inequalities. Secondly, a sequence of approximative problems involving polynomials
From playlist Research in Mathematics
Real Analysis Ep 15: Closure of a set
Episode 15 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is about the closure of a set. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/courses/2020f3371/ Chris Staecker webpage: http://faculty.f
From playlist Math 3371 (Real analysis) Fall 2020
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
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
What is a Manifold? Lesson 2: Elementary Definitions
This lesson covers the basic definitions used in topology to describe subsets of topological spaces.
From playlist What is a Manifold?
Metric Spaces - Lectures 11 & 12: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 6th of 11 videos. The course is about the notion of distance. You ma
From playlist Oxford Mathematics Student Lectures - Metric Spaces
Antonio Rieser (03/29/23) Algebraic Topology for Graphs & Mesoscopic Spaces: Homotopy & Sheaf Theory
Title: Algebraic Topology for Graphs and Mesoscopic Spaces: Homotopy and Sheaf Theory Abstract: In this talk, we introduce the notion of a mesoscopic space: a metric space decorated with a privileged scale, and we survey recent developments in the algebraic topology of such spaces. Our ap
From playlist AATRN 2023
2c Data Analytics Reboot: Bayesian Probability
Lecture on Bayesian probability. From the product rule to the derivation of Bayes' Theorem, to solving a variety of probability problems and making observations. Bayesian approaches for updating prior probabilities with new information. Follow along with the demonstration workflow in Pyt
From playlist Data Analytics and Geostatistics
Didac Martinez-Granado: Volume Bounds for a Random Canonical Lift Complement
Didac Martinez-Granado, University of California, Davis Title: Volume Bounds for a Random Canonical Lift Complement Given a filling closed geodesic on a hyperbolic surface, one can consider its canonical lift in the projective tangent bundle. Drilling this knot, one obtains a hyperbolic 3-
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Frederic Legoll: Variance reduction approaches for stochastic homogenization
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Probability and Statistics