Theorems in differential topology
In differential topology, the Whitney immersion theorem (named after Hassler Whitney) states that for , any smooth -dimensional manifold (required also to be Hausdorff and second-countable) has a one-to-one immersion in Euclidean -space, and a (not necessarily one-to-one) immersion in -space. Similarly, every smooth -dimensional manifold can be immersed in the -dimensional sphere (this removes the constraint). The weak version, for , is due to transversality (general position, dimension counting): two m-dimensional manifolds in intersect generically in a 0-dimensional space. (Wikipedia).
Lagrangian Whitney sphere links - Ivan Smith
Princeton/IAS Symplectic Geometry Seminar Topic: Lagrangian Whitney sphere links Speaker: Ivan Smith Affiliation: University of Cambridge Date: Novmeber 1, 2016 For more video, visit http://video.ias.edu
From playlist Mathematics
Introduction to Homogeneous Differential Equations
Introduction to Homogeneous Differential Equations A full introduction to homogeneous differential equations.
From playlist Differential Equations
Solve a Bernoulli Differential Equation (Part 2)
This video provides an example of how to solve an Bernoulli Differential Equation. The solution is verified graphically. Library: http://mathispower4u.com
From playlist Bernoulli Differential Equations
Totally nonparallel immersions - Michael Harrison
Seminar in Analysis and Geometry Topic: Totally nonparallel immersions Speaker: Michael Harrison Affiliation: Member, School of Mathematics Date: February 08, 2022 An immersion from a smooth n-dimensional manifold M into Rq is called totally nonparallel if, for every pair of distinct poi
From playlist Mathematics
Nonparallel immersions, skew fibrations, and Borsuk-Ulam type results - Michael Harrison
Short Talks by Postdoctoral Members Topic: Nonparallel immersions, skew fibrations, and Borsuk-Ulam type results Speaker: Michael Harrison Affiliation: Member, School of Mathematics Date: September 23, 2021
From playlist Mathematics
Classify a polynomial then determining if it is a polynomial or not
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
Lecture 11: Discrete Curves (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Determining if a equation is a polynomial or not
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
What is the multiplicity of a zero?
👉 Learn about zeros and multiplicity. The zeroes of a polynomial expression are the values of x for which the graph of the function crosses the x-axis. They are the values of the variable for which the polynomial equals 0. The multiplicity of a zero of a polynomial expression is the number
From playlist Zeros and Multiplicity of Polynomials | Learn About
Divergence Theorem. In this video, I give an example of the divergence theorem, also known as the Gauss-Green theorem, which helps us simplify surface integrals tremendously. It's, in my opinion, the most important theorem in multivariable calculus. It is also extremely useful in physics,
From playlist Vector Calculus
Lecture 10: Smooth Curves (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
C07 Homogeneous linear differential equations with constant coefficients
An explanation of the method that will be used to solve for higher-order, linear, homogeneous ODE's with constant coefficients. Using the auxiliary equation and its roots.
From playlist Differential Equations
In preparation for finding the formula for divergence, we start getting an intuition for what points of positive, negative and zero divergence should look like.
From playlist Multivariable calculus
Convolution Theorem: Fourier Transforms
Free ebook https://bookboon.com/en/partial-differential-equations-ebook Statement and proof of the convolution theorem for Fourier transforms. Such ideas are very important in the solution of partial differential equations.
From playlist Partial differential equations
Capturing the Year in an Instant | Podcast | Overheard at National Geographic
We’ll unpack 2021 with Whitney Johnson, National Geographic’s director of visuals and immersive experiences, as she works on the special Year in Pictures issue and shares what makes an unforgettable image. And we’ll talk with photographers who documented the COVID-19 pandemic and the sprea
From playlist Podcast | Overheard at National Geographic
Jose Perea (6/15/22): Vector bundles for data alignment and dimensionality reduction
A vector bundle can be thought of as a family of vector spaces parametrized by a fixed topological space. Vector bundles have rich structure, and arise naturally when trying to solve synchronization problems in data science. I will show in this talk how the classical machinery (e.g., class
From playlist AATRN 2022
[BOURBAKI 2019] Infinité d’hypersurfaces minimales en basses dimensions - Rivière - 15/06/19
Tristan RIVIÈRE Infinité d’hypersurfaces minimales en basses dimensions, d’après Fernando Codá Marques, André Neves et Antoine Song Une conjecture de Shing Tung Yau du début des années 80 pose le problème de l’existence d’une infinité de surfaces minimales (points critiques de la foncti
From playlist BOURBAKI - 2019
Learn how and why multiplicity of a zero make sense
👉 Learn about zeros and multiplicity. The zeroes of a polynomial expression are the values of x for which the graph of the function crosses the x-axis. They are the values of the variable for which the polynomial equals 0. The multiplicity of a zero of a polynomial expression is the number
From playlist Zeros and Multiplicity of Polynomials | Learn About
Ryan Budney, "Filtrations of smooth manifolds from maps to the plane"
The talk is part of the Workshop Topology of Data in Rome (15-16/09/2022) https://www.mat.uniroma2.it/Eventi/2022/Topoldata/topoldata.php The event was organized in partnership with the Romads Center for Data Science https://www.mat.uniroma2.it/~rds/about.php The Workshop was hosted and
From playlist Workshop: Topology of Data in Rome