Theorems in differential topology
In mathematics, particularly in differential topology, there are two Whitney embedding theorems, named after Hassler Whitney: * The strong Whitney embedding theorem states that any smooth real m-dimensional manifold (required also to be Hausdorff and second-countable) can be smoothly embedded in the real 2m-space (R2m), if m > 0. This is the best linear bound on the smallest-dimensional Euclidean space that all m-dimensional manifolds embed in, as the real projective spaces of dimension m cannot be embedded into real (2m β 1)-space if m is a power of two (as can be seen from a characteristic class argument, also due to Whitney). * The weak Whitney embedding theorem states that any continuous function from an n-dimensional manifold to an m-dimensional manifold may be approximated by a smooth embedding provided m > 2n. Whitney similarly proved that such a map could be approximated by an immersion provided m > 2n β 1. This last result is sometimes called the Whitney immersion theorem. (Wikipedia).
How To Multiply Using Foil - Math Tutorial
π Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Multiplying the Difference of Two Squares - Math Tutorial
π Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
How do we multiply polynomials
π Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Easiest Way To Multiply Two Binomials Using Foil - Math Tutorial
π Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Steven Kleiman - "Equisingularity of germs of isolated singularities"
Steven Kleiman delivers a research lecture at the Worldwide Center of Mathematics.
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Resolution in characteristic 0 using weighted blowing up. - Abramovich - Workshop 2 - CEB T2 2019
Dan Abramovich (Brown University) / 28.06.2019 Resolution in characteristic 0 using weighted blowing up. Given a variety, one wants to blow up the worst singular locus, show that it gets better, and iterate until the singularities are resolved. Examples such as the whitney umbrella show
From playlist 2019 - T2 - Reinventing rational points
Multiplying Using the Difference of Two Squares - Math Tutorial
π Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
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
π Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
How to Multiply Polynomials Using the Foil Face - Math Tutorial
π Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Richard Thomas - Vafa-Witten Invariants of Projective Surfaces 4/5
This course has 4 sections split over 5 lectures. The first section will be the longest, and hopefully useful for the other courses. 1. Sheaves, moduli and virtual cycles 2. Vafa-Witten invariants: stable and semistable cases 3. Techniques for calculation --- virtual degeneracy loci, c
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Hannah Schwartz - The presence of 2-torsion
June 21, 2018 - This talk was part of the 2018 RTG mini-conference Low-dimensional topology and its interactions with symplectic geometry Two knots in S^3 are ambiently isotopic if and only if there is an orientation preserving automorphism of S^3 carrying one knot to the other (this foll
From playlist 2018 RTG mini-conference on low-dimensional topology and its interactions with symplectic geometry I
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
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
Multiplying Two Binomials - Math Tutorial
π Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Multiplying Two Binomials - Math Tutorial
π Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
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
Multiplying Polynomials - Math Tutorial
π Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
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