Field Theory - (optional) Primitive Element Theorem - Lecture 15
For finite extensions L \supset F we show that there exists an element \gamma in L such that F(\gamma) = L. This is called the primitive element theorem.
From playlist Field Theory
Extend a linearly independent set to a basis In this video, I show how to concretely extend any linearly independent subset of a vector space to a basis of that vector space. We know we can do that in theory (using the replacement theorem), but this video shows how to do it in concrete si
From playlist Linear Equations
Field Theory: Let F be a subfield of the field K. We consider K as a vector space over F and define the degree of K over F as the dimension. We give a degree formula for successive extensions, and consider extensions in terms of bases. EDIT: Typo - around 3:15, it should be cube root(2
From playlist Abstract Algebra
In this video, I prove one of the cornerstones of linear algebra: The Linear Extension Theorem, which intuitively says that, in order to define a linear transformation T, you only need to know the values of T on a basis. In other words, if you only know T on a couple of vectors, you can ac
From playlist Linear Transformations
This video is about extensions of fields.
From playlist Basics: Field Theory
Basic/Primitive Extensions and Minimal Polynomials - Field Theory - Lecture 02
A "basic" or "primitive" extension of a field F is a new field F(alpha) where alpha in K an extension of F. We give some basic properties of extensions. Most importantly introduce the concept of minimal polynomials. @MatthewSalomone has some good videos on this already which might be mor
From playlist Field Theory
FIT2.3.3. Algebraic Extensions
Field Theory: We define an algebraic extension of a field F and show that successive algebraic extensions are also algebraic. This gives a useful criterion for checking algberaic elements. We finish with algebraic closures.
From playlist Abstract Algebra
Degrees in Towers - Field Theory - Lecture 05
Let L contain K which contains F where all extensions are finite. In this video we prove [L:F] = [L:K][K:F]. This is a super useful formula.
From playlist Field Theory
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
Non-trivial Hamiltonian fibrations via K-theory quantization - Egor Shelukhin
Egor Shelukhin Member, School of Mathematics October 2, 2015 http://www.math.ias.edu/calendar/event/88094/1443814200/1443817800 We produce examples of non-trivial Hamiltonian fibrations that are not detected by previous methods (the characteristic classes of Reznikov for example), and im
From playlist Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar
FEM@LLNL | Unifying the Analysis of Geometric Decomposition in FEEC
Sponsored by the MFEM project, the FEM@LLNL Seminar Series focuses on finite element research and applications talks of interest to the MFEM community. On March 22, 2022, Tobin Isaac of Georgia Tech presented "Unifying the Analysis of Geometric Decomposition in FEEC." Two operations take
From playlist FEM@LLNL Seminar Series
In this video, I show that two vector spaces are isomorphic if and only if they have the same dimension. This is an important fact in linear algebra. The proof is very cute and uses the linear extension theorem which I talked about in another video. Enjoy! Linear Extension Theorem https:/
From playlist Linear Transformations
Pascal Auscher: On representation for solutions of boundary value problems for elliptic systems (2)
In order to extend the first order approach to BVP with Lp data in the sense of Kenig-Pipher, we need to extend our semigroups to Lp setting. Unfortunately, our semigroups are seldom bounded on all of Lp. They turn out to be bounded on some abstract Hardy spaces associated to a first order
From playlist HIM Lectures: Trimester Program "Harmonic Analysis and Partial Differential Equations"
Arun Debray - Stable diffeomorphism classification of some unorientable 4-manifolds
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Arun Debray, The University of Texas at Austin Title: Stable diffeomorphism classification of some unorientable 4-manifolds Abstract: Kreck's modified surgery theory provides a bordism-theoretic classification of closed, c
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
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
Lê Dũng Tráng - "Equisingularity Problems"
Research lecture at the Worldwide Center of Mathematics
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Charles Fefferman : Whitney problems and real algebraic geometry
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 Analysis and its Applications
The Cayley-Hamilton Theorem is Easy with F[x]-Modules
Invariant factors proof: https://youtu.be/gWIRI43h0ic Characteristic polynomial explanation: https://youtu.be/jCt6mR3QtPk Intro to F[x]-modules: https://youtu.be/H44q_Urmts0 The Cayley-Hamilton theorem says that every matrix is a root of its own characteristic polynomial, det(xI-A). Wit
From playlist Ring & Module Theory
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