Foliations | Differential systems | Theorems in differential topology | Theorems in differential geometry
In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an overdetermined system of first-order homogeneous linear partial differential equations. In modern geometric terms, given a family of vector fields, the theorem gives necessary and sufficient integrability conditions for the existence of a foliation by maximal integral manifolds whose tangent bundles are spanned by the given vector fields. The theorem generalizes the existence theorem for ordinary differential equations, which guarantees that a single vector field always gives rise to integral curves; Frobenius gives compatibility conditions under which the integral curves of r vector fields mesh into coordinate grids on r-dimensional integral manifolds. The theorem is foundational in differential topology and calculus on manifolds. (Wikipedia).
C73 Introducing the theorem of Frobenius
The theorem of Frobenius allows us to calculate a solution around a regular singular point.
From playlist Differential Equations
Differential Equations | Frobenius' Method part 2
From Garden of the Gods in Colorado Springs, we present a Theorem regarding Frobenius Series solutions to a certain family of second order homogeneous differential equations. An example is also explored. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Series Solutions for Differential Equations
Differential Equations | Frobenius' Method part 1
From the bridge of the Starship Enterprise, we present a Theorem which will form the basis for a Frobenius solution to a certain family of 2nd order differential equations. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Series Solutions for Differential Equations
Differential Equations | Frobenius' Method: Example 2
We give an example of solving a second order differential equations using Frobenius' method. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Series Solutions for Differential Equations
Differential Equations | Frobenius' Method -- Example 1
From the desert, we present an example of a Frobenius series solution to a second order homogeneous differential equation. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Series Solutions for Differential Equations
Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
The Frenet Serret equations (example) | Differential Geometry 19 | NJ Wildberger
Following from the last lecture on the Frenet Serret equations, we here look in detail at an important illustrative example--that of a helix. The Fundamental theorem of curves is stated--that the curvature and torsion essentially determine a 3D curve up to congruence. We introduce the osc
From playlist Differential Geometry
Here we give a definition of the relative Frobenius. We also give a good notation that helps you forget about the annoying tensor product that nobody can remember.
From playlist Cartier Operator
Lars Hesselholt: Around topological Hochschild homology (Lecture 2)
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Workshop: Hermitian K-theory and trace methods" Introduced by Bökstedt in the late eighties, topological Hochschild homology is a manifestation of the dual visions of Connes and Waldhausen to
From playlist HIM Lectures: Junior Trimester Program "Topology"
String topology coproduct: geometric and algebraic aspects - Manuel Rivera
Princeton/IAS Symplectic Geometry Seminar Topic: String topology coproduct: geometric and algebraic aspects Speaker: Manuel Rivera Affiliation: University of Miami Date: May 11, 2017 For more info, please visit http://video.ias.edu
From playlist Mathematics
Lars Hesselholt: Around topological Hochschild homology (Lecture 8)
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Workshop: Hermitian K-theory and trace methods" Introduced by Bökstedt in the late eighties, topological Hochschild homology is a manifestation of the dual visions of Connes and Waldhausen to
From playlist HIM Lectures: Junior Trimester Program "Topology"
B. Bhatt - Prisms and deformations of de Rham cohomology
Prisms are generalizations of perfectoid rings to a setting where "Frobenius need not be an isomorphism". I will explain the definition and use it to construct a prismatic site for any scheme. The resulting prismatic cohomology often gives a one-parameter deformation of de Rham cohomology.
From playlist Arithmetic and Algebraic Geometry: A conference in honor of Ofer Gabber on the occasion of his 60th birthday
Jacob Lurie: A Riemann-Hilbert Correspondence in p-adic Geometry Part 2
At the start of the 20th century, David Hilbert asked which representations can arise by studying the monodromy of Fuchsian equations. This question was the starting point for a beautiful circle of ideas relating the topology of a complex algebraic variety X to the study of algebraic diffe
From playlist Felix Klein Lectures 2022
Power series solution to differential equations: a tutorial
Free ebook http://tinyurl.com/EngMathYT How to solve differential equations using power series. An example is discussed involving the method of Frobenius where linear differential equation (with variable coefficients) is solved by using a power series. The ideas are seen in university
From playlist A second course in university calculus.
Gromov–Witten Invariants and the Virasoro Conjecture. III by Ezra Getzler
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
Group theory 20: Frobenius groups
This lecture is part of an online mathematics course on group theory. It gives several examples of Frobenius groups (permutation groups where any element fixing two points is the identity).
From playlist Group theory