Monoidal categories | Algebras | Module theory
In mathematics, especially in the fields of representation theory and module theory, a Frobenius algebra is a finite-dimensional unital associative algebra with a special kind of bilinear form which gives the algebras particularly nice duality theories. Frobenius algebras began to be studied in the 1930s by Richard Brauer and Cecil Nesbitt and were named after Georg Frobenius. Tadashi Nakayama discovered the beginnings of a rich duality theory,. Jean Dieudonné used this to characterize Frobenius algebras. Frobenius algebras were generalized to quasi-Frobenius rings, those Noetherian rings whose right regular representation is injective. In recent times, interest has been renewed in Frobenius algebras due to connections to topological quantum field theory. (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
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
The Frobenius Problem - Method for Finding the Frobenius Number of Two Numbers
Goes over how to find the Frobenius Number of two Numbers.
From playlist ℕumber Theory
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
Representation theory: Frobenius groups
We recall the definition of a Frobenius group as a transitive permutation group such that any element fixing two points is the identity. Then we prove Frobenius's theorem that the identity together with the elements fixing no points is a normal subgroup. The proof uses induced representati
From playlist Representation theory
Mike Boyle - Nonnegative matrices : Perron Frobenius theory and related algebra (Part 1)
Lecture I. I’ll give a complete elementary presentation of the essential features of the Perron Frobenius theory of nonnegative matrices for the central case of primitive matrices (the "Perron" part). (The "Frobenius" part, for irreducible matrices, and finally the case for general nonnega
From playlist École d’été 2013 - Théorie des nombres et dynamique
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
The Frobenius Norm for Matrices
This video describes the Frobenius norm for matrices as related to the singular value decomposition (SVD). These lectures follow Chapter 1 from: "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz Amazon: https://www.amazon.com/Da
From playlist Data-Driven Science and Engineering
Noémie Combe - How many Frobenius manifolds are there?
In this talk an overview of my recent results is presented. In a joint work with Yu. Manin (2020) we discovered that an object central to information geometry: statistical manifolds (related to exponential families) have an F-manifold structure. This algebraic structure is a more general v
From playlist Research Spotlight
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
The Tamagawa Number Formula via Chiral Homology - Dennis Gaitsgory
Dennis Gaitsgory Harvard University March 1, 2012 Let X a curve over F_q and G a semi-simple simply-connected group. The initial observation is that the conjecture of Weil's which says that the volume of the adelic quotient of G with respect to the Tamagawa measure equals 1, is equivalent
From playlist Mathematics
David Zywina, Computing Sato-Tate and monodromy groups.
VaNTAGe seminar on May 5, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
Algebraic groups in positive characteristic - Srimathy Srinivasan
Short talks by postdoctoral members Topic: Algebraic groups in positive characteristic Speaker: Srimathy Srinivasan Affiliation: Member, School of Mathematics Date: October 4, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Richard Taylor "Reciprocity Laws" [2012]
Slides for this talk: https://drive.google.com/file/d/1cIDu5G8CTaEctU5qAKTYlEOIHztL1uzB/view?usp=sharing Richard Taylor "Reciprocity Laws" Abstract: Reciprocity laws provide a rule to count the number of solutions to a fixed polynomial equation, or system of polynomial equations, modu
From playlist Number Theory
Perfect points on abelian varieties in positive characteristic. - Rössler - Workshop 2 - CEB T2 2019
Damian Rössler (University of Oxford) / 24.06.2019 Perfect points on abelian varieties in positive characteristic. Let K be the function field over a smooth curve over a perfect field of characteristic p 0. Let Kperf be the maximal purely inseparable extension of K. Let A be an abelian
From playlist 2019 - T2 - Reinventing rational points
Isocrystals associated to arithmetic jet spaces by Arnab Saha
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
Mike Boyle - Nonnegative matrices : Perron Frobenius theory and related algebra (Part 4)
Lecture I. I’ll give a complete elementary presentation of the essential features of the Perron Frobenius theory of nonnegative matrices for the central case of primitive matrices (the "Perron" part). (The "Frobenius" part, for irreducible matrices, and finally the case for general nonnega
From playlist École d’été 2013 - Théorie des nombres et dynamique
Canonical lifts in families by James Borger
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019