Finite fields | Galois theory | Algebraic number theory
In commutative algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with prime characteristic p, an important class which includes finite fields. The endomorphism maps every element to its p-th power. In certain contexts it is an automorphism, but this is not true in general. (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
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
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
Galois theory: Frobenius automorphism
This lecture is part of an online graduate course on Galois theory. We show that the Frobenius automorphism of a finite field an sometimes be lifted to characteristic 0. As an example we use the Frobenius automorphisms of Q[i] to prove that -1 i a square mod an odd prime p if and only if
From playlist Galois theory
The Frobenius Problem - Problem Statement
Describes the Frobenius Problem and goes over some trivial cases
From playlist ℕumber Theory
Geometry of Frobenioids - part 3 - What is a Frobenioid?
We will talk about the construction of Frobenioids in Mochizuki's Geometry of Frobenioids 1. Some nice links: https://plus.google.com/+lievenlebruyn/posts/Y1XVCDLWRP5https://plus.google.com/+lievenlebruyn/posts/Y1XVCDLWRP5 http://mathoverflow.net/questions/195353/what-is-a-frobenioid
From playlist Geometry of Frobenioids
The Frobenius conjecture in dimension two - Tony Yue Yu
Topic: The Frobenius conjecture in dimension two Speaker: Tony Yue Yu Affiliation: IAS Date: March 16, 2017 For more video, visit http://video.ias.edu
From playlist Mathematics
Geometry of Frobenioids - part 2 - (Set) Monoids
This is an introduction to the basic properties of Monoids. This video intended to be a starting place for log-schemes, Mochizuki's IUT or other absolute geometric constructions using monoids.
From playlist Geometry of Frobenioids
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)
Lecture 17: Frobenius lifts and group rings
In this video, we "compute" TC of spherical group rings and more generally cyclotomic spectra with Frobenius lifts. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://
From playlist Topological Cyclic Homology
Stefano Marseglia, Computing isomorphism classes of abelian varieties over finite fields
VaNTAGe Seminar, February 1, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in this talk: Honda: https://doi.org/10.2969/jmsj/02010083 Tate: https://link.springer.com/article/10.1007/BF01404549 Deligne: https://eudml.org/doc/141987 Hofmann, Sircana: https://arxiv.org/ab
From playlist Curves and abelian varieties over finite fields
Steven Galbraith, Isogeny graphs, computational problems, and applications to cryptography
VaNTAGe Seminar, September 20, 2022 License: CC-BY-NC-SA Some of the papers mentioned in this talk: Ducas, Pierrot 2019: https://link.springer.com/article/10.1007/s10623-018- 0573-3 (https://rdcu.be/cVYrC) Kohel 1996: http://iml.univ-mrs.fr/~kohel/pub/thesis.pdf Fouquet, Morain 2002: ht
From playlist New developments in isogeny-based cryptography
Padma Srinivasan, Computing exceptions primes for Galois representations of abelian surfaces
VaNTAGe Seminar on Dec 8, 2020 License CC-BY-NC-SA
From playlist ICERM/AGNTC workshop updates
The Structure of the Group of Rational Points of an Abelian Variety (CTNT Online, June 12-14, 2020)
This video was created for the CTNT 2020 Conference (June 12-14, 2020): https://ctnt-summer.math.uconn.edu/ctnt-conference-2020-online/ (Preprint) The Structure of the Group of Rational Points of an Abelian Variety over a Finite Field: https://arxiv.org/abs/2006.00637 My contact informat
From playlist CTNT 2020 - Conference Videos
Francesc Fité, Sato-Tate groups of abelian varieties of dimension up to 3
VaNTAGe seminar on April 7, 2020 License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
Jeffrey Achter, Equidistribution counts abelian varieties
VaNTAGe Seminar, February 22, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in this talk are listed below. Sutherland: https://arxiv.org/abs/1604.01256 Gekeler: https://academic.oup.com/imrn/article/2003/37/1999/863196 Job Rauch: https://www.universiteitleiden.nl/binar
From playlist Curves and abelian varieties over finite fields
Ben Howard: Supersingular points on som orthogonal and unitary Shimura varieties
To an orthogonal group of signature (n,2), or to a unitary group of any signature, one can attach a Shimura variety. The general problem is to describe the integral models of these Shimura varieties, and their reductions modulo various primes. I will give a conjectural description of the s
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
The Frobenius Problem - Proof of the Formula for the Frobenius Number for Two Numbers
Describes how to derive the general formula for the Frobenius Number of two Numbers. Proves why Frob(m,n) = mn - m - n.
From playlist Proofs
Mathematics in Post-Quantum Cryptography II - Kristin Lauter
2018 Program for Women and Mathematics Topic: Mathematics in Post-Quantum Cryptography II Speaker: Kristin Lauter Affiliation: Microsoft Research Date: May 22, 2018 For more videos, please visit http://video.ias.edu
From playlist My Collaborators