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
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
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)
Group theory 4: Lagrange's theorem
This is lecture 4 of an online course on mathematical group theory. It introduces Lagrange's theorem that the order of a subgroup divides the order of a group, and uses it to show that all groups of prime order are cyclic, and to prove Fermat's theorem and Euler's theorem.
From playlist Group theory
Jacob explains the fundamental concepts in group theory of what groups and subgroups are, and highlights a few examples of groups you may already know. Abelian groups are named in honor of Niels Henrik Abel (https://en.wikipedia.org/wiki/Niels_Henrik_Abel), who pioneered the subject of
From playlist Basics: Group Theory
Group theory 2: Cayley's theorem
This is lecture 2 of an online mathematics course on group theory. It describes Cayley's theorem that every abstract group is the group of symmetries of something, and as examples shows the Cayley graphs of the Klein 4-group and the symmetric group on 3 points.
From playlist Group 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
We finally get to Lagrange's theorem for finite groups. If this is the first video you see, rather start at https://www.youtube.com/watch?v=F7OgJi6o9po&t=6s In this video I show you how the set that makes up a group can be partitioned by a subgroup and its cosets. I also take a look at
From playlist Abstract algebra
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
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
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
Introduction to p-adic Hodge theory (Lecture 1) by Denis Benois
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) Eknat
From playlist Perfectoid Spaces 2019
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
CTNT 2022 - An Introduction to Galois Representations (Lecture 3) - by Alvaro Lozano-Robledo
This video is part of a mini-course on "An Introduction to Galois Representations" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - An Introduction to Galois Representations (by Alvaro Lozano-Robledo)
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"
CTNT 2022 - 100 Years of Chebotarev Density (Lecture 2) - by Keith Conrad
This video is part of a mini-course on "100 Years of Chebotarev Density" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - 100 Years of Chebotarev Density (by Keith Conrad)
Chapter 6: Homomorphism and (first) isomorphism theorem | Essence of Group Theory
The isomorphism theorem is a very useful theorem when it comes to proving novel relationships in group theory, as well as proving something is a normal subgroup. But not many people can understand it intuitively and remember it just as a kind of algebraic coincidence. This video is about t
From playlist Essence of Group Theory