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)
Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem
In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Irreducibility and the Schoenemann-Eisenstein criterion | Famous Math Probs 20b | N J Wildberger
In the context of defining and computing the cyclotomic polynumbers (or polynomials), we consider irreducibility. Gauss's lemma connects irreducibility over the integers to irreducibility over the rational numbers. Then we describe T. Schoenemann's irreducibility criterion, which uses some
From playlist Famous Math Problems
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
Rufus Willett: Decomposable C*-algebras and the UCT
Talk by Rufus Willett in in Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/tba-25/ on March 11, 2022.
From playlist Global Noncommutative Geometry Seminar (Americas)
Gilles Pisier: The lifting property for C*-algebras
Talk by Gilles Pisier in Global Noncommutative Geometry Seminar (Americas) on January 14, 2022 in https://globalncgseminar.org/talks/the-lifting-property-for-c-algebras/
From playlist Global Noncommutative Geometry Seminar (Americas)
Ralf Meyer: On the classification of group actions on C*-algebras up to equivariant KK-equivalence
Talk by Ralf Meyer in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on November 10, 2020.
From playlist Global Noncommutative Geometry Seminar (Europe)
Applying reimann sum for the midpoint rule and 3 partitions
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
Connes Embedding Problem, Kirchberg's Conjecture and Tsirelson's Problem - Thomas Vidick
Marston Morse Lectures Topic: Connes Embedding Problem, Kirchberg's Conjecture and Tsirelson's Problem Speaker: Thomas Vidick Affiliation: California Institute of Technology Date: March 27, 2023 The three problems referred to in the title originate in the theory of von Neumann algebras,
From playlist Mathematics
Christopher Schafhauser: On the classification of nuclear simple C*-algebras, Lecture 3
Mini course of the conference YMC*A, August 2021, University of Münster. Abstract: A conjecture of George Elliott dating back to the early 1990’s asks if separable, simple, nuclear C*-algebras are determined up to isomorphism by their K-theoretic and tracial data. Restricting to purely i
From playlist YMC*A 2021
Kristin Courtney: Generalized inductive limits with asymptotically order zero maps
Talk by Kristin Courtney in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on March 2, 2021
From playlist Talks of Mathematics Münster's reseachers
Ralf Meyer: A new method to classify C*-algebras up to KK-equivalence
Using a homological invariant together with an obstruction class in a certain Ext?-group, we may classify objects in triangulated categories that have projective resolutions of length two. This invariant gives strong classification results for actions of the circle group on C*-algebras, C*
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Christopher Schafhauser: "Non-stable extension theory and the classification of C∗-algebras"
Actions of Tensor Categories on C*-algebras 2021 "Non-stable extension theory and the classification of C∗-algebras" Christopher Schafhauser - University of Nebraska-Lincoln Abstract: Over the last decade, much of the progress in the classification and regularity theory of simple, nuclea
From playlist Actions of Tensor Categories on C*-algebras 2021
Euler's Formula for the Quaternions
In this video, we will derive Euler's formula using a quaternion power, instead of a complex power, which will allow us to calculate quaternion exponentials such as e^(i+j+k). If you like quaternions, this is a pretty neat formula and a simple generalization of Euler's formula for complex
From playlist Math
Maxim Kazarian - 1/3 Mathematical Physics of Hurwitz numbers
Hurwitz numbers enumerate ramified coverings of a sphere. Equivalently, they can be expressed in terms of combinatorics of the symmetric group; they enumerate factorizations of permutations as products of transpositions. It turns out that these numbers obey a huge num
From playlist Physique mathématique des nombres de Hurwitz pour débutants
Jean-Marie de Koninck: On the proximity of additive and multiplicative functions
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 Number Theory
Christopher Schafhauser: On the classification of nuclear simple C*-algebras, Lecture 2
Mini course of the conference YMC*A, August 2021, University of Münster. Abstract: A conjecture of George Elliott dating back to the early 1990’s asks if separable, simple, nuclear C*-algebras are determined up to isomorphism by their K-theoretic and tracial data. Restricting to purely i
From playlist YMC*A 2021
Weil conjectures 1 Introduction
This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie
From playlist Algebraic geometry: extra topics
Introduction to additive combinatorics lecture 5.8 --- Freiman homomorphisms and isomorphisms.
The notion of a Freiman homomorphism and the closely related notion of a Freiman isomorphism are fundamental concepts in additive combinatorics. Here I explain what they are and prove a lemma that states that a subset A of F_p^N such that kA - kA is not too large is "k-isomorphic" to a sub
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Kant's Dove & Wittgenstein's Ice Walker
A clip of James Conant comparing and discussing a metaphor from Kant and the later Wittgenstein. It is from the 5th Wittgenstein Summer School in Kirchberg am Wechsel in Lower Austria, 2013. More Short/Shorter Clips: https://www.youtube.com/playlist?list=PLhP9EhPApKE8v8UVlc7JuuNHwvhkaOvzc
From playlist Wittgenstein