Field Definition (expanded) - Abstract Algebra
The field is one of the key objects you will learn about in abstract algebra. Fields generalize the real numbers and complex numbers. They are sets with two operations that come with all the features you could wish for: commutativity, inverses, identities, associativity, and more. They
From playlist Abstract Algebra
Field Theory: Definition/ Axioms
This video is about the basics axioms of fields.
From playlist Basics: Field Theory
Definition of a Field In this video, I define the concept of a field, which is basically any set where you can add, subtract, add, and divide things. Then I show some neat properties that have to be true in fields. Enjoy! What is an Ordered Field: https://youtu.be/6mc5E6x7FMQ Check out
From playlist Real Numbers
Field Theory -- Qbar, the field of algebraic numbers -- Lecture 8
In this video we show that QQbar, the algebraic closure of the rational numbers is countable.
From playlist Field Theory
Field Theory: Fields of Order a Power of a Prime
This video is about finite fields and some of their properties.
From playlist Basics: Field Theory
Abstract Algebra: The definition of a Field
Learn the definition of a Field, one of the central objects in abstract algebra. We give several familiar examples and a more unusual example. ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://www.patreon.com/socratica ► Make a one-time PayPal donation: https://www
From playlist Abstract Algebra
This video is about polynomials with coefficients in a field.
From playlist Basics: Field Theory
Field Examples - Infinite Fields (Abstract Algebra)
Fields are a key structure in Abstract Algebra. Today we give lots of examples of infinite fields, including the rational numbers, real numbers, complex numbers and more. We also show you how to extend fields using polynomial equations and convergent sequences. Be sure to subscribe so y
From playlist Abstract Algebra
Arithmetic statistics over number fields and function fields - Alexei Entin
Alexei Entin Member, School of Mathematics September 23, 2014 More videos on http://video.ias.edu
From playlist Mathematics
Profinite Completions and Representation Rigidity - Ryan Spitler
Arithmetic Groups Topic: Profinite Completions and Representation Rigidity Speaker: Ryan Spitler Affiliation: Rice University Date: February 02, 2022 Taking up the terminology established in the first lecture, in 1970 Grothendieck showed that when two groups (G,H) form a Grothendieck pai
From playlist Mathematics
Chao Li - 2/2 Geometric and Arithmetic Theta Correspondences
Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. I will give an introduction focusing on the example of unitary groups and highlight recent advances in the arithmetic theory (also know
From playlist 2022 Summer School on the Langlands program
Spectra in locally symmetric spaces by Alan Reid
PROGRAM ZARISKI-DENSE SUBGROUPS AND NUMBER-THEORETIC TECHNIQUES IN LIE GROUPS AND GEOMETRY (ONLINE) ORGANIZERS: Gopal Prasad, Andrei Rapinchuk, B. Sury and Aleksy Tralle DATE: 30 July 2020 VENUE: Online Unfortunately, the program was cancelled due to the COVID-19 situation but it will
From playlist Zariski-dense Subgroups and Number-theoretic Techniques in Lie Groups and Geometry (Online)
Robert Kucharczyk: The geometry and arithmetic of triangular modular curves
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: In this talk I will take a closer look at triangle groups acting on the upper half plane. Except for finitely many special cases, which are hig
From playlist HIM Lectures: Trimester Program "Periods in Number Theory, Algebraic Geometry and Physics"
Ian Agol, Lecture 2: Finiteness of Arithmetic Hyperbolic Reflection Groups
24th Workshop in Geometric Topology, Calvin College, June 29, 2007
From playlist Ian Agol: 24th Workshop in Geometric Topology
Salma Kuhlmann: Real closed fields and models of Peano arithmetic
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 SPECIAL 7th European congress of Mathematics Berlin 2016.
Prasad's volume formula and its applications by Mikhail Belolipetsky
PROGRAM ZARISKI-DENSE SUBGROUPS AND NUMBER-THEORETIC TECHNIQUES IN LIE GROUPS AND GEOMETRY (ONLINE) ORGANIZERS: Gopal Prasad, Andrei Rapinchuk, B. Sury and Aleksy Tralle DATE: 30 July 2020 VENUE: Online Unfortunately, the program was cancelled due to the COVID-19 situation but it will
From playlist Zariski-dense Subgroups and Number-theoretic Techniques in Lie Groups and Geometry (Online)
Ordine aritmetico e caos logico: congetture in teoria dei modelli
I numeri interi sono uno degli oggetti matematici dalla struttura più semplice e chiara, ma... lo sono per davvero? Negli occhi di un logico, essi potrebbero al contrario scoprirsi portatori di un caos insostenibile e inverecondo. Simone Ramello (Universität Münster) ci mostrerà come la te
From playlist Mathematics Münster News
A. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part1)
Let X be an algebraic curve of genus g⩾2 embedded in its Jacobian variety J. The Manin-Mumford conjecture (proved by Raynaud) asserts that X contains only finitely many points of finite order. When X is defined over a number field, Bogomolov conjectured a refinement of this statement, name
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
Number theory Full Course [A to Z]
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio
From playlist Number Theory
From PSL2 representation rigidity to profinite rigidity - Alan Reid and Ben McReynolds
Arithmetic Groups Topic: From PSL2 representation rigidity to profinite rigidity Speakers: Alan Reid and Ben McReynolds Affiliations: Rice University; Purdue University Date: February 9, 2022 In the first part of this talk, we take the ideas of the second talk and focus on the case of (a
From playlist Mathematics