Galois theory: Algebraic closure
This lecture is part of an online graduate course on Galois theory. We define the algebraic closure of a field as a sort of splitting field of all polynomials, and check that it is algebraically closed. We hen give a topological proof that the field C of complex numbers is algebraically
From playlist Galois theory
Field Theory - Algebraically Closed Fields (part 2) - Lecture 10
In this video we should that algebraically closed fields exist and are unique. We assume that the direct limit construction works. The construction here depends on the axiom of choice.
From playlist Field Theory
FIT2.3.3. Algebraic Extensions
Field Theory: We define an algebraic extension of a field F and show that successive algebraic extensions are also algebraic. This gives a useful criterion for checking algberaic elements. We finish with algebraic closures.
From playlist Abstract Algebra
Field Theory - Algebraically Closed Fields - Lecture 9
In this video we define what an algebraically closed field and assert without proof that they exist. We also explain why if you can find a single root for any polynomial, then you can find them all.
From playlist Field Theory
23 Algebraic system isomorphism
Isomorphic algebraic systems are systems in which there is a mapping from one to the other that is a one-to-one correspondence, with all relations and operations preserved in the correspondence.
From playlist Abstract algebra
All About Closed Sets and Closures of Sets (and Clopen Sets) | Real Analysis
We introduced closed sets and clopen sets. We'll visit two definitions of closed sets. First, a set is closed if it is the complement of some open set, and second, a set is closed if it contains all of its limit points. We see examples of sets both closed and open (called "clopen sets") an
From playlist Real Analysis
Algebraic Calculus One ... and Two! | Algebraic Calculus Info | N J Wildberger
The online course Algebraic Calculus One at openlearning.com has had its first beta run at openlearning.com over the last two years. Overall it has been a very pleasant success. In this video we recount the main innovative aspects of this purely algebraic approach to a classical subject. T
From playlist Algebraic Calculus One Info
Commutative Algebra - Integral Closures - part 03 - Integral Closedness is Local (an Normality)
In this video we show that being integrally closed is a local property.
From playlist Integral Closures
Alex Wright - Minicourse - Lecture 5
Alex Wright Dynamics, geometry, and the moduli space of Riemann surfaces We will discuss the GL(2,R) action on the Hodge bundle over the moduli space of Riemann surfaces. This is a very friendly action, because it can be explained using the usual action of GL(2,R) on polygons in the plane
From playlist Maryland Analysis and Geometry Atelier
Pseudo-finite dimensions, modularity, and generalisations (...) - M. Bays - Workshop 1 - CEB T1 2018
Martin Bays (Münster) / 29.01.2018 Pseudo-finite dimensions, modularity, and generalisations of Elekes–Szab´o. Given a system of polynomial equations in m complex variables with solution set V of dimension d, if we take finite subsets Xi of C each of size N, then the number of solutions
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Invariant theory and optimization by Ankit Garg
Discussion Meeting Workshop on Algebraic Complexity Theory  ORGANIZERS Prahladh Harsha, Ramprasad Saptharishi and Srikanth Srinivasan DATE & TIME 25 March 2019 to 29 March 2019 VENUE Madhava Lecture Hall, ICTS Bangalore Algebraic complexity aims at understanding the computationa
From playlist Workshop on Algebraic Complexity Theory 2019
Yoshinori Namikawa: Symplectic singularities and nilpotent orbits
Abstract: I will characterzize, among conical symplectic varieties, the nilpotent orbit closures of a complex semisimple Lie algebra and their finite coverings. Recording during the meeting "Symplectic Representation Theory" the April 3, 2019 at the Centre International de Rencontres Math
From playlist Algebraic and Complex Geometry
Title: Differential Fields—A Model Theorist's View May 2016 Kolchin Seminar Workshop
From playlist May 2016 Kolchin Seminar Workshop
Nonlinear algebra, Lecture 7: "Toric Varieties", by Mateusz Michalek
This is the seventh lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Algebraic topology: Introduction
This lecture is part of an online course on algebraic topology. This is an introductory lecture, where we give a quick overview of some of the invariants of algebraic topology (homotopy groups, homology groups, K theory, and cobordism). The book "algebraic topology" by Allen Hatcher men
From playlist Algebraic topology
Rahim Moosa: Nonstandard compact complex manifolds with a generic auto-morphism
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 Logic and Foundations