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
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
AlgTopReview4: Free abelian groups and non-commutative groups
Free abelian groups play an important role in algebraic topology. These are groups modelled on the additive group of integers Z, and their theory is analogous to the theory of vector spaces. We state the Fundamental Theorem of Finitely Generated Commutative Groups, which says that any such
From playlist Algebraic Topology
What is a Group? | Abstract Algebra
Welcome to group theory! In today's lesson we'll be going over the definition of a group. We'll see the four group axioms in action with some examples, and some non-examples as well which violate the axioms and are thus not groups. In a fundamental way, groups are structures built from s
From playlist Abstract Algebra
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
A Finite Nonempty Subset of G Closed under the Group Operation is a Subgroup Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys A Finite Nonempty Subset of G Closed under the Group Operation is a Subgroup Proof
From playlist Abstract Algebra
Michael Wibmer: Etale difference algebraic groups
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 Algebraic and Complex Geometry
Definition of a group Lesson 24
In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el
From playlist Abstract algebra
AlgTopReview2: Introduction to group theory
This lecture gives a brief overview or introduction to group theory, concentrating on commutative groups (future lectures will talk about the non-commutative case). We generally use additive notation + for the operation in a commutative group, and 0 for the (additive) inverse. The main sta
From playlist Algebraic Topology
Title: Interpretations and Differential Galois Extensions
From playlist Fall 2014
On a Hecke algebra isomorphism of Kazhdan by Radhika Ganapathy
PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund
From playlist Group Algebras, Representations And Computation
Lie groups: Lie groups and Lie algebras
This lecture is part of an online graduate course on Lie groups. We discuss the relation between Lie groups and Lie algebras, and give several examples showing how they behave differently. Lie algebras turn out to correspond more closely to the simply connected Lie groups. We then explain
From playlist Lie groups
Daniel Hoffmann, University of Warsaw
May 14, Daniel Hoffmann, University of Warsaw Fields with derivations and action of finite group
From playlist Spring 2021 Online Kolchin Seminar in Differential Algebra
Finiteness theorems for Kolchin's constrained cohomology
By Anand Pillay, University of Notre Dame Finiteness theorems for Kolchin's constrained cohomology Kolchin Seminar, CUNY Graduate Center, October 4, 2019
From playlist Fall 2019 Kolchin Seminar in Differential Algebra
Algorithmic Construction of Representations of Finite Solvable Groups by Ravi S Kulkarni
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
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)
Strongly minimal groups in o-minimal structures - K. Peterzil - Workshop 3 - CEB T1 2018
Kobi Peterzil (Haifa) / 27.03.2018 Strongly minimal groups in o-minimal structures Let G be a definable two-dimensional group in an o-minimal structure M and let D be a strongly minimal expansion of G, whose atomic relations are definable in M. We prove that if D is not locally modular t
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Support Varieties for Modular Representations - Eric M. Friedlander
Members’ Seminar Topic: Support Varieties for Modular Representations Speaker: Eric M. Friedlander Affiliation: University of Southern California; Member, School of Mathematics Date: November 30, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
AlgTopReview3: More on commutative groups---isomorphisms, homomorphisms, cosets and quotient groups
We present more information on commutative groups and the fundamental structure theorem that every such group is isomorphic to a direct sum of cyclic groups Z_n. We discuss the notions of isomorphism, homomorphism, cosets of a subgroup, and the quotient of a group by a subgroup. *********
From playlist Algebraic Topology