Commutative algebra

Commutative algebra 2 (Rings, ideals, modules)

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. This lecture is a review of rings, ideals, and modules, where we give a few examples of non-commutative rings and rings without

From playlist Commutative algebra

Commutative algebra 1 (Introduction)

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. https://link.springer.com/book/10.1007/978-1-4612-5350-1 This is a short introductory lecture, and gives a few examples of the

From playlist Commutative algebra

Commutative algebra 53: Dimension Introductory survey

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give an introductory survey of many different ways of defining dimension. Reading: Section Exercises:

From playlist Commutative algebra

Groups that commute Lesson 27

You might find that for certain groups, the commutative property hold. In this video we will assume the existence of such a group and prove a few properties that it may have, by way of some example problems.

From playlist Abstract algebra

Commutative algebra 27 (Associated primes)

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We show that every finitely generated module M over a Noetherian ring R can broken up into modules of the form R/p for p prime

From playlist Commutative algebra

5B Commutative Law of Matrix Multiplication-YouTube sharing.mov

A closer look at three examples of the Commutative Law of Matrix Multiplication.

From playlist Linear Algebra

Commutative algebra 46: Limits and colimits of modules

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We define limits and colimits of modules, and give several examples (direct sums and products, kernels, cokernels, inverse lim

From playlist Commutative algebra

Commutative algebra 16 Localization

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we construct the localization R[S^-1] of a ring with respect to a multiplicative subset S, and give some examp

From playlist Commutative algebra

Commutative algebra 28 Geometry of associated primes

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give a geometric interpretation of Ass(M), the set of associated primes of M, by showing that its closure is the support Su

From playlist Commutative algebra

A gentle description of a vertex algebra.

Working from the notions of associative algebras, Lie algebras, and Poisson algebras we build the idea of a vertex algebra. We end with the proper definition as well as an "intuition" for how to think of the parts. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation

From playlist Vertex Operator Algebras

Dan-Virgil Voiculescu: Around the Quasicentral Modulus

Talk by Dan-Virgil Voiculescu in Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/tba-9/ on March 26, 2021.

From playlist Global Noncommutative Geometry Seminar (Americas)

Pre-recorded lecture 9: Homogeneous linear Nijenhuis operators and left-symmetric algebras

MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet

From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)

Noncommutative Geometric Invariant Theory (Lecture 2) by Arvid Siqveland

PROGRAM :SCHOOL ON CLUSTER ALGEBRAS ORGANIZERS :Ashish Gupta and Ashish K Srivastava DATE :08 December 2018 to 22 December 2018 VENUE :Madhava Lecture Hall, ICTS Bangalore In 2000, S. Fomin and A. Zelevinsky introduced Cluster Algebras as abstractions of a combinatoro-algebra

From playlist School on Cluster Algebras 2018

Pre-recorded lecture 16: Frolicher-Nijenhuis bracket and Frolicher-Nijenhuis cohomology

MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet

From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)

Matthew Kennedy: Noncommutative convexity

Talk by Matthew Kennedy in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on May 5, 2021

From playlist Global Noncommutative Geometry Seminar (Europe)

Frédéric Patras - Noncommutative Wick Polynomials

Wick polynomials are at the foundations of QFT (they encode normal orderings) and probability (they encode chaos decompositions). In this lecture, we survey the construction and properties of noncommutative (or free) analogs using shuffle Hopf algebra techniques. Based on joint works wit

From playlist Combinatorics and Arithmetic for Physics: special days

Ben Webster - Representation theory of symplectic singularities

Research lecture at the Worldwide Center of Mathematics

From playlist Center of Math Research: the Worldwide Lecture Seminar Series

Commutative algebra 61: Examples of regular local rings

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give some examples of regular local rings. We first give an example of a regular local ring that is not geometrically regul

From playlist Commutative algebra

The vector spaces for vertex algebras.

We give some examples of the types of vector spaces it is important to be comfortable with in order to study vertex algebras. We look at three main example, a polynomial ring in infinitely many variables, the exterior algebra of infinitely many variables, and the universal enveloping algeb

From playlist Vertex Operator Algebras