algebraic geometry 15 Projective space
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It introduces projective space and describes the synthetic and analytic approaches to projective geometry
From playlist Algebraic geometry I: Varieties
algebraic geometry 29 Automorphisms of space
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It describes the automorphisms of affine and projective space, and gives a brief discussion of the Jacobian conjecture.
From playlist Algebraic geometry I: Varieties
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology
algebraic geometry 14 Dimension
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the dimension of a topological space, algebraic set, or ring.
From playlist Algebraic geometry I: Varieties
AlgTopReview: An informal introduction to abstract algebra
This is a review lecture on some aspects of abstract algebra useful for algebraic topology. It provides some background on fields, rings and vector spaces for those of you who have not studied these objects before, and perhaps gives an overview for those of you who have. Our treatment is
From playlist Algebraic Topology
Algebraic Spaces and Stacks: Representabilty
We define what it means for a functor to be representable. We define what it means for a category to be representable.
From playlist Stacks
Algebraic Spaces and Stacks: Ideas
We try to give some motivation for the definitions we give in the subsequent videos.
From playlist Stacks
What is a Vector Space? (Abstract Algebra)
Vector spaces are one of the fundamental objects you study in abstract algebra. They are a significant generalization of the 2- and 3-dimensional vectors you study in science. In this lesson we talk about the definition of a vector space and give a few surprising examples. Be sure to su
From playlist Abstract Algebra
Algebraic Spaces and Stacks: Definitions
We give the definition of algebraic stacks and spaces! Woot! I think algebraic spaces don't get enough love or stacks get too much love. I'm not sure which one... Algebraic Spaces: http://stacks.math.columbia.edu/tag/025X Algebraic Stacks: http://stacks.math.columbia.edu/tag/026N
From playlist Stacks
Higher Algebra 10: E_n-Algebras
In this video we introduce E_n-Algebras in arbitrary symmetric monoidal infinity-categories. These interpolate between associated algebras (= E_1) and commutative algebras (= E_infinity). We also establish some categorical properties and investigate the case of the symmetric monoidal infin
From playlist Higher Algebra
A Swift Introduction to Spacetime Algebra
This video is a fast-paced introduction to Spacetime Algebra (STA), which is the geometric algebra of Minkowski space. In it, we figure out what the problems are with the way introductory textbooks usually describe special relativity and how we can solve those problems by using spacetime
From playlist Miscellaneous Math
QED Prerequisites Geometric Algebra: Introduction and Motivation
This lesson is the beginning of a significant diversion from QED prerequisites. No student needs to understand Geometric Algebra in order to begin the study of QED. However, since we have pushed the formal structure of Maxwell's Equations as far as I know how to go, I think it makes sense
From playlist QED- Prerequisite Topics
[BOURBAKI 2017] 14/01/2017 - 3/4 - Maxim KONTSEVICH
Derived Grothendieck-Teichmüller group and graph complexes, after T. Willwacher Graph complex is spanned by equivalence classes of finite connected graphs with the dual differential given by the sum of all contractions of edges, with appropriate signs. This complex forms a differential g
From playlist BOURBAKI - 2017
Francesca Arici: SU(2)-symmetries and exact sequences of C*-algebras through subproduct systems
Talk by Francesca Arici in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on November 17, 2020.
From playlist Global Noncommutative Geometry Seminar (Europe)
Even spaces and motivic resolutions - Michael Hopkins
Vladimir Voevodsky Memorial Conference Topic: Even spaces and motivic resolutions Speaker: Michael Hopkins Affiliation: Harvard University Date: September 13, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
QED Prerequisites Geometric Algebra: Spacetime.
In this lesson we continue our reading of an excellent paper on Geometric Algebra and spacetime algebra. The paper can be found here: https://arxiv.org/abs/1411.5002 We will cover section 3.1 and begin section 3.2. This material includes our first expansion of the vector space of spacet
From playlist QED- Prerequisite Topics
The Heisenberg Algebra in Symplectic Algebraic Geometry - Anthony Licata
Anthony Licata Institute for Advanced Study; Member, School of Mathematics April 2, 2012 Part of geometric representation theory involves constructing representations of algebras on the cohomology of algebraic varieties. A great example of such a construction is the work of Nakajima and Gr
From playlist Mathematics
Simon Brain: The Gysin Sequence for Quantum Lens Spaces
This is a joint with Francesca Arici and Giovanni Landi. We construct an analogue of the Gysin sequence for circle bundles, now for q-deformed lens spaces in the sense of Vaksman-Soibelman. Our proof that the sequence is exact relies heavily on the non commutative APS index theory of Care
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
What is a Vector Space? Definition of a Vector space.
From playlist Linear Algebra
Gilles de Castro: C*-algebras and Leavitt path algebras for labelled graphs
Talk by Gilles de Castro at Global Noncommutative Geometry Seminar (Americas) on November 19, 2021. https://globalncgseminar.org/talks/tba-16/
From playlist Global Noncommutative Geometry Seminar (Americas)