Schemes 5: Definition of a scheme
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We give some historical background, then give the definition of a scheme and some simple examples, and finish by explaining the origin of the word "spectrum".
From playlist Algebraic geometry II: Schemes
What are the Types of Numbers? Real vs. Imaginary, Rational vs. Irrational
We've mentioned in passing some different ways to classify numbers, like rational, irrational, real, imaginary, integers, fractions, and more. If this is confusing, then take a look at this handy-dandy guide to the taxonomy of numbers! It turns out we can use a hierarchical scheme just lik
From playlist Algebra 1 & 2
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
Category Theory 3.1: Examples of categories, orders, monoids
Examples of categories, orders, monoids.
From playlist Category Theory
Are You Romantic or Classical?
The words 'Romantic' and 'Classical' usefully bring into focus important themes in our personalities. We're all both, but which are you a little more of? If you like our films take a look at our shop (we ship worldwide): http://www.theschooloflife.com/shop/all/ SUBSCRIBE to our channel for
From playlist RELATIONSHIPS
This lecture is part of an online course in algebraic geometry giving an introduction to schemes. It is loosely based on chapter II Hartshorne's book "Algebraic geometry". (For chapter 1 see the playlist "Algebraic geometry".) This introductory lecture gives some motivation for schemes and
From playlist Algebraic geometry II: Schemes
Ring Theory: We define rings and give many examples. Items under consideration include commutativity and multiplicative inverses. Example include modular integers, square matrices, polynomial rings, quaternions, and adjoins of algebraic and transcendental numbers.
From playlist Abstract Algebra
Federico Binda - Triangulated Categories of Log Motives over a Field
In this talk I will sketch the construction and highlight the main properties of a new motivic category for logarithmic schemes, log smooth over a ground field k (without log structure). This construction is based on a new Grothendieck topology (called the “dividing topology”) and on the p
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Algebraic Spaces and Stacks: Ideas
We try to give some motivation for the definitions we give in the subsequent videos.
From playlist Stacks
Fibered Categories, Descent Data and The Definition of a Stack. (This was the first video I made.)
From playlist Stacks
A stacky approach to crystalline (and prismatic) cohomology - Vladimir Drinfeld
Joint IAS/Princeton University Number Theory Seminar Topic: A stacky approach to crystalline (and prismatic) cohomology Speaker: Vladimir Drinfeld Affiliation: The University of Chicago; Visiting Professor, School of Mathematics Date: October 3, 2019 For more video please visit http://vi
From playlist Mathematics
Towards a modular "2 realizations" equivalence - Simon Riche
Geometric and Modular Representation Theory Seminar Topic: Towards a modular "2 realizations" equivalence Speaker: Simon Riche Affiliation: Université Clermont Auvergne; Member, School of Mathematics Date: May 05, 2021 For more video please visit http://video.ias.edu
From playlist Seminar on Geometric and Modular Representation Theory
Frobenius exact symmetric tensor categories - Pavel Etingof
Geometric and Modular Representation Theory Seminar Topic: Frobenius exact symmetric tensor categories Speaker: Pavel Etingof Affiliation: Massachusetts Institute of Technology Date: May 12, 2021 For more video please visit https://www.ias.edu/video
From playlist Seminar on Geometric and Modular Representation Theory
Bertrand Toën - Deformation quantization and derived algebraic geometry
Bertrand TOËN (CNRS - Univ. de Montpellier 2, France)
From playlist Algèbre, Géométrie et Physique : une conférence en l'honneur
Kevin Coulembier: Frobenius exact tensor categories
Abstract: Partly motivated by Grothendieck’s original vision for motives, the question arises of when a tensor category (k-linear symmetric monoidal rigid abelian category) is tannakian, i.e. is the representation category of an affine group scheme, or more generally of a groupoid in schem
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne.. We use the fiber product define last lecture to define group schemes, and give a few non-classical examples of them.
From playlist Algebraic geometry II: Schemes
Étale cohomology lecture 3, August 27, 2020
Sites and sheaves, the étale and fppf site, representable functors
From playlist Étale cohomology and the Weil conjectures