Algebraic curves | Algebraic geometry | Moduli theory
In mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory. Many moduli spaces are constructed using techniques specific to algebraic stacks, such as Artin's representability theorem, which is used to construct the moduli space of pointed algebraic curves and the moduli stack of elliptic curves. Originally, they were introduced by Grothendieck to keep track of automorphisms on moduli spaces, a technique which allows for treating these moduli spaces as if their underlying schemes or algebraic spaces are smooth. But, through many generalizations the notion of algebraic stacks was finally discovered by Michael Artin. (Wikipedia).
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: 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
Algebraic Spaces and Stacks: Ideas
We try to give some motivation for the definitions we give in the subsequent videos.
From playlist Stacks
Algebraic Structures: Groups, Rings, and Fields
This video covers the definitions for some basic algebraic structures, including groups and rings. I give examples of each and discuss how to verify the properties for each type of structure.
From playlist Abstract Algebra
Algebraic Fractions | Algebra | Maths | FuseSchool
Algebraic fractions are simply fractions with algebraic expressions either on the top, bottom or both. We treat them in the same way as we would numerical fractions. In this video we look at how to simplify algebraic fractions, and how to add and subtract them. We can simplify by cance
From playlist MATHS
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
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology
Algebraic Expressions (Basics)
This video is about Algebraic Expressions
From playlist Algebraic Expressions and Properties
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
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
David Rydh. Local structure of algebraic stacks and applications
Abstract: Some natural moduli problems, such as moduli of sheaves and moduli of singular curves, give rise to stacks with infinite stabilizers that are not known to be quotient stacks. The local structure theorem states that many stacks locally look like the quotient of a scheme by the act
From playlist CORONA GS
Some directions in derived geometry - Gabriele Vezzosi
Gabriele Vezzosi March 10, 2015 Workshop on Chow groups, motives and derived categories More videos on http://video.ias.edu
From playlist Mathematics
CTNT 2020 - Stacky curves in characteristic p - Andrew Kobin
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Conference Videos
On the notion of λ-connection - Carlos Simpson
Geometry and Arithmetic: 61st Birthday of Pierre Deligne Carlos Simpson University of Nice October 18, 2005 Pierre Deligne, Professor Emeritus, School of Mathematics. On the occasion of the sixty-first birthday of Pierre Deligne, the School of Mathematics will be hosting a four-day confe
From playlist Pierre Deligne 61st Birthday
Vincent LAFFORGUE - Stacks of Shtukas and spectral decompositions
https://ams-ems-smf2022.inviteo.fr/
From playlist International Meeting 2022 AMS-EMS-SMF
Moduli Stacks of Galois Representations by Mathew Emerton
Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last year arou
From playlist Recent Developments Around P-adic Modular Forms (Online)
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
Lance Gurney: The geometric approach to cohomology Part II
SMRI Seminar Course: 'The geometric approach to cohomology' Part II Lance Gurney (Australian National University) Abstract: The aim of these two talks is to give an overview of the geometric aka stacky approach to various cohomology theories for schemes: de Rham, Hodge, crystalline and p
From playlist SMRI Course: The geometric approach to cohomology
Stack Data Structure - Algorithm
This is an explanation of the dynamic data structure known as a stack. It includes an explanation of how a stack works, along with pseudocode for implementing the push and pop operations with a static array variable.
From playlist Data Structures