Affine differential geometry is a type of differential geometry which studies invariants of volume-preserving affine transformations. The name affine differential geometry follows from Klein's Erlangen program. The basic difference between affine and Riemannian differential geometry is that affine differential geometry studies manifolds equipped with a volume form rather than a metric. (Wikipedia).
algebraic geometry 17 Affine and projective varieties
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the relation between affine and projective varieties, with some examples such as a cubic curve and the twisted cubic.
From playlist Algebraic geometry I: Varieties
Calculus and affine geometry of the magical parabola | Algebraic Calc and dCB curves 3 | Wild Egg
Algebraic Calculus naturally lives in affine geometry, not Euclidean geometry. Affine geometry is the geometry of parallelism, or (almost the same thing) --- the geometry of pure linear algebra. The parabola is characterized projectively in this geometry as the unique conic which is tangen
From playlist Algebraic Calculus One Info
Classical curves | Differential Geometry 1 | NJ Wildberger
The first lecture of a beginner's course on Differential Geometry! Given by Prof N J Wildberger of the School of Mathematics and Statistics at UNSW. Differential geometry is the application of calculus and analytic geometry to the study of curves and surfaces, and has numerous applications
From playlist Differential Geometry
algebraic geometry 5 Affine space and the Zariski topology
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the definition of affine space and its Zariski topology.
From playlist Algebraic geometry I: Varieties
Tangent conics and tangent quadrics | Differential Geometry 5 | NJ Wildberger
In this video we further develop and extend Lagrange's algebraic approach to the differential calculus. We show how to associate to a polynomial function y=p(x) at a point x=r not just a tangent line, but also a tangent conic, a tangent cubic and so on. Only elementary high school manipul
From playlist Differential Geometry
The differential calculus for curves (II) | Differential Geometry 8 | NJ Wildberger
In this video we extend Lagrange's approach to the differential calculus to the case of algebraic curves. This means we can study tangent lines, tangent conics and so on to a general curve of the form p(x,y)=0; this includes the situation y=f(x) as a special case. It also allows us to deal
From playlist Differential Geometry
Novel Algebraic Operations for Affine Geometry | Algebraic Calculus One | Wild Egg
We introduce some novel conventions to help us set up the foundations of affine geometry. We learn about differences of points, sums of points and vectors, affine combinations and vector proportions. And then use these to state a number of important results from affine geometry, including
From playlist Algebraic Calculus One from Wild Egg
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We define the cotangent sheaf of a scheme, and calculate it for the projective line and then for general projective space.
From playlist Algebraic geometry II: Schemes
Introduction to Projective Geometry (Part 2)
The second video in a series about projective geometry. We list the axioms for projective planes, give an examle of a projective plane with finitely many points, and define the real projective plane.
From playlist Introduction to Projective Geometry
Schemes 29: Invertible sheaves over the projective line
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we classify the invertible sheaves over the projective line, and use them to show that several properties of quasiprojective sheaves over affi
From playlist Algebraic geometry II: Schemes
A Gentle Approach to Crystalline Cohomology - Jacob Lurie
Members’ Colloquium Topic: A Gentle Approach to Crystalline Cohomology Speaker: Jacob Lurie Affiliation: Professor, School of Mathematics Date: February 28, 2022 Let X be a smooth affine algebraic variety over the field C of complex numbers (that is, a smooth submanifold of C^n which can
From playlist Mathematics
algebraic geometry 26 Affine algebraic sets and commutative rings
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the relation between morphisms of affine algebraic sets and homomorphisms of commutative rings. As examples it describes some homomorphisms of commutative rings
From playlist Algebraic geometry I: Varieties
Dynamics on character varieties - William Goldman
Character Varieties, Dynamics and Arithmetic Topic: Dynamics on character varieties Speaker: William Goldman Affiliation: University of Maryland; Member, School of Mathematics Date: November 10, 2021 In these two talks, I will describe how the classification of locally homogeneous geomet
From playlist Mathematics
Commutative algebra 37 Blowup algebras
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 survey several different ways of constructing a commutative ring from an increasing or decreasing filtration on a ring. The
From playlist Commutative algebra
Rings 11 Tensor products of modules
This lecture is part of an online course on rings and modules. We define tensor prducts of modules over more general rings, and give some examples: coproducts of commutative rings, tensors in differential geometry, tensor products of group representations, and tensor products of fields.
From playlist Rings and modules
Duality, polarity and projective linear algebra | Differential Geometry 10 | NJ Wildberger
Projective geometry is a fundamental subject in mathematics, which remarkably is little studied by undergraduates these days. But this situation is about to change---there are just too many places where a projective point of view illuminates mathematics. We will see that differential geome
From playlist Differential Geometry
D. Chen - Are affine invariant submanifolds affine
We study the question whether affine invariant submanifolds arising from Teichmueller dynamics are affine varieties in the sense of algebraic geometry.
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications