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
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
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
CurvesSurfaces1: Affine and Projective Geometry, and the Problem of Lines
N J Wildberger from UNSW introduces a new series on Curves and Surfaces, aiming for a concrete and more geometrical approach to Algebraic Geometry. This introductory lecture introduces basic notation and terminology for affine and projective points, and associated vector spaces, using proj
From playlist MathSeminars
Geometric and algebraic aspects of space curves | Differential Geometry 20 | NJ Wildberger
A space curve has associated to it various interesting lines and planes at each point on it. The tangent vector determines a line, normal to that is the normal plane, while the span of adjacent normals (or equivalently the velocity and acceleration) is the osculating plane. In this lectur
From playlist Differential Geometry
Summary of Curve Sketching Rational Exponent Odd Function Calculus 1 AB
I work through finding the Domain, x-intercept, y-intercept, symmetry, horizontal asymptote, slant asymptote, vertical asymptote and holes, first derivative, intervals of increasing and decreasing, relative maximums and minimums, second derivative, intervals of concave up and down, and fin
From playlist Calculus
11_6_1 Contours and Tangents to Contours Part 1
A contour is simply the intersection of the curve of a function and a plane or hyperplane at a specific level. The gradient of the original function is a vector perpendicular to the tangent of the contour at a point on the contour.
From playlist Advanced Calculus / Multivariable Calculus
This talk is about some properties of plane curves used in the Riemann-Roch theorem. We first show that every nonsingular curve is isomorphic to a resolution of a plane curve with no singularities worse than ordinary double points (nodes). We then calculate the genus of plane curves with o
From playlist Algebraic geometry: extra topics
Curvature for the general parabola | Differential Geometry 13 | NJ Wildberger
We now extend the discussion of curvature to a general parabola, not necessarily one of the form y=x^2. This involves first of all understanding that a parabola is defined projectively as a conic which is tangent to the line at infinity. We find the general projective 3x3 matrix for suc
From playlist Differential Geometry
Adolfo Guillot: Complete holomorphic vector fields and their singular points - lecture 3
CIRM VIRTUAL EVENT Recorded during the research school "Geometry and Dynamics of Foliations " the May 11, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on C
From playlist Virtual Conference
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
David Nadler: Betti Langlands in genus one
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Quantum Finite Elements: Lattice Field Theory on Curved Manifolds by Richard Brower
PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II
From playlist NUMSTRING 2022
Quadrance, perpendicularity and pedal curves | Algebraic Calculus One | Wild Egg
We want to introduce metrical structure into our affine setting, allowing us to access Euclidean geometry and physical applications. To do this logically and carefully, with precise definitions, we want to take the view point of Rational Trigonometry: with quadrance and perpendicularity pl
From playlist Algebraic Calculus One from Wild Egg
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
Rod Gover - Geometric Compactification, Cartan holonomy, and asymptotics
Conformal compactification has long been recognised as an effective geometric framework for relating conformal geometry, and associated field theories « at infinity », to the asymptotic phenomena of an interior (pseudo‐)‐Riemannian geometry of one higher dimension. It provides an effective
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale
Tropical Geometry - Lecture 3 - Fields and Varieties | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
algebraic geometry 31 Rational maps
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the definition of rational functions and rational maps, and gives an example of a cubic curve that is not birational to the affine line.
From playlist Algebraic geometry I: Varieties