Complex surfaces | Algebraic surfaces
In algebraic geometry, the Cayley surface, named after Arthur Cayley, is a cubic nodal surface in 3-dimensional projective space with four conical points. It can be given by the equation when the four singular points are those with three vanishing coordinates. Changing variables gives several other simple equations defining the Cayley surface. As a del Pezzo surface of degree 3, the Cayley surface is given by thelinear system of cubics in the projective plane passing through the 6 verticesof the complete quadrilateral. This contracts the 4 sides of the completequadrilateral to the 4 nodes of the Cayley surface, while blowing up its 6vertices to the lines through two of them. The surface is a section through the Segre cubic. The surface contains nine lines, 11 tritangents and no double-sixes. A number of affine forms of the surface have been presented. Hunt uses by transforming coordinates to and dehomogenizing by setting . A more symmetrical form is (Wikipedia).
C39 A Cauchy Euler equation that is nonhomogeneous
A look at what to do with a Cauchy Euler equation that is non-homogeneous.
From playlist Differential Equations
I continue the look at higher-order, linear, ordinary differential equations. This time, though, they have variable coefficients and of a very special kind.
From playlist Differential Equations
Complex Analysis: Cauchy-Riemann Equations
From playlist Complex Analysis
Complex Analysis 03: The Cauchy-Riemann Equations
Complex differentiable functions, the Cauchy-Riemann equations and an application.
From playlist MATH2069 Complex Analysis
This video defines a cylindrical surface and explains how to graph a cylindrical surface. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
Tropical Geometry - Lecture 8 - Surfaces | 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
How to find the volume of a pentagonal pyramid
👉 Learn how to find the volume and the surface area of a pyramid. A pyramid is a 3-dimensional object having a polygon as its base and triangular surfaces converging at a single point called its apex. A pyramid derives its name from the shape of its base, i.e. a pyramid with a triangular b
From playlist Volume and Surface Area
http://www.mekanizmalar.com This is a flash animation of a hydraulic closed center valve.
From playlist Pneumatic and Hydraulics
This is a recreation of a short clip from a long form video showing six different ways to construct the Sierpinski triangle: https://youtu.be/IZHiBJGcrqI In this short, we shade odd entries of the Halayuda/Pascal triangle to obtain the Sierpinski triangle. Can you explain why this works?
From playlist Fractals
Robert Lazarsfeld: Cayley-Bacharach theorems with excess vanishing
A classical result usually attributed to Cayley and Bacharach asserts that if two plane curves of degrees c and d meet in cd points, then any curve of degree (c + d - 3) passing through all but one of these points must also pass through the remaining one. In the late 1970s, Griffiths and H
From playlist Algebraic and Complex Geometry
C37 Example problem solving a Cauchy Euler equation
Example problem solving a homogeneous Cauchy-Euler equation.
From playlist Differential Equations
P. Salberger - Quantitative aspects of rational points on algebraic varieties (part1)
Let X be a subvariety of Pn defined over a number field and N(B) be the number of rational points of height at most B on X. There are then general conjectures of Manin on the asymptotic behaviour of N(B) when B goes to infinity. These conjectures can be studied using the Hardy-Littlewood m
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
Topological magnon Dirac points in a 3D antiferromagnet by Yuan Li
Program The 2nd Asia Pacific Workshop on Quantum Magnetism ORGANIZERS: Subhro Bhattacharjee, Gang Chen, Zenji Hiroi, Ying-Jer Kao, SungBin Lee, Arnab Sen and Nic Shannon DATE: 29 November 2018 to 07 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Frustrated quantum magne
From playlist The 2nd Asia Pacific Workshop on Quantum Magnetism
Dominique Cerveau - Holomorphic foliations of codimension one, elementary theory (Part 4)
In this introductory course I will present the basic notions, both local and global, using classical examples. I will explain statements in connection with the resolution of singularities with for instance the singular Frobenius Theorem or the Liouvilian integration. I will also present so
From playlist École d’été 2012 - Feuilletages, Courbes pseudoholomorphes, Applications
Lec 20 | MIT Finite Element Procedures for Solids and Structures, Nonlinear Analysis
Lecture 20: Beam, plate, and shell elements II Instructor: Klaus-Jürgen Bathe View the complete course: http://ocw.mit.edu/RES2-002S10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Nonlinear Finite Element Analysis
Moduli of degree 4 K3 surfaces revisited - Radu Laza
Radu Laza Stony Brook University; von Neumann Fellow, School of Mathematics February 3, 2015 For low degree K3 surfaces there are several way of constructing and compactifying the moduli space (via period maps, via GIT, or via KSBA). In the case of degree 2 K3 surface, the relationship be
From playlist Mathematics
Integral points on Markoff-type cubic surfaces - Amit Ghosh
Special Seminar Topic: Integral points on Markoff-type cubic surfaces Speaker: Amit Ghosh Affiliation: Oklahoma State University Date: December 8, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Hülya Argüz - Gromov-Witten Theory of Complete Intersections 1/3
I will describe an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. This uses a monodromy analysis, as well as new degeneration and splitting formulas for nodal Gromov--Witten invariants
From playlist Workshop on Quantum Geometry
Counting planar (genus 0) degree d curves in P^3 by Ritwik Mukherjee
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
C43 Example problem solving a Cauchy Euler equation
Another Cauchy-Euler equation example problem solved.
From playlist Differential Equations