Theorems in geometry | Algebraic surfaces
In mathematics, Castelnuovo's contraction theorem is used in the classification theory of algebraic surfaces to construct the minimal model of a given smooth algebraic surface. More precisely, let be a smooth projective surface over and a (−1)-curve on (which means a smooth rational curve of self-intersection number −1), then there exists a morphism from to another smooth projective surface such that the curve has been contracted to one point , and moreover this morphism is an isomorphism outside (i.e., is isomorphic with ). This contraction morphism is sometimes called a blowdown, which is the inverse operation of blowup. The curve is also called an exceptional curve of the first kind. (Wikipedia).
What is length contraction? Length contraction gives the second piece (along with time dilation) of the puzzle that allows us to reconcile the fact that the speed of light is constant in all reference frames.
From playlist Relativity
What is General Relativity? Lesson 68: The Einstein Tensor
What is General Relativity? Lesson 68: The Einstein Tensor The Einstein tensor defined! Using the Ricci tensor and the curvature scalar we can calculate the curvature scalar of a slice of a manifold using the Einstein tensor. Please consider supporting this channel via Patreon: https:/
From playlist What is General Relativity?
Special Relativity C2 Length Contraction
Relativistic length contraction.
From playlist Physics - Special Relativity
Applications of analysis to fractional differential equations
I show how to apply theorems from analysis to fractional differential equations. The ideas feature the Arzela-Ascoli theorem and Weierstrass' approximation theorem, leading to a new approach for solvability of certain fractional differential equations. When do fractional differential equ
From playlist Mathematical analysis and applications
On the algebraic fundamental group of surfaces of general type by Margarida Lopes
Algebraic Surfaces and Related Topics PROGRAM URL : http://www.icts.res.in/program/AS2015 DESCRIPTION : This is a joint program of ICTS with TIFR, Mumbai and KIAS, Seoul. The theory of surfaces has been the cradle to many powerful ideas in Algebraic Geometry. The problems in this area
From playlist Algebraic Surfaces and Related Topics
Complex surfaces 2: Minimal surfaces
This talk is part of a series about complex surfaces, and explains what minimal surfaces are. A minimial surfaces is one that cannot be obtained by blowing up a nonsingular surfaces at a point. We explain why every surface is birational to a minimal nonsingular projective surface. We disc
From playlist Algebraic geometry: extra topics
Brill-Noether part 2: Castelnuovo's Inequality
From playlist Brill-Noether
Mechanics and curves | Math History | NJ Wildberger
The laws of motion as set out by Newton built upon work of Oresme, Galileo and others on dynamics, and the relations between distance, velocity and acceleration in trajectories. With Newton's laws and the calculus, a whole new arena of practical and theoretical investigations opened up to
From playlist MathHistory: A course in the History of Mathematics
Length contraction: the real explanation
Relativity has many mind-bending consequences, but one of the weirdest is the idea that objects in motion get shorter. Bizarre or not, Fermilab’s Dr. Don Lincoln explains just how it works. You’ll be a believer.
From playlist Relativity
Regis de la Breteche (Paris): Higher moments of primes in arithmetic progressions
Since the work of Barban, Davenport and Halberstam, the variances of primes in arithmetic progressions have been widely studied and continue to be an active topic of research. However, much less is known about higher moments. Hooley established a bound on the third moment in progressions,
From playlist Seminar Series "Arithmetic Applications of Fourier Analysis"
On the algebraic fundamental group of surfaces of general type by Margarida Lopes
Algebraic Surfaces and Related Topics PROGRAM URL : http://www.icts.res.in/program/AS2015 DESCRIPTION : This is a joint program of ICTS with TIFR, Mumbai and KIAS, Seoul. The theory of surfaces has been the cradle to many powerful ideas in Algebraic Geometry. The problems in this area
From playlist Algebraic Surfaces and Related Topics
Algebraic and Convex Geometry of Sums of Squares on Varieties (Lecture 4) by Greg Blekherman
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is the study o
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Special Relativity C3 Length Contraction
Relativistic length contraction.
From playlist Physics - Special Relativity
Graph Theory: 62. Graph Minors and Wagner's Theorem
In this video, we begin with a visualisation of an edge contraction and discuss the fact that an edge contraction may be thought of as resulting in a multigraph or simple graph, depending on the application. We then state the definition a contraction of edge e in a graph G resulting in a
From playlist Graph Theory part-10
Ethereum Smart Contracts Tutorial | Deploying Smart Contracts | Blockchain Training | Edureka
( Blockchain Training : https://www.edureka.co/blockchain-tra... ) This Edureka Ethereum Smart Contracts Tutorial (Ethereum blog: https://goo.gl/9vFwJj ) video will give you a complete understanding on Ethereum and Smart Contracts. This video helps you to learn following topics: 1. Why is
From playlist Blockchain Tutorial Videos | Edureka
T. Richard - Lower bounds on Ricci curvature, with a glimpse on limit spaces (Part 2)
The goal of these lectures is to introduce some fundamental tools in the study of manifolds with a lower bound on Ricci curvature. We will first state and prove the laplacian comparison theorem for manifolds with a lower bound on the Ricci curvature, and derive some important consequences
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
Ethereum Development Tools | Ethereum Development Tutorial | Ethereum Developer Course | Edureka
** Ethereum Developer's Certification course: https://www.edureka.co/ethereum-developer-course ** This Edureka's Ethereum video is intended to provide you with a list of Ethereum Development Tools and what are their benefits. Here is the link to the Blockchain blog series: https://goo.gl
From playlist Blockchain Tutorial Videos | Edureka
T. Richard - Lower bounds on Ricci curvature, with a glimpse on limit spaces (Part 4)
The goal of these lectures is to introduce some fundamental tools in the study of manifolds with a lower bound on Ricci curvature. We will first state and prove the laplacian comparison theorem for manifolds with a lower bound on the Ricci curvature, and derive some important consequences
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie