Duality theories | Projective geometry
In geometry, a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept. There are two approaches to the subject of duality, one through language and the other a more functional approach through special mappings. These are completely equivalent and either treatment has as its starting point the axiomatic version of the geometries under consideration. In the functional approach there is a map between related geometries that is called a duality. Such a map can be constructed in many ways. The concept of plane duality readily extends to space duality and beyond that to duality in any finite-dimensional projective geometry. (Wikipedia).
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
Duality, polarity and projective linear algebra (II) | Differential Geometry 11 | NJ Wildberger
We review the simple algebraic set-up for projective points and projective lines, expressed as row and column 3-vectors. Transformations via projective geometry are introduced, along with an introduction to quadratic forms, associated symmetrix bilinear forms, and associated projective 3x3
From playlist Differential Geometry
Introduction to Projective Geometry (Part 1)
The first video in a series on projective geometry. We discuss the motivation for studying projective planes, and list the axioms of affine planes.
From playlist Introduction to Projective Geometry
Duality: magic in simple geometry #SoME2
Two inaccuracies: 2:33 explains the first property (2:16), not the second one (2:24) Narration at 5:52 should be "intersections of GREEN and orange lines" Time stamps: 0:00 — Intro 0:47 — Polar transform 4:46 — Desargues's Theorem 6:29 — Pappus's Theorem 7:18 — Sylvester-Gallai Theorem 8
From playlist Summer of Math Exposition 2 videos
Duality in Algebraic Geometry by Suresh Nayak
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Duality and perpendicularity | Universal Hyperbolic Geometry 9 | NJ Wildberger
Perpendicularity in universal hyperbolic geometry is defined in terms of duality. One big difference with classical HG is that points can also be perpendicular, not just lines. Once we have perpendicularity, we can define altitudes. We also state the collinear points theorem and concurrent
From playlist Universal Hyperbolic Geometry
Duality in Linear Algebra: Dual Spaces, Dual Maps, and All That
An exploration of duality in linear algebra, including dual spaces, dual maps, and dual bases, with connections to linear and bilinear forms, adjoints in real and complex inner product spaces, covariance and contravariance, and matrix rank. More videos on linear algebra: https://youtube.c
From playlist Summer of Math Exposition Youtube Videos
algebraic geometry 16 Desargues's theorem
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers Desargues's theorem and duality of projective space.
From playlist Algebraic geometry I: Varieties
Helge Ruddat: Global smoothings of toroidal crossing varieties
HYBRID EVENT Recorded during the meeting "Faces of Singularity Theory " the November 23, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovis
From playlist Mathematical Physics
Schemes 48: The canonical sheaf
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 define the canonical sheaf, giev a survey of some applications (Riemann-Roch theorem, Serre duality, canonical embeddings, Kodaira dimensio
From playlist Algebraic geometry II: Schemes
From Cohomology to Derived Functors by Suresh Nayak
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Duality in Higher Categories-I by Pranav Pandit
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Geometric Algebra - Duality and the Cross Product
In this video, we will introduce the concept of duality, involving a multiplication by the pseudoscalar. We will observe the geometric meaning of duality and also see that the cross product and wedge product are dual to one another, which means that the cross product is already contained w
From playlist Geometric Algebra
The Three/Four bridge and Apollonius duality for conics | Six: A course in pure maths 5 | Wild Egg
The Three / Four bridge plays an important role in understanding the remarkable duality discover by Apollonius between points and lines in the plane once a conic is specified. This is a purely projective construction that works for ellipses, and their special case of a circle, for parabola
From playlist Six: An elementary course in Pure Mathematics
Verdier And Grothendieck Duality (Lecture 4) by Suresh Nayak
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
PGA Ep 3 : Revenge of Infinity
Episode 3 of 6 of the SIBGRAPI2021 tutorial on Projective Geometric Algebra All the details in the writeup at https://bivector.net/PGADYN.html All demos and implementation details at https://enki.ws/ganja.js/examples/pga_dyn.html
From playlist PGA Tutorial SIBGRAPI2021
Quantum representations and higher-rank Prym varieties by Martens Johan
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles
Perpendicularity, polarity and duality on a sphere | Universal Hyperbolic Geometry 37
This video discusses perpendicularity on a sphere, associating two poles to every great circle, and one polar line (great circle) to every point. This association is cleaner in elliptic geometry, where there is then a 1-1 correspondence between elliptic points (pairs of antipodal points on
From playlist Universal Hyperbolic Geometry