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, 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
algebraic geometry 15 Projective space
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It introduces projective space and describes the synthetic and analytic approaches to projective geometry
From playlist Algebraic geometry I: Varieties
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
Projective view of conics and quadrics | Differential Geometry 9 | NJ Wildberger
In this video we introduce projective geometry into the study of conics and quadrics. Our point of view follows Mobius and Plucker: the projective plane is considered as the space of one-dimensional subspaces of a three dimensional vector space, or in other words lines through the origin.
From playlist Differential Geometry
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
The circle and projective homogeneous coordinates (cont.) | Universal Hyperbolic Geometry 7b
Universal hyperbolic geometry is based on projective geometry. This video introduces this important subject, which these days is sadly absent from most undergrad/college curriculums. We adopt the 19th century view of a projective space as the space of one-dimensional subspaces of an affine
From playlist Universal Hyperbolic Geometry
The circle and projective homogeneous coordinates | Universal Hyperbolic Geometry 7a | NJ Wildberger
Universal hyperbolic geometry is based on projective geometry. This video introduces this important subject, which these days is sadly absent from most undergrad/college curriculums. We adopt the 19th century view of a projective space as the space of one-dimensional subspaces of an affine
From playlist Universal Hyperbolic Geometry
Algebraic geometry 44: Survey of curves
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives an informal survey of complex curves of small genus.
From playlist Algebraic geometry I: Varieties
Nijenhuis geometry for ECRs: pre-recorded Lecture 1
Pre-recorded Lecture 1: Nijenhuis geometry for ECRs Date: 8 February 2022 Lecture slides: https://mathematical-research-institute.sydney.edu.au/wp-content/uploads/2022/02/Lecture-1_matveev.pdf -------------------------------------------------------------------------------------------------
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems
Andrzej Sitarz: Spectral action for 3+1 geometries
I'll demonstrate a class of models, to illustrate a principle of evolution for 3-dimensional noncommutative geometries, determined exclusively by a spectral action. One particular case is a model, which allows evolution of noncommutativeness (deformation parameter) itself for a specific c
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Robert Bryant, A visit to the Finsler world
Robert Bryant, Duke University, USA A visit to the Finsler world
From playlist Conférence en l'honneur de Jean-Pierre Bourguignon
Jacob Lurie: A Riemann-Hilbert Correspondence in p-adic Geometry Part 1
At the start of the 20th century, David Hilbert asked which representations can arise by studying the monodromy of Fuchsian equations. This question was the starting point for a beautiful circle of ideas relating the topology of a complex algebraic variety X to the study of algebraic diffe
From playlist Felix Klein Lectures 2022
Fields Medal Lecture: Classification of algebraic varieties — Caucher Birkar — ICM2018
Classification of algebraic varieties Caucher Birkar Abstract: The aim of this talk is to describe the classification problem of algebraic varieties in the framework of modern birational geometry. This problem which lies at the heart of algebraic geometry has seen tremendous advances in t
From playlist Special / Prizes Lectures
New Methods in Finsler Geometry - 22 May 2018
http://www.crm.sns.it/event/415 Centro di Ricerca Matematica Ennio De Giorgi The workshop has limited funds to support lodging (and in very exceptional cases, travel) costs of some participants, with priority given to young researchers. When you register, you will have the possibility to
From playlist Centro di Ricerca Matematica Ennio De Giorgi
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
Lagrangians, symplectomorphisms and zeroes of moment maps - Yann Rollin
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Lagrangians, symplectomorphisms and zeroes of moment maps Speaker: Yann Rollin Affiliation: Nantes University Date: April 08, 2022 I will present two constructions of Kähler manifolds, endowed with Hamiltonia
From playlist Mathematics
Dynamics, numerical analysis and some geometry – Christian Lubich – ICM2018
Plenary Lecture 18 Dynamics, numerical analysis and some geometry Christian Lubich Abstract: Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we revi
From playlist Plenary Lectures
A brief history of geometry II: The European epoch | Sociology and Pure Mathematics | N J Wildberger
Let's have a quick overview of some of the developments in the European story of geometry -- at least up to the 19th century. We'll discuss Cartesian geometry, Projective geometry, Descriptive geometry, Algebraic geometry and Differential geometry. This is meant for people from outside m
From playlist Sociology and Pure Mathematics
Projective geometry | Math History | NJ Wildberger
Projective geometry began with the work of Pappus, but was developed primarily by Desargues, with an important contribution by Pascal. Projective geometry is the geometry of the straightedge, and it is the simplest and most fundamental geometry. We describe the important insights of the 19
From playlist MathHistory: A course in the History of Mathematics