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
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
Hyperbolic Geometry is Projective Relativistic Geometry (full lecture)
This is the full lecture of a seminar on a new way of thinking about Hyperbolic Geometry, basically viewing it as relativistic geometry projectivized, that I gave a few years ago at UNSW. We discuss three dimensional relativistic space and its quadratic/bilinear form, particularly the uppe
From playlist MathSeminars
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
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
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
What is a Vector Space? (Abstract Algebra)
Vector spaces are one of the fundamental objects you study in abstract algebra. They are a significant generalization of the 2- and 3-dimensional vectors you study in science. In this lesson we talk about the definition of a vector space and give a few surprising examples. Be sure to su
From playlist Abstract Algebra
Isometry groups of the projective line (I) | Rational Geometry Math Foundations 138 | NJ Wildberger
The projective line can be given a Euclidean structure, just as the affine line can, but it is a bit more complicated. The algebraic structure of this projective line supports some symmetries. Symmetry in mathematics is often most efficiently encoded with the idea of a group--a technical t
From playlist Math Foundations
The projective Quadruple quad formula | Rational Geometry Math Foundations 148 | NJ Wildberger
In this video we introduce the projective version of the Quadruple quad formula, which not only controls the relationship between four projective points, but has a surprising connection with the geometry of the cyclic quadrilateral. The projective quadruple quad function is called R(a,b,
From playlist Math Foundations
Ruud Pellikaan: The coset leader weight enumerator of the code of the twisted cubic
In general the computation of the weight enumerator of a code is hard and even harder so for the coset leader weight enumerator. Generalized Reed Solomon codes are MDS, so their weight enumerators are known and its formulas depend only on the length and the dimension of the code. The coset
From playlist Combinatorics
Sudhir Ghorpade : Projective Reed Muller codes revisited
CONFERENCE Recording during the thematic meeting : « ALgebraic and combinatorial methods for COding and CRYPTography» the February 23, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given b
From playlist Combinatorics
Alexandru Dimca: Betti numbers of hypersurfaces and defects of linear systems I
Abstract: Our approach is a generalization of Griffiths' results expressing the cohomology ofa smooth hypersurface V: f=0 in a projective space P^n in terms of some graded pieces of the Jacobian algebra of f. We will start by recalling these classical results. Then we explain that when
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Kieran Child - Computation of weight 1 modular forms
A major achievement of modern number theory is the proof of a bijection between odd, irreducible, 2-dimensional Artin representations and holomorphic weight 1 Hecke eigenforms. Despite this result, concrete examples have proven difficult to produce owing to weight 1 being non-cohomological
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Projective structures on Riemann surfaces and their monodromy by Subhojoy Gupta
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
Miroslav Englis: Analytic continuation of Toeplitz operators
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 Analysis and its Applications
NIPS 2011 Sparse Representation & Low-rank Approximation Workshop: Dictionary-Dependent Penalties...
Sparse Representation and Low-rank Approximation Workshop at NIPS 2011 Invited Talk: Dictionary-Dependent Penalties for Sparse Estimation and Rank Minimization by David Wipf, University of California at San Diego Abstract: In the majority of recent work on sparse estimation algorit
From playlist NIPS 2011 Sparse Representation & Low-rank Approx Workshop
Jens Eberhardt: Motivic Springer Theory
27 September 2021 Abstract: Algebras and their representations can often be constructed geometrically in terms of convolution of cycles. For example, the Springer correspondence describes how irreducible representations of a Weyl group can be realised in terms of a convolution action on
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
Robert Scheichl: Generalised finite elements: domain decomposition, optimal local approximation...
I will present an efficient implementation of the highly robust and scalable GenEO preconditioner in the high-performance PDE framework DUNE. The GenEO coarse space is constructed by combining low energy solutions of local generalised eigenproblems using a partition of unity. In this talk,
From playlist Numerical Analysis and Scientific Computing
Quiver moduli and applications, Markus Reineke (Bochum), Lecture 3
Quiver moduli spaces are algebraic varieties encoding the continuous parameters of linear algebra type classification problems. In recent years their topological and geometric properties have been explored, and applications to, among others, Donaldson-Thomas and Gromov-Witten theory have
From playlist Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum)
The formal definition of a vector space.
From playlist Linear Algebra Done Right