Singular point of an algebraic variety

Algebraic geometry 37: Singular points (replacement video))

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It defines singular points and tangents spaces, and shows that the set of nonsingular points of a variety is open and dense. This is a replacement for the original video,

From playlist Algebraic geometry I: Varieties

C72 What to do about the singular point

Now that we can calculate a solution at analytical points, what can we do about singular points. It turns out, not all singular points are created equal. The regular and irregular singular point.

From playlist Differential Equations

algebraic geometry 34 Blowing up a point

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers blowing up a point of affine space, and gives some examples of using this to resolve singularities of plane curves.

From playlist Algebraic geometry I: Varieties

Algebraic geometry 47: Resolution of curve singularities

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It sketches a proof that singularities of plane curves in characteristic 0 can be resolved by repeated blowups, using a method essentially due to Issac Newton.

From playlist Algebraic geometry I: Varieties

Differential Equations | Definition of a regular singular point.

We give the definition of a regular singular point of a differential equation as well as some examples of differential equations with regular singular points. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Differential Equations

algebraic geometry 40 Examples of resolutions

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives some examples of resoutions of singularities, and describes an application of resolution to a problem about analytic continuation of integrals.

From playlist Algebraic geometry I: Varieties

Projective Coordinates for Points and Lines | Algebraic Calculus One | Wild Egg and Anna Tomskova

Dr Anna Tomskova explains a more modern framework for projective geometry where the extra coordinate often associated with infinity is the first coordinate in a projective vector. This gives us a uniform way to associate to affine points and lines projective points and lines, with the adva

From playlist Algebraic Calculus One

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

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

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

Hodge Theory -- From Abel to Deligne - Phillip Griffiths

Phillip Griffiths School of Mathematics, Institute for Advanced Study October 14, 2013 For more videos, visit http://video.ias.edu

From playlist Mathematics

Anthony Henderson: Hilbert Schemes Lecture 4

SMRI Seminar Series: 'Hilbert Schemes' Lecture 4 Kleinian singularities 1 Anthony Henderson (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students interested i

From playlist SMRI Course: Hilbert Schemes

Hodge theory and algebraic cycles - Phillip Griffiths

Geometry and Arithmetic: 61st Birthday of Pierre Deligne Phillip Griffiths Institute for Advanced Study October 18, 2005 Pierre Deligne, Professor Emeritus, School of Mathematics. On the occasion of the sixty-first birthday of Pierre Deligne, the School of Mathematics will be hosting a f

From playlist Pierre Deligne 61st Birthday

Lie Fu: K-theoretical and motivic hyperKähler resolution conjecture

The lecture was held within the framework of the Hausdorff Trimester Program : Workshop "K-theory in algebraic geometry and number theory"

From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"

Kenneth Ascher: What is a moduli space?

Abstract: Moduli spaces are geometric spaces which parametrize equivalence classes of algebraic varieties. I will discuss the moduli space of algebraic curves equivalently Riemann surfaces) of genus g, and use this example to motivate some interesting questions in higher dimensions. Biogr

From playlist What is...? Seminars

Jonathan Pila - Multiplicative relations among singular moduli

December 15, 2014 - Analysis, Spectra, and Number theory: A conference in honor of Peter Sarnak on his 61st birthday. I will report on some joint work with Jacob Tsimerman concerning multiplicative relations among singular moduli. Our results rely on the "Ax-Schanuel'' theorem for the j

From playlist Analysis, Spectra, and Number Theory - A Conference in Honor of Peter Sarnak on His 61st Birthday

algebraic geometry 39 Du Val singularities

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It discusses the Du Val singularites, and sketches how to desingularize the E8 Du Val singularity.

From playlist Algebraic geometry I: Varieties

Resolution of singularities of complex algebraic varieties – D. Abramovich – ICM2018

Algebraic and Complex Geometry Invited Lecture 4.13 Resolution of singularities of complex algebraic varieties and their families Dan Abramovich Abstract: We discuss Hironaka’s theorem on resolution of singularities in charactetistic 0 as well as more recent progress, both on simplifying

From playlist Algebraic & Complex Geometry