algebraic geometry 14 Dimension
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the dimension of a topological space, algebraic set, or ring.
From playlist Algebraic geometry I: Varieties
Algebraic geometry 50: The degree of a projective variety
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It defines the degree of a projective variety and gives a few examples.
From playlist Algebraic geometry I: Varieties
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 25 Morphisms of varieties
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the definition of a morphism of varieties and compares algebraic varieties with other types of locally ringed spaces.
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
algebraic geometry 22 Toric varieties
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It describes toric varieties as examples of abstract varieties. For more about these see the book "Introduction to toric varieties" by Fulton.
From playlist Algebraic geometry I: Varieties
algebraic geometry 24 Regular functions
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers regular functions on affine and quasiprojective varieties.
From playlist Algebraic geometry I: Varieties
Bernd Sturmfels (8/28/18): Learning algebraic varieties from samples
We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies on aspects of topology and algebraic geometry, such as dimension and defining polynomials. All algorithms are tested on a range of
From playlist AATRN 2018
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
Nonlinear algebra, Lecture 2: "Algebraic Varieties", by Mateusz Michałek
This is the second lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences. In this lecture, Mateusz Michalek describes the main characters in algebraic geometry: algebraic varieties.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Ax-Schanuel for Shimura varieties - J. Pila- Workshop 3 - CEB T1 2018
Jonathan Pila (Oxford) / 27.03.2018 Ax-Schanuel for Shimura varieties In 1971, Ax proved functional versions of Scahanuel’s conjecture for the expoential function, including in the setting of differential fields. This result is known as “Ax-Schanuel”. I will describe joint work with N. M
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Pavel Etingof - "D-modules on Poisson varieties and Poisson traces"
Pavel Etingof delivers a research talk on "D-modules on Poisson varieties and Poisson traces" at the Worldwide Center of Mathematics
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
algebraic geometry 26 Affine algebraic sets and commutative rings
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the relation between morphisms of affine algebraic sets and homomorphisms of commutative rings. As examples it describes some homomorphisms of commutative rings
From playlist Algebraic geometry I: Varieties
Olivier Benoist: Algebraic approximation of submanifolds of real algebraic varieties
CONFERENCE Recording during the thematic meeting : "Real Aspects of Geometry" the November 1, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audi
From playlist Algebraic and Complex Geometry
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
Anthony Henderson: Hilbert Schemes Lecture 1
SMRI Seminar Series: 'Hilbert Schemes' Lecture 1 Introduction 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 in representa
From playlist SMRI Course: Hilbert Schemes
Hsueh-Yung Lin: On the existence of algebraic approximations of compact Kähler manifolds
Abstract: Let X be a compact Kähler manifold. The so-called Kodaira problem asks whether X has arbitrarily small deformations to some projective varieties. While Kodaira proved that such deformations always exist for surfaces. Starting from dimension 4, there are examples constructed by Vo
From playlist Analysis and its Applications
algebraic geometry 17 Affine and projective varieties
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the relation between affine and projective varieties, with some examples such as a cubic curve and the twisted cubic.
From playlist Algebraic geometry I: Varieties
Gonçalo Tabuada - 3/3 Noncommutative Counterparts of Celebrated Conjectures
Some celebrated conjectures of Beilinson, Grothendieck, Kimura, Tate, Voevodsky, Weil, and others, play a key central role in algebraic geometry. Notwithstanding the effort of several generations of mathematicians, the proof of (the majority of) these conjectures remains illusive. The aim
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory