This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In it we explain why the obvious definition of an epimorphism of sheaves is wrong, and construct the etale space of a presheaf as preparation for giving the c
From playlist Algebraic geometry II: Schemes
Schemes 42: Very ample sheaves
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We define ample and very ample invertible sheaves for projective varieties, and gives some examples for complex elliptic curves. We also show that some sect
From playlist Algebraic geometry II: Schemes
Schemes 3: exactness and sheaves
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In it we discuss exactness of morphisms of sheaves over a topological space.
From playlist Algebraic geometry II: Schemes
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. Given a continuous map between topological spaces there are two natural ways to transfer sheaves from one space to another. We summarize the main properties of
From playlist Algebraic geometry II: Schemes
Schemes 29: Invertible sheaves over the projective line
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 classify the invertible sheaves over the projective line, and use them to show that several properties of quasiprojective sheaves over affi
From playlist Algebraic geometry II: Schemes
Who Gives a Sheaf? Part 1: A First Example
We take a first look at (pre-)sheaves, as being inspired from first year calculus.
From playlist Who Gives a Sheaf?
Algebraic Spaces and Stacks: Definitions
We give the definition of algebraic stacks and spaces! Woot! I think algebraic spaces don't get enough love or stacks get too much love. I'm not sure which one... Algebraic Spaces: http://stacks.math.columbia.edu/tag/025X Algebraic Stacks: http://stacks.math.columbia.edu/tag/026N
From playlist Stacks
Algebraic Spaces and Stacks: Representabilty
We define what it means for a functor to be representable. We define what it means for a category to be representable.
From playlist Stacks
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 16
SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro
From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence
Dennis Gaitsgory - Tamagawa Numbers and Nonabelian Poincare Duality, II [2013]
Dennis Gaitsgory Wednesday, August 28 4:30PM Tamagawa Numbers and Nonabelian Poincare Duality, II Gelfand Centennial Conference: A View of 21st Century Mathematics MIT, Room 34-101, August 28 - September 2, 2013 Abstract: This will be a continuation of Jacob Lurie’s talk. Let X be an al
From playlist Number Theory
Alexander A. Beilinson: The singular support of a constructible sheaf
Find 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, bibliographies,
From playlist Algebraic and Complex Geometry
Schemes 5: Definition of a scheme
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We give some historical background, then give the definition of a scheme and some simple examples, and finish by explaining the origin of the word "spectrum".
From playlist Algebraic geometry II: Schemes
What is a Tensor? Lesson 39: All Possible Operations
What is a Tensor? Lesson 39: All Possible Operations I moved rather quickly through this material because it is not a critical "need to know" topic. However, it was more interesting than I expected it to be.
From playlist What is a Tensor?
An algebro-geometric theory of vector-valued modular forms of half-integral weight - Luca Candelori
Luca Candelori Lousiana State University October 23, 2014 We give a geometric theory of vector-valued modular forms attached to Weil representations of rank 1 lattices. More specifically, we construct vector bundles over the moduli stack of elliptic curves, whose sections over the complex
From playlist Mathematics
What is a Tensor? Lesson 38: Visualization of Forms: Tacks and Sheaves. And Honeycombs.
What is a Tensor? Lesson 38: Visualization of Forms Part 2 Continuing to complete the "visualization" of the four different 3-dimensional vector spaces when dim(V)=3. Erratta: Note: When the coordinate system is expanded the density of things *gets numerically larger* and the area/volum
From playlist What is a Tensor?
Nonetheless one should learn the language of topos: Grothendieck... - Colin McLarty [2018]
Grothendieck's 1973 topos lectures Colin McLarty 3 mai 2018 In the summer of 1973 Grothendieck lectured on several subjects in Buffalo NY, and these lectures were recorded, including 33 hours on topos theory. The topos lectures were by far the most informal of the series, with the most si
From playlist Number Theory
Equivariantization and de-equivariantization - Shotaro Makisumi
Geometric and Modular Representation Theory Seminar Topic: Equivariantization and de-equivariantization Speaker: Shotaro Makisumi Affiliation: Columbia University; Member, School of Mathematics Date: February 10, 2021 For more video please visit http://video.ias.edu
From playlist Seminar on Geometric and Modular Representation Theory
Fourier transform for Class D-modules - David Ben Zvi
Locally Symmetric Spaces Seminar Topic: Fourier transform for Class D-modules Speaker: David Ben Zvi Affiliation: University of Texas at Austin; Member, School of Mathematics Date: Febuary 13, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
DT curve counting for CY3's and birational transformations - John Calabrese
Workshop on Homological Mirror Symmetry: Methods and Structures Speaker:John Calabrese Title: DT curve counting for CY3's and birational transformations Affiliation: Rice University Date: November 8, 2016 For more video, visit http://video.ias.edu
From playlist Mathematics
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