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?
Who Gives a Sheaf? Part 3: Mighty Morph'n Morphisms
In this video we discuss the definition of a morphism of sheaves.
From playlist Who Gives a Sheaf?
Who Gives a Sheaf? Part 2: A non-example
In this video we compare two pre-sheaves, one which is a sheaf, and one which is not.
From playlist Who Gives a Sheaf?
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
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 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
Microlocal theory of sheaves and link with symplectic geometry II - Stephane Guillermou
Stephane Guillermou University Grenoble May 10, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Joel Friedman - Sheaves on Graphs, L^2 Betti Numbers, and Applications.
Joel Friedman (University of British Columbia, Canada) Sheaf theory and (co)homology, in the generality developed by Grothendieck et al., seems to hold great promise for applications in discrete mathematics. We shall describe sheaves on graphs and their applications to (1) solving the
From playlist T1-2014 : Random walks and asymptopic geometry of groups.
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
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
Marc Levine: The rational motivic sphere spectrum and motivic Serre finiteness
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 SPECIAL 7th European congress of Mathematics Berlin 2016.
Robert Ghrist, Lecture 2: Topology Applied II
27th Workshop in Geometric Topology, Colorado College, June 11, 2010
From playlist Robert Ghrist: 27th Workshop in Geometric Topology
Alex SIMPSON - Probability sheaves
In [2], Tao observes that the probability theory concerns itself with properties that are \preserved with respect to extension of the underlying sample space", in much the same way that modern geometry concerns itself with properties that are invariant with respect to underlying symmetries
From playlist Topos à l'IHES
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?
Robert Ghrist (5/1/21): Laplacians and Network Sheaves
This talk will begin with a simple introduction to cellular sheaves as a generalized notion of a network of algebraic objects. With a little bit of geometry, one can often define a Laplacian for such sheaves. The resulting Hodge theory relates the geometry of the Laplacian to the algebraic
From playlist TDA: Tutte Institute & Western University - 2021
This lecture is part of an online course in algebraic geometry giving an introduction to schemes. It is loosely based on chapter II Hartshorne's book "Algebraic geometry". (For chapter 1 see the playlist "Algebraic geometry".) This introductory lecture gives some motivation for schemes and
From playlist Algebraic geometry II: Schemes
Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs
❤️ Become The AI Epiphany Patreon ❤️ https://www.patreon.com/theaiepiphany 👨👩👧👦 Join our Discord community 👨👩👧👦 https://discord.gg/peBrCpheKE In this video I cover "Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs" paper. The paper takes id
From playlist Graph Neural Nets
Matthew Morrow: Relative integral p-adic Hodge theory
Abstract: Given a smooth scheme X over the ring of integers of a p-adic field, we introduce the notion of a relative Breuil-Kisin-Fargues module M on X. Each such M simultaneously encodes the data of a lisse étale sheaf, a module with flat connection, and a crystal, whose cohomologies are
From playlist Algebraic and Complex Geometry
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
Robert Ghrist (8/29/21): Laplacians and Network Sheaves
This talk will begin with a simple introduction to cellular sheaves as a generalized notion of a network of algebraic objects. With a little bit of geometry, one can often define a Laplacian for such sheaves. The resulting Hodge theory relates the geometry of the Laplacian to the algebraic
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021