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?
Dennis Gaitsgory - 4/4 Singular support of coherent sheaves
Singular support is an invariant that can be attached to a coherent sheaf on a derived scheme which is quasi-smooth (a.k.a. derived locally complete intersection). This invariant measures how far a given coherent sheaf is from being perfect. We will explain how the subtle difference betwee
From playlist Dennis Gaitsgory - Singular support of coherent sheaves
Dennis Gaitsgory - 3/4 Singular support of coherent sheaves
Singular support is an invariant that can be attached to a coherent sheaf on a derived scheme which is quasi-smooth (a.k.a. derived locally complete intersection). This invariant measures how far a given coherent sheaf is from being perfect. We will explain how the subtle difference betwee
From playlist Dennis Gaitsgory - Singular support of coherent sheaves
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
Nicolas Berkouk (6/22/20): Sheaves as computable and stable topological invariants for datasets:
Title: Sheaves as computable and stable topological invariants for datasets: From level-sets persistence and beyond Abstract: Persistent homology has been recently studied with the tools of sheaf theory in the derived setting by Kashiwara and Schapira after J. Curry has made the first lin
From playlist ATMCS/AATRN 2020
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?
Takeshi Saito - Micro support of a constructible sheaf in mixed characteristic
Correction: The affiliation of Lei Fu is Tsinghua University. One of the obstacles in the definition of the singular support of a constructible sheaf in mixed characteristic is the absence of the cotangent bundle. We define a ‘Frobenius pull-back’ of the cotangent bundle restricted on the
From playlist Conférence « Géométrie arithmétique en l’honneur de Luc Illusie » - 5 mai 2021
From Cohomology to Derived Functors by Suresh Nayak
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Dennis Gaitsgory - 1/4 Singular support of coherent sheaves
Singular support is an invariant that can be attached to a coherent sheaf on a derived scheme which is quasi-smooth (a.k.a. derived locally complete intersection). This invariant measures how far a given coherent sheaf is from being perfect. We will explain how the subtle difference betwee
From playlist Dennis Gaitsgory - Singular support of coherent sheaves
Georg Biedermann - Higher Sheaves
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Joint work with Mathieu Anel, Eric Finster, and André Joyal Even though on the surface the theories look similar, there are basic differences between the classical theory of 1-t
From playlist Toposes online
Dennis Gaitsgory - 2/4 Singular support of coherent sheaves
Singular support is an invariant that can be attached to a coherent sheaf on a derived scheme which is quasi-smooth (a.k.a. derived locally complete intersection). This invariant measures how far a given coherent sheaf is from being perfect. We will explain how the subtle difference betwee
From playlist Dennis Gaitsgory - Singular support of coherent sheaves
Finiteness, Z_l-sheaves
From playlist Étale cohomology and the Weil conjectures
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
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
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.
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
Proper base change continued, compactly supported cohomology, cohomology with supports, Gysin sequences and purity
From playlist Étale cohomology and the Weil conjectures
Artin comparison, intro to pi_1
From playlist Étale cohomology and the Weil conjectures
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.
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