Sites/Coverings part 2: Grothendieck Topologies
Definition of a Grothendieck topology. This is just the axiomatization of coverings.
From playlist Sites, Coverings and Grothendieck Topologies
An introduction to the Gromov-Hausdorff distance
Title: An introduction to the Gromov-Hausdorff distance Abstract: We give a brief introduction to the Hausdorff and Gromov-Hausdorff distances between metric spaces. The Hausdorff distance is defined on two subsets of a common metric space. The Gromov-Hausdorff distance is defined on any
From playlist Tutorials
Filtering the Grothendieck ring of varieties - Inna Zakharevich
Filtering the Grothendieck ring of varieties - Inna Zakharevich Inna Zakharevich University of Chicago; Member, School of Mathematics March 10, 2014 The Grothendieck ring of varieties over k k is defined to be the free abelian group generated by varieties over k k , modulo the relation
From playlist Mathematics
I define closed sets, an important notion in topology and analysis. It is defined in terms of limit points, and has a priori nothing to do with open sets. Yet I show the important result that a set is closed if and only if its complement is open. More topology videos can be found on my pla
From playlist Topology
Symplectic homology via Gromov-Witten theory - Luis Diogo
Luis Diogo Columbia University February 13, 2015 Symplectic homology is a very useful tool in symplectic topology, but it can be hard to compute explicitly. We will describe a procedure for computing symplectic homology using counts of pseudo-holomorphic spheres. These counts can sometime
From playlist Mathematics
Jesper Grodal: Burnside rings in algebra and topology (Part 2)
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: Workshop "Fusion systems and equivariant algebraic topology"
From playlist HIM Lectures: Junior Trimester Program "Topology"
Topology 1.7 : More Examples of Topologies
In this video, I introduce important examples of topologies I didn't get the chance to get to. This includes The discrete and trivial topologies, subspace topology, the lower-bound and K topologies on the reals, the dictionary order, and the line with two origins. I also introduce (again)
From playlist Topology
Verdier And Grothendieck Duality (Lecture 4) 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)
Huawei Young Talents Programme - Laurent Lafforgue
The online ceremony celebrating the official launch of the Huawei Young Talents Program at the Institut des Hautes Etudes Scientifiques was held on 6 November 2020. This program aims to support the work of talented researchers in mathematics and theoretical physics at the beginning of thei
From playlist Huawei Young Talents Program - November 2020
Jesper Grodal: Burnside rings in algebra and topology (Part 1)
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: Workshop "Fusion systems and equivariant algebraic topology"
From playlist HIM Lectures: Junior Trimester Program "Topology"
Jean-Pierre Serre & Alain Connes - Alexandre Grothendieck
Entretien enregistré à la Fondation Hugot du Collège de France le 27 novembre 2018 entre les mathématiciens Jean-Pierre Serre et Alain Connes à propos de la correspondance Serre / Grothendieck (Correspondance Grothendieck-Serre, Société mathématique de France, 2001 ; Grothendieck-Serre Cor
From playlist Math History
Mr LIMA de CARVALHO e SILVA - From Essential Inclusions to Local Geometric Morphisms
It is well known that, given a site of denition, a subtopos of Grothendieck topos can be obtained by strengthening the Grothendieck topology, thus obtaining an inclusion of toposes. An essential inclusion is one where the inverse image functor of this inclusion has a left adjoint. Kelly an
From playlist Topos à l'IHES
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
Laurent Lafforgue - 3/4 Classifying toposes of geometric theories
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/LafforgueSlidesToposesOnline.pdf The purpose of these lectures will be to present the theory of classifying topose
From playlist Toposes online
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
Geometers Abandoned 2,000 Year-Old Math. This Million-Dollar Problem was Born - Hodge Conjecture
The Hodge Conjecture is one of the deepest problems in analytic geometry and one of the seven Millennium Prize Problems worth a million dollars, offered by the Clay Mathematical Institute in 2000. It consists of drawing shapes known topological cycles on special surfaces called projective
From playlist Math
Anne-Sandrine Paumier - Quel(s) lieu(x) pour quelle(s) mathématique(s) ?
Quel(s) lieu(x) pour quelle(s) mathématique(s) ? Penser et construire l’Institut de Hautes Études Scientifiques Conférence donnée devant L'Association des Amis de l'IHES à l'IHES le 4 mai 2017. L’IHES est créé officiellement le 27 juin 1958, dans le bureau de Joseph Pérès, doyen de la Fa
From playlist Évenements grand public
algebraic geometry 30 The Ax Grothendieck theorem
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the Ax-Grothendieck theorem, which states that an injective regular map between varieties is surjective. The proof uses a strange technique: first prove the resu
From playlist Algebraic geometry I: Varieties