Algebraic structures | Homological algebra | K-theory
In mathematics, the Grothendieck group, or group of differences, of a commutative monoid M is a certain abelian group. This abelian group is constructed from M in the most universal way, in the sense that any abelian group containing a homomorphic image of M will also contain a homomorphic image of the Grothendieck group of M. The Grothendieck group construction takes its name from a specific case in category theory, introduced by Alexander Grothendieck in his proof of the Grothendieck–Riemann–Roch theorem, which resulted in the development of K-theory. This specific case is the monoid of isomorphism classes of objects of an abelian category, with the direct sum as its operation. (Wikipedia).
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
Roland Bauerschmidt - The Renormalisation Group - a Mathematical Perspective (3/4)
In physics, the renormalisation group provides a powerful point of view to understand random systems with strong correlations. Despite advances in a number of particular problems, in general its mathematical justification remains a holy grail. I will give an introduction to the main concep
From playlist Roland Bauerschmidt - The Renormalisation Group - a Mathematical Perspective
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
Roland Bauerschmidt - The Renormalisation Group - a Mathematical Perspective (2/4)
In physics, the renormalisation group provides a powerful point of view to understand random systems with strong correlations. Despite advances in a number of particular problems, in general its mathematical justification remains a holy grail. I will give an introduction to the main concep
From playlist Roland Bauerschmidt - The Renormalisation Group - a Mathematical Perspective
Roland Bauerschmidt - The Renormalisation Group - a Mathematical Perspective (4/4)
In physics, the renormalisation group provides a powerful point of view to understand random systems with strong correlations. Despite advances in a number of particular problems, in general its mathematical justification remains a holy grail. I will give an introduction to the main concep
From playlist Roland Bauerschmidt - The Renormalisation Group - a Mathematical Perspective
Grothendieck Pairs and Profinite Rigidity - Martin Bridson
Arithmetic Groups Topic: Grothendieck Pairs and Profinite Rigidity Speaker: Martin Bridson Affiliation: Oxford University Date: January 26, 2022 If a monomorphism of abstract groups H↪G induces an isomorphism of profinite completions, then (G,H) is called a Grothendieck pair, recalling t
From playlist Mathematics
Rostislav Grigorchuk - Invariant random subgroups of groups of the lamplighter type
Rostislav Grigorchuk (Texas A&M University, USA) After a short introduction to invariant random subgroups (IRS) I will present some results obtained in collaboration with L.Bowen, R.Kravchenko and T.Nagnibeda and with M.Benli and T.Nagnibeda. First I will talk about IRS of groups
From playlist T1-2014 : Random walks and asymptopic geometry of groups.
Céline Pessis - L'engagement d'Alexandre Grothendieck durant la première moitié des années 1970
Militant singulier ou porte-parole ? Retour sur l'engagement d'Alexandre Grothendieck durant la première moitié des années 1970 Le 27 janvier 1972, au Centre Européen de Recherches Nucléaires (CERN), citadelle d'une recherche de pointe, des centaines de technicien.
From playlist Séminaire Grothendieck 30 mars 2016
Grothendieck-Gruppe - Konstruktion
Abonniert den Kanal, damit er auch in Zukunft bestehen kann. Es ist vollkommen kostenlos und ihr werdet direkt informiert, wenn ich einen Livestream anbiete. Hier erzähle ich etwas über die Konstruktion der Grothendieck-Gruppe in einem abstrakten Rahmen, aber mit elementaren Rechnungen. E
From playlist 1. Semester
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
David Hernandez, Quantum Kac-Moody algebras and categorifications
David HERNANDEZ (Université Paris-Diderot - Paris 7) "Quantum Kac-Moody algebras and categorifications"
From playlist Après-midi en l'honneur de Victor KAC
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
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
With Olivia Caramello, André Joyal, Laurent Lafforgue et Alain Connes
From playlist Topos à l'IHES
[BOURBAKI 2017] 14/01/2017 - 3/4 - Maxim KONTSEVICH
Derived Grothendieck-Teichmüller group and graph complexes, after T. Willwacher Graph complex is spanned by equivalence classes of finite connected graphs with the dual differential given by the sum of all contractions of edges, with appropriate signs. This complex forms a differential g
From playlist BOURBAKI - 2017
On Grothendieck–Serre conjecture concerning principal bundles – Ivan Panin – ICM2018
Algebra Invited Lecture 2.1 On Grothendieck–Serre conjecture concerning principal bundles Ivan Panin Abstract: Let R be a regular local ring. Let G be a reductive group scheme over R. A well-known conjecture due to Grothendieck and Serre assertes that a principal G-bundle over R is trivi
From playlist Algebra
Roland Bauerschmidt - The Renormalisation Group - a Mathematical Perspective (1/4)
In physics, the renormalisation group provides a powerful point of view to understand random systems with strong correlations. Despite advances in a number of particular problems, in general its mathematical justification remains a holy grail. I will give an introduction to the main concep
From playlist Roland Bauerschmidt - The Renormalisation Group - a Mathematical Perspective