Act globally, compute...points and localization - Tara Holm
Tara Holm Cornell University; von Neumann Fellow, School of Mathematics October 20, 2014 Localization is a topological technique that allows us to make global equivariant computations in terms of local data at the fixed points. For example, we may compute a global integral by summing inte
From playlist Mathematics
Localization and flexibilization in symplectic geometry - Oleg Lazarev
Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Localization and flexibilization in symplectic geometry Speaker: Oleg Lazarev Affiliation: University of Massachusetts, Boston Date: December 13, 2021 Localization is an important construction in algebra and topology that
From playlist PU/IAS Symplectic Geometry Seminar
Localization of Rings as Localizations of Categories
We show what it means to localize a category at a set of morphisms and show that usual localization of rings is an instance of this definition.
From playlist Category Theory
This lecture is part of an online course on rings and modules. We discuss the operation of inverting the elements of a subset S of a ring R, called localization. We describe the localization in detail for commutative rings, and briefly discuss the non-commutative case. For the other lec
From playlist Rings and modules
Metric space definition and examples. Welcome to the beautiful world of topology and analysis! In this video, I present the important concept of a metric space, and give 10 examples. The idea of a metric space is to generalize the concept of absolute values and distances to sets more gener
From playlist Topology
20/11/2015 - Richard Schoen - Localizing Solutions of the Einstein Equations
Abstract. In general it is not possible to localize solutions of the Einstein equations since there are asymptotic conserved quantities such as the total mass which are nonzero for every nontrivial space-time. In this lecture we will describe work with A. Carlotto which achieves a localiza
From playlist 2015-T3 - Mathematical general relativity - CEB Trimester
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We will review the localization of a ring at a multiplicative subset or prime ideal, and describe what this does to the spectrum of a ring.
From playlist Algebraic geometry II: Schemes
Francesco Ciraulo: Notions of Booleanization in pointfree Topology
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Boolean algebras play a key role in the foundations of classical mathematics. And a similar role is played by Heyting algebras for constructive mathematics. But this is
From playlist Workshop: "Constructive Mathematics"
Centralizer of a set in a group
A centralizer consider a subset of the set that constitutes a group and included all the elements in the group that commute with the elements in the subset. That's a mouthful, but in reality, it is actually an easy concept. In this video I also prove that the centralizer of a set in a gr
From playlist Abstract algebra
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
Jens Hemelaer: Toposes in arithmetic noncommutative geometry
Talk by Jens Hemelaer in Global Noncommutative Geometry Seminar (Americas) on February 5, 2021
From playlist Global Noncommutative Geometry Seminar (Americas)
Jezus Gonzalez (6/25/17) Bedlewo: Topological complexity and the motion planning problem in robotics
Early this century Michael Farber introduced the concept of Topological Complexity (TC), a model to study the continuity instabilities in the motion planning problem in robotics. Farber’s model has captured much attention since then due to the rich algebraic topology properties encoded by
From playlist Applied Topology in Będlewo 2017
Anthony Bordg - How to Do Maths Without Dependent Types
What can be done when formalising mathematics without dependent types? I will give you new insights into this question by exploring the capability and possible limitations of the Isabelle/HOL proof assistant. I will explain what we learnt formalising Grothendieck's schemes using only Isabe
From playlist Workshop Schlumberger 2022 : types dépendants et formalisation des mathématiques
MAST30026 Lecture 12: Function spaces (Part 3)
We continued the discussion of the compact-open topology on function spaces. Guided by Part 2 we defined this topology, and got about half way through the proof that the adjunction property (aka the exponential law) holds when function spaces are given this topology. Lecture notes: http:/
From playlist MAST30026 Metric and Hilbert spaces
Lecture 7: Sheaves of sets (Part 2)
The most important examples of topoi are categories of sheaves of sets on a small category. Patrick Eilliott introduced this class of examples over two talks, of which is the second. In this talk he defines Grothendieck topologies and the category of sheaves on a site, and develops the exa
From playlist Topos theory seminar
Charles Rezk - 4/4 Higher Topos Theory
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/RezkNotesToposesOnlinePart4.pdf In this series of lectures I will give an introduction to the concept of "infinity
From playlist Toposes online
Today, we begin the manifolds series by introducing the idea of a topological manifold, a special type of topological space which is locally homeomorphic to Euclidean space.
From playlist Manifolds
José Manuel García-Calcines (6/24/21): Topological complexity using arbitrary covers
Title: Topological complexity using arbitrary covers
From playlist Topological Complexity Seminar
Clark Barwick - 1/3 Exodromy for ℓ-adic Sheaves
In joint work with Saul Glasman and Peter Haine, we proved that the derived ∞-category of constructible ℓ-adic sheaves ’is’ the ∞-category of continuous functors from an explicitly defined 1-category to the ∞-category of perfect complexes over ℚℓ. In this series of talks, I want to offer s
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Localization of Spaces by Somnath Basu
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)