Functional analysis | Topological vector spaces | Topology of function spaces
In the mathematical field of functional analysis there are several standard topologies which are given to the algebra B(X) of bounded linear operators on a Banach space X. (Wikipedia).
André JOYAL - 3/4 A crash course in topos theory : the big picture
I will sketch an overall picture of topos theory and of the theory of locales. It includes the notion of sheaf on a site, the notion of forcing topology, of geometric morphism and Giraud's theorem. A useful principle is that a topos is a commutative ring-like object. Every topos is a quoti
From playlist Topos à l'IHES
André JOYAL - 4/4 A crash course in topos theory : the big picture
I will sketch an overall picture of topos theory and of the theory of locales. It includes the notion of sheaf on a site, the notion of forcing topology, of geometric morphism and Giraud's theorem. A useful principle is that a topos is a commutative ring-like object. Every topos is a quoti
From playlist Topos à l'IHES
André JOYAL - 2/4 A crash course in topos theory : the big picture
I will sketch an overall picture of topos theory and of the theory of locales. It includes the notion of sheaf on a site, the notion of forcing topology, of geometric morphism and Giraud's theorem. A useful principle is that a topos is a commutative ring-like object. Every topos is a quoti
From playlist Topos à l'IHES
Simon HENRY - Operator algebras from toposes
Abstract: Grothendieck Toposes and $C^*$-algebras are two distinct generalizations of the concept of topological space and there is a lot of examples of objects to which one can attach both a topos and a $C^*$-algebra in order to study there properties: dynamical systems, foliations, Graph
From playlist Topos à l'IHES
To a topologist, a coffee cup and a donut are the same thing.
From playlist Algebraic Topology
Mathieu ANEL - Toposes are commutative rings
Abstract: In this talk, we shall develop the point of view comparing (higher) toposes to commutative rings. We shall then see how the corresponding integral and differential calculus are related respectively to Verdier duality and Goodwillie calculus of functors.
From playlist Topos à l'IHES
Topoi 3: The definition of a topos
This is video number 3 in the series defining topoi. Here's the updated text used in the video: https://gist.github.com/Nikolaj-K/469b9ca1c085ea4ac4e3d7d0008913f5 Fourth video on Power and Negation in a topos: https://youtu.be/dvXRQI8RonY
From playlist Algebra
Ingo BLECHSCHMIDT - Using the internal language of toposes in algebraic geometry
We describe how the internal language of certain toposes, the associated petit and gros Zariski toposes of a scheme, can be used to give simpler denitions and more conceptual proofs of the basic notions and observations in algebraic geometry. The starting point is that, from the internal p
From playlist Topos à l'IHES
Charles Rezk - 3/4 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/RezkNotesToposesOnlinePart3.pdf In this series of lectures I will give an introduction to the concept of "infinity
From playlist Toposes online
Symmetries in QFT and Their Relationship With Category Theory (Lecture 1) by Lakshya Bhardwaj
INFOSYS-ICTS STRING THEORY LECTURES SYMMETRIES IN QFT AND THEIR RELATIONSHIP WITH CATEGORY THEORY SPEAKER Lakshya Bhardwaj (Mathematical Institute, University of Oxford) DATE & TIME 10 October 2022 to 12 October 2022 VENUE Madhava Lecture Hall (Hybrid) Lecture 1: 10 October 2022 at 3:30 p
From playlist Infosys-ICTS String Theory Lectures
Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined
Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined In this lecture we define a "continuous groups" and show the connection between the algebraic properties of a group with topological properties. Please consider supporting this channel via Patreon: https://www.patreon.co
From playlist Lie Groups and Lie Algebras
Ginestra Bianconi (8/28/21): The topological Dirac operator and the dynamics of topological signals
Topological signals associated not only to nodes but also to links and to the higher dimensional simplices of simplicial complexes are attracting increasing interest in signal processing, machine learning and network science. Typically, topological signals of a given dimension are investig
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
The Homework Problem That Started as a Phd Thesis: 14 set theorem
In a handful of introductory topology textbooks, Kuratowski's 14 set theorem is given as an exercise despite it being one of the results proven as a part of his phd thesis in 1922. This homework problem that started out as a phd thesis is not an easy exercise if you don't know how to think
From playlist The New CHALKboard
Markus Haase : Operators in ergodic theory - Lecture 3 : Compact semigroups and splitting theorems
Abstract : The titles of the of the individual lectures are: 1. Operators dynamics versus base space dynamics 2. Dilations and joinings 3. Compact semigroups and splitting theorems Recording during the thematic meeting : "Probabilistic Aspects of Multiple Ergodic Averages " the December 8
From playlist Dynamical Systems and Ordinary Differential Equations
Geometric Representation of Structured Extensions in Ergodic Theory - Henrik Kreidler
Special Year Research Seminar Topic: Geometric Representation of Structured Extensions in Ergodic Theory Speaker: Henrik Kreidler Affiliation: Bergische Universität Wuppertal Date: March 14, 2023 The Mackey-Zimmer representation theorem is a key structural result from ergodic theory: Eve
From playlist Mathematics
Hermann Schulz-Baldes: Invariants of disordered topological insulators
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.
PiTP 2015 - "Fermion Path Integrals and Topological Phases" - Edward Witten
https://pitp2015.ias.edu/
From playlist 2015 Prospects in Theoretical Physics Program
Olivia Caramello - 2/4 ntroduction to categorical logic, classifying toposes...
Introduction to categorical logic, classifying toposes and the « bridge » technique Construction of classifying toposes for geometric theories. Duality between the subtoposes of the classifying topos of a geometric theory and the quotients of the theory. Transfer of topos‐the
From playlist Topos à l'IHES
Hermann Schulz-Baldes: Computational K-theory via the spectral localizer.
Talk by Hermann Schulz-Baldes in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on March 24, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)