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 - 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
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
Jean BÉNABOU - Very, almost, and so on, ...
Very, almost, and so on, ... (when fragments of the language find their way into Topos Theory)
From playlist Topos à l'IHES
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
Chris SOGGE - Toponogov's theorem and improved Kakeya-Nikodym estimates...
Toponogov's theorem and improved Kakeya-Nikodym estimates for eigenfunctions on manifolds of nonpositive curvature This is joint work with Matthew Blair. Using wave equation techniques and elementary facts from Riemannian geometry, we show that, on negatively curved manifolds, eigenfuncti
From playlist Trimestre "Ondes Non linéaires" - June Conference
T. Richard - Advanced basics of Riemannian geometry 2 (version temporaire)
We will present some of the tools used by the more advanced lectures. The topics discussed will include : Gromov Hausdorff distance, comparison theorems for sectional and Ricci curvature, the Bochner formula and basics of Ricci flow.
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
T. Richard - Advanced basics of Riemannian geometry 2
We will present some of the tools used by the more advanced lectures. The topics discussed will include : Gromov Hausdorff distance, comparison theorems for sectional and Ricci curvature, the Bochner formula and basics of Ricci flow.
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Mikhail Katz (7/14/20): Collapsing surfaces
The collapse of Riemannian manifolds M and more general metric spaces to a lower-dimensional space X in the presence of a uniform lower bound on the Alexandrov curvature is a much-studied subject where many open questions remain. We examine the case of surfaces M collapsing to circles or s
From playlist AATRN 2021
André JOYAL - New variations on the notion of topos
The notion topos is a prominent member of a family of notions which includes that of abelian category, of locally presentable category and of higher topos. We propose two new members: the notion of locus and that of para-topos. The category of pointed spaces and the category of spectra are
From playlist Topos à l'IHES
Nima Rasekh - Every Elementary Higher Topos has a Natural Number Object
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/NimaSlidesToposesOnline.pdf One key aspect of elementary topos theory is the existence of a natural number object. W
From playlist Toposes online
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
Lecture 8: Higher-order logic and topoi (Part 1)
The goal of the seminar in S1 of 2018 is to understand classifying topoi. These are topoi which have a universal property with respect to a particular geometric theory, and they are constructed as categories of sheaves on a site, the underlying category of which is defined in terms of the
From playlist Topos theory seminar
Calculus 1 (Stewart) Ep 22, Mean Value Theorem (Oct 28, 2021)
This is a recording of a live class for Math 1171, Calculus 1, an undergraduate course for math majors (and others) at Fairfield University, Fall 2021. The textbook is Stewart. PDF of the written notes, and a list of all episodes is at the class website. Class website: http://cstaecker.f
From playlist Math 1171 (Calculus 1) Fall 2021
Equidistribution of Unipotent Random Walks on Homogeneous spaces by Emmanuel Breuillard
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
What is Green's theorem? Chris Tisdell UNSW
This lecture discusses Green's theorem in the plane. Green's theorem not only gives a relationship between double integrals and line integrals, but it also gives a relationship between "curl" and "circulation". In addition, Gauss' divergence theorem in the plane is also discussed, whic
From playlist Vector Calculus @ UNSW Sydney. Dr Chris Tisdell
Real Analysis Ep 32: The Mean Value Theorem
Episode 32 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is more about the mean value theorem and related ideas. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/courses/2020f3371/ Chris Staecker
From playlist Math 3371 (Real analysis) Fall 2020
Pythagorean theorem - What is it?
► My Geometry course: https://www.kristakingmath.com/geometry-course Pythagorean theorem is super important in math. You will probably learn about it for the first time in Algebra, but you will literally use it in Algebra, Geometry, Trigonometry, Precalculus, Calculus, and beyond! That’s
From playlist Geometry
Wolfram Physics Project: Working Session Sept. 15, 2020 [Physicalization of Metamathematics]
This is a Wolfram Physics Project working session on metamathematics and its physicalization in the Wolfram Model. Begins at 10:15 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the
From playlist Wolfram Physics Project Livestream Archive
Lecture 5: The definition of a topos (Part 2)
A topos is a Cartesian closed category with all finite limits and a subobject classifier. In his two seminar talks (of which this is the second) James Clift will explain all of these terms in detail. In his first talk he defined products, pullbacks, general limits, and exponentials and in
From playlist Topos theory seminar