In mathematics, especially in topology, a stratified space is a topological space that admits or is equipped with a stratification, a decomposition into subspaces, which are nice in some sense (e.g., smooth or flat). A basic example is a subset of a smooth manifold that admits a Whitney stratification. But there is also an abstract stratified space such as a Thom–Mather stratified space. On a stratified space, a constructible sheaf can be defined as a sheaf that is locally constant on each stratum. Among the several ideals, Grothendieck's Esquisse d’un programme considers (or proposes) a stratified space with what he calls the tame topology. (Wikipedia).
What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:
From playlist Science Unplugged: Physics
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
What is the Universe expanding into?
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From playlist Science Unplugged: Cosmology
Is there any place in the Universe where there's truly nothing? Consider the gaps between stars and galaxies? Or the gaps between atoms? What are the properties of nothing?
From playlist Guide to Space
MAST30026 Lecture 2: Examples of spaces (Part 1)
I started with the definition of a metric space, we briefly discussed the example of Euclidean space (proofs next time) and then I started to explain a few natural metrics on the circle. Lecture notes: http://therisingsea.org/notes/mast30026/lecture2.pdf The class webpage: http://therisin
From playlist MAST30026 Metric and Hilbert spaces
The Human Body in Space - What happens to your body in space? Start learning with Brilliant today for FREE: http://brilliant.org/aperture Follow me on Instagram: https://www.instagram.com/mcewen/ Space is the final frontier. But you know, it’s not like space has a lot going on. There is q
From playlist Science & Technology 🚀
Thermodynamic System | Open, Closed, Adiabatic, Isolated | Statistical Mechanics
In this video, we will define a thermodynamic system, in particular what kinds of thermodynamic systems there are and how they can interact with their surroundings. References: [1] Ansermet, Brechet, "Principles of Thermodynamics", Cambridge University Press (2019). Follow us on Insta
From playlist Thermodynamics, Statistical Mechanics
Clark Barwick - 2/3 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
David Ayala: Factorization homology (part 2)
The lecture was held within the framework of the Hausdorff Trimester Program: Homotopy theory, manifolds, and field theories and Introductory School (7.5.2015)
From playlist HIM Lectures 2015
Ilaria Mondello : An Obata-Lichnerowicz theorem for stratified spaces
Abstract : In the first part of this talk we will show how classical tools of Riemannian geometry can be used in the setting of stratfied spaces in order to obtain a lower bound for the spectrum of the Laplacian, under an appropriate assumption of positive curvature. Such assumption involv
From playlist Topology
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From playlist Science Unplugged: Special Relativity
Clark Barwick - 3/3 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
David Ayala: Factorization homology (part 3)
The lecture was held within the framework of the Hausdorff Trimester Program: Homotopy theory, manifolds, and field theories and Introductory School (8.5.2015)
From playlist HIM Lectures 2015
Small scale formations in the incompressible porous media equation - Yao Yao
Workshop on Recent developments in incompressible fluid dynamics Topic: Small scale formations in the incompressible porous media equation Speaker: Yao Yao Affiliation: National University of Singapore Date: April 05, 2022 The incompressible porous media (IPM) equation describes the evol
From playlist Mathematics
Ask the Space Lab Expert: What is Space?
Have you ever wanted to go to Space? In this first episode of Space Lab, Brad and Liam from "World of the Orange" take you on an adventure to discover exactly what is Space. You'll find out about the solar system, the big bang, Sci-Fi movies that are becoming reality, and more!
From playlist What is Space? YouTube Space Lab with Liam and Brad
Ryan Grady - Persistence over the Circle
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Ryan Grady, Montana State University Title: Persistence over the Circle Abstract: In this talk we will construct algebraic topological invariants of persistence modules on the circle. In particular, we will discuss the K-t
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
Complete metric space: example & proof
This video discusses an example of particular metric space that is complete. The completeness is proved with details provided. Such ideas are seen in branches of analysis.
From playlist Mathematical analysis and applications
David Ayala: Factorization homology (part 1)
The lecture was held within the framework of the Hausdorff Trimester Program: Homotopy theory, manifolds, and field theories and Introductory School (6.5.2015)
From playlist HIM Lectures 2015