What is a Manifold? Lesson 2: Elementary Definitions
This lesson covers the basic definitions used in topology to describe subsets of topological spaces.
From playlist What is a Manifold?
What is a Manifold? Lesson 6: Topological Manifolds
Topological manifolds! Finally! I had two false starts with this lesson, but now it is fine, I think.
From playlist What is a Manifold?
What is a Manifold? Lesson 14: Quotient Spaces
I AM GOING TO REDO THIS VIDEO. I have made some annotations here and annotations are not visible on mobile devices. STAY TUNED. This is a long lesson about an important topological concept: quotient spaces.
From playlist What is a Manifold?
What is a Manifold? Lesson 5: Compactness, Connectedness, and Topological Properties
The last lesson covering the topological prep-work required before we begin the discussion of manifolds. Topics covered: compactness, connectedness, and the relationship between homeomorphisms and topological properties.
From playlist What is a Manifold?
Stable Homotopy Seminar, 8: The Stable Model Category of Spectra
We discuss the enrichment of spectra over spaces, and the compatibility of this enrichment with the model structure. Then we define the stable model structure by adding extra cofibrations to the levelwise model category of spectra, and restricting the weak equivalences to those maps which
From playlist Stable Homotopy Seminar
I define topological manifolds. Motivated by the prospect of calculus on topological manifolds, I introduce smooth manifolds. At the end I point out how one needs to change the definitions, to obtain C^1 or even complex manifolds. To learn more about manifolds, see Lee's "Introduction to
From playlist Differential geometry
Stable Homotopy Seminar, 7: Constructing Model Categories
A stroll through the recognition theorem for cofibrantly generated model categories, using it to construct (1) the Quillen/Serre model structure on topological spaces and (2) the levelwise model structure on spectra. The latter captures the idea that spectra are sequences of spaces, but no
From playlist Stable Homotopy Seminar
What is a Manifold? Lesson 4: Countability and Continuity
In this lesson we review the idea of first and second countability. Also, we study the topological definition of a continuous function and then define a homeomorphism.
From playlist What is a Manifold?
Minimality and stable ergodicity by Jana Rodriguez Hertz
PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.
From playlist Smooth And Homogeneous Dynamics
Surfaces of Section, Anosov Reeb Flows, and the C2-Stability Conjecture for... - Marco Mazzucchelli
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar 9:15am|Remote Access Topic: Surfaces of Section, Anosov Reeb Flows, and the C2-Stability Conjecture for Geodesic Flows Speaker: Marco Mazzucchelli Affiliation: École Normale Supérieure de Lyon Date: March 03, 2023 In
From playlist Mathematics
The Hartman-Grobman Theorem, Structural Stability of Linearization, and Stable/Unstable Manifolds
This video explores a central result in dynamical systems: The Hartman-Grobman theorem. This theorem establishes when a fixed point of a nonlinear system will resemble its linearization. In particular, hyperbolic fixed points, where every eigenvalue has a non-zero real part, will be "str
From playlist Engineering Math: Differential Equations and Dynamical Systems
Arun Debray - Stable diffeomorphism classification of some unorientable 4-manifolds
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Arun Debray, The University of Texas at Austin Title: Stable diffeomorphism classification of some unorientable 4-manifolds Abstract: Kreck's modified surgery theory provides a bordism-theoretic classification of closed, c
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
Weak Stability Boundary and Capture in the Three-Body Problem - Edward Belbruno
Edward Belbruno NASA/AISR & IOD, Inc. January 19, 2011 GEOMETRY/DYNAMICAL SYSTEMS The problem of capture in the planar restricted three-body problem is addressed. In particular, weak capture is described, which occurs at a complicated region called the weak stability boundary, where the m
From playlist Mathematics
J. Wang - Topological rigidity and positive scalar curvature (version temporaire)
In this talk, we shall describe some topological rigidity and its relationship with positive scalar curvature. Precisely, we will present a proof that a complete contractible 3-manifold with positive scalar curvature is homeomorphic to the Euclidean 3-space. We will furthermore explain the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Floer theory in spaces of stable pairs over Riemann surfaces - Timothy Perutz
Floer theory in spaces of stable pairs over Riemann surfaces Timothy Perutz University of Texas, Austin; von Neumann Fellow, School of Mathematics May 4, 2017
From playlist Mathematics
J. Wang - Topological rigidity and positive scalar curvature
In this talk, we shall describe some topological rigidity and its relationship with positive scalar curvature. Precisely, we will present a proof that a complete contractible 3-manifold with positive scalar curvature is homeomorphic to the Euclidean 3-space. We will furthermore explain the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
On the existence of minimal Heegaard splittings - Dan Ketover
Variational Methods in Geometry Seminar Topic: On the existence of minimal Heegaard splittings Speaker: Dan Ketover Affiliation: Princeton University; Member, School of Mathematics Date: Oct 2, 2018 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
Manifolds 1.1 : Basic Definitions
In this video, I give the basic intuition and definitions of manifolds. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Manifolds
Existence of Quasigeodesic Anosov Flows in Hyperbolic 3-Manifolds - Sergio Fenley
Members' Colloquium Topic: Existence of Quasigeodesic Anosov Flows in Hyperbolic 3-Manifolds Speaker: Sergio Fenley Affiliation: Florida State University; Member, School of Mathematics Date: March 06, 2023 A quasigeodesic in a manifold is a curve so that when lifted to the universal cove
From playlist Mathematics