Definition of a Topological Space
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From playlist Topology
Said Hamoun (2/23/23): On the rational topological complexity of coformal elliptic spaces
We establish some upper and lower bounds of the rational topological complexity for certain classes of elliptic spaces. Our techniques permit us in particular to show that the rational topological complexity coincides with the dimension of the rational homotopy for some special families of
From playlist Topological Complexity Seminar
This video is about topological spaces and some of their basic properties.
From playlist Basics: Topology
The Computational Complexity of Geometric Topology Problems - Greg Kuperberg
Greg Kuperberg University of California, Davis September 24, 2012 This talk will be a partial survey of the first questions in the complexity theory of geometric topology problems. What is the complexity, or what are known complexity bounds, for distinguishing n-manifolds for various n? Fo
From playlist Mathematics
Bárbara M. Gutiérrez (7/22/21): Effectual topological complexity
In this talk we will introduce the concept of Effectual Topological Complexity, which is a new version of the Topological Complexity (TC) for G-Spaces. We will state some of its main properties, for instance, we will explain the relation between this notion with the standard version of TC
From playlist Topological Complexity Seminar
Dan Guralnik (3/23/2023): Wanted: Topologists for Autonomous Robots Community
Topological Complexity (TC) addresses a foundational problem in Robotics from the 2nd half of the 20th century: Quantify the complexity of planning continuous paths through a topological space, regarded as the configuration/state space of a programmable synthetic system. Technological bre
From playlist Topological Complexity Seminar
Steve Scheirer (10/28/21): Relative topological complexity and configuration spaces
Joint work with Bryan Boehnke and Shuhang Xue
From playlist Topological Complexity Seminar
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?
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
Ulysses Alvarez - The Up Topology on the Grassmann Poset
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Ulysses Alvarez, Binghamton University Title: The Up Topology on the Grassmann Poset Abstract: For a discrete poset X, McCord proved that there exists a weak homotopy equivalence from the order complex |X| to where X has
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
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
Emilie Purvine (5/2/21): Homology of Graphs and Hypergraphs
Graphs and hypergraphs are typically studied from a combinatorial perspective. A graph being a collection of vertices and pairwise relationships (edges) among the vertices, and a hypergraph capturing multi-way or groupwise relationships (hyperedges) among the vertices. But both of these ob
From playlist TDA: Tutte Institute & Western University - 2021
Topological similarity of random cell complexes, and applications - Benjamin Schweinhart
Benjamin Schweinhart Princeton University December 10, 2014 Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. I'll introduce the notions of a 'swatch' and a 'cloth',
From playlist Mathematics
Topological Message Passing on GNN | SIMPLICIAL COMPLEXES on CW Networks #ai
We go from Message Passing GNN (MPGNN) to TOPOLOGICAL Message Passing on CW Networks: Lifting a Graph to a higher topological space allows for high-dimensional interactions (greater than 2) given our higher-dim topological spaces. Computational Graph Neural Networks increase its complexiti
From playlist Learn Graph Neural Networks: code, examples and theory
Henry Adams (5/1/21): Bridging applied and quantitative topology
I will survey emerging connections between applied topology and quantitative topology. Vietoris-Rips complexes were invented by Vietoris in order to define a (co)homology theory for metric spaces, and by Rips for use in geometric group theory. More recently, they have found applications in
From playlist TDA: Tutte Institute & Western University - 2021
Andrea Bianchi (12/17/20): An upper bound on the topological complexity of discriminantal varieties
Title: An upper bound on the topological complexity of discriminantal varieties Abstract: A discriminantal variety V is the complement in C^m of the zero locus of a polynomial. Many interesting spaces arise in this way: for example both the ordered configuration space F_n(R^2) and the uno
From playlist Topological Complexity Seminar
Enrique Macias-Virgo (5/27/21): Homotopic distance and Generalized motion planning
Lusternik-Schnirelmann category and topological complexity are particular cases of a more general notion, that we call homotopic distance between two maps. As a consequence, several properties of those invariants can be proved in a unified way and new results arise. For instance, we prove
From playlist Topological Complexity Seminar
José Manuel García-Calcines (6/24/21): Topological complexity using arbitrary covers
Title: Topological complexity using arbitrary covers
From playlist Topological Complexity Seminar
This video is about compactness and some of its basic properties.
From playlist Basics: Topology
Exploring state-space topology in the geosciences - Sciamarella - Workshop 1 - CEB T3 2019
Sciamarella (CNRS) / 11.10.2019 Exploring state-space topology in the geosciences ************************************* Langue : Anglais ; Date : 11.10.2019; Conférencier : Sciamarella, Denisse; Évenement : Workshop 1 - CEB T3 2019; Lieu : IHP; Mots Clés :
From playlist 2019 - T3 - The Mathematics of Climate and the Environment