14 Matching Annotations
  1. Jun 2021
    1. To put it succinctly, differential topology studies structures on manifolds that, in a sense, have no interesting local structure. Differential geometry studies structures on manifolds that do have an interesting local (or sometimes even infinitesimal) structure.

      Differential topology take a more global view and studies structures on manifolds that have no interesting local structure while differential geometry studies structures on manifolds that have interesting local structures.

  2. May 2021
    1. In an individual model of privacy, we are only as private as our least private friend.

      So don't have any friends?

      Obviously this isn't a thing, but the implications of this within privacy models can be important.

      Are there ways to create this as a ceiling instead of as a floor? How might we use topology to flip this script?

  3. Jan 2021
    1. In a more recent paper, Michelle Feng and Mason Porter used a new technique called persistent homology to detect political islands — geographical holes in one candidate’s support that serve as spots of support for the other candidate — in California during the 2016 presidential election.
  4. Nov 2020
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  11. Dec 2015
    1. All this time, however, category theory was consistently seen by much of the mathe-matical community as ridiculously abstract. But in the 21st century it has finally cometo find healthy respect within the larger community of pure mathematics. It is the lan-guage of choice for graduate-level algebra and topology courses, and in my opinion willcontinue to establish itself as the basic framework in which mathematics is done