The Niyogi-Smale-Weinberger Approximation Theorem
Josué Tonelli-Cueto (TU Berlin)
At the end of the 19th century, the artists Georges Seurat and Paul Signac developed the technique of pointillism, which is based in the idea that a continuous shape can be represented by a discrete cloud of points. This principle, which is the foundation of all screens, was incorporated almost a century later to what is known as Topological Data Analysis. However, how good can a cloud of points approximate a geometric object?
In this talk, we will review the Niyogi-Smale-Weinberger Approximation Theorem which relates how difficult is to approximate topologically a geometric object by a cloud of points to the geometric quantity known as reach.
Talk given during the 6th BMS Student Conference on the 21st of February of 2018.
