Robert D. MacPherson

Is the Abstract Mathematics of Topology Applicable to the Real World?

Robert D. MacPherson; Randall D. Kamien; Raúl Rabadán
Hermann Weyl Professor, School of Mathematics; University of Pennsylvania; Columbia University
May 1, 2015
Topology is the only major branch of modern mathematics that wasn't anticipated by the ancient mathematicians. Throughout most of its history, topology has been regarded as strictly abstract mathematics, without applications. However, illustrating Wigner's principle of "the unreasonable effectiveness of mathematics in the natural sciences", topology is now beginning to come up in our understanding of many different real world phenomena.

Measuring Shape With Homology

Robert MacPherson
Institute for Advanced Study
April 7, 2010

The ordinary homology of a subset S of Euclidean space depends only on its topology. By systematically organizing homology of neighborhoods of S, we get quantities that measure the shape of S, rather than just its topology. These quantities can be used to define a new notion of fractional dimension of S. They can also be effectively calculated on a computer.