Tuesday, February 25, 2020
02/25/2020 - 4:15pm
This is an expository talk on various methodologies to integrate and build geometries as they relate to analytic tasks.
The simplest paradigm is the construction of good metrics on a space given a collection of functions. This requires building a metric on the functions as well as on the space (duality).
Various geometric organization methods are going to be described as well as applications to empirical Riemannian geometry using Deep Neural Nets leading to a discrete version of isometric embeddings.
02/25/2020 - 6:00pm
An Apollonian circle packing is an ancient Greek construction which is made by repeatedly inscribing circles into the triangular interstices of four mutually tangent circles, via an old theorem of Apollonius of Perga (262-190 BC). After explaining constructions, I will introduce various geometric and arithmetic problems regarding these circle packings.