Modeling Shapes and Fields

The Fall 2022 SDS Seminar Series continues on Friday, October 7th from 2:00 p.m. to 3:00 p.m. with Dr. Sayan Mukherjee (Professor of Statistical Science at Duke University). This event is virtual.

Title: Modeling Shapes and Fields

Abstract: We will consider modeling shapes and fields via topological and lifted-topological transforms. Specifically, we show how the Euler Characteristic Transform and the Lifted Euler Characteristic Transform can be used in practice for statistical analysis of shape and field data. The advantage of these transforms is we can analyze sets of shapes that are not diffeomorphic, indeed the shapes can have different topology. We also state a moduli space of shapes for which we can provide a complexity metric for the shapes. We also provide a sheaf theoretic construction of shape space that does not require diffeomorphisms or correspondence. A direct result of this sheaf theoretic construction is that in three dimensions for meshes, 0-dimensional homology is enough to characterize the shape. We will show applications of these ideas to radiogenomics as well as evolutionary models to test for selection in shape phenotypes. This talk will combine topology/geometry with statistics and probability. Knowledge of geometry and topology is not required.