Abstract

In this speculative and informal talk, I will share some research progress and open problems at the intersection of machine learning and spectral geometry.  My talk will consider two problems:

How can the theory of and algorithms for spectral geometry benefit applications in machine learning? How can machine learning tools accelerate numerical solution of spectral geometry problems?

In particular, we will see how ideas from spectral geometry can help featurize 3D shapes and entire datasets, as well as how neural networks, neural ODEs, and other function representations suggest new approaches to solving spectral geometry problems in practice. Joint work with Ana Dodik, Hamid Kamkari, Mohammad Sina Nabizadeh, David Palmer, Dmitriy Smirnov, Oded Stein, Yu Wang, and other members of the MIT Geometric Data Processing group.