In this talk, I will discuss how incorporating geometric information into classical learning algorithms can improve their performance. The main focus will be on optimal mass transport (OMT), which has evolved as a major method to analyze distributional data.  In particular, I will show how embeddings can be used to build OMT-based classifiers, both in supervised and unsupervised learning settings. The proposed framework significantly…

Qualitatively, a tipping point in a dynamical system is when a small change in system inputs causes the system to move to a drastically different state. The discussion of tipping points in climate and related fields has become increasingly urgent as scientists are concerned that different aspects of Earth’s climate could tip to a qualitatively different state without…

In many recent works, analysis and number theory go beyond working side by side and team up in an interconnected back and forth interplay to become a powerful force. Here I describe two distinct meetings of the pair, which result in sharp counts for equilateral triangles in Euclidean space and statistics for how often a random polynomial has Galois group not isomorphic to the full symmetric group. https://ncsu.zoom.us/j/91896366693?pwd=YnFuZURGc1NNenRTQ3YrbjVTK0dQZz09 Meeting ID: 918 9636 6693 Passcode: 875811