Research

According to the geometry of Einstein’s theory of gravity, a straight line can be perpendicular to itself, and the distance between a point and itself can be infinite! This is because concepts such as length, angle, distance, and curvature all depend, not just on the shape of the space you are studying, but also on the ruler and protractor you are using.  Studying these shapes, together with the different kinds of “geometries” available on them, is one of my primary research interests.

What do distances we measure on a surface tell us about how it curves? As it turns out, quite a bit. And if we know how it curves everywhere, can we determine if it has a hole like a bagel or two or three holes like a pretzel? If we consider all the shapes a balloon can take, is the perfectly spherical one, the one whose curvature is most equally distributed everywhere? Can we tell if we are walking on a surface whether we can continue forever, or are bound to fall off it at the horizon? In differential geometry, we explore such questions on spaces that may have more than just the two dimensions that surfaces have. Complex geometry explores the same topics on spaces that are constrained in ways that are related to the invention of complex numbers.

What is a good statistical model? My goal is understanding the practice and theory of Statistics.

What is the need for these models? But raw data is too chaotic. All the information is there, but it’s so wild that we can’t use it.

A statistical model partitions data for our consumption. It provides a framework for understanding existing data and predicting future data.

I’m currently interested in Bayesian models, and in the variety of computational methods that make them work. I enjoy working from data, applying the practice, and reconciling results. I also enjoy the mathematical study of these and other statistical models.

Natalia Sternberg’s research interests include applied mathematics, differential equations, and scientific computing. She collaborates with physicists and engineers on modeling plasmas.