Benjamin Jaye Awarded Simons Fellowship

Imagine a restaurant door swinging open, then closing again. You hear a burst of noise: chattering voices, clattering silverware, and shuffling feet. Now imagine if the sound were to go on for a long time — hours, days, or even years. You’d probably start to hear it as something you could tune out, a drone of noise without the individual “frequencies” that make up the noise.

School of Mathematics Associate Professor Benjamin Jaye has been awarded a prestigious Simons Fellowship in support of his research into these types of related qualities (like time and frequency), and how precisely we can know one without knowing the other.

Called the Fourier uncertainty principle, it’s a centuries-old subject, but progress on this topic is still in its infancy, Jaye says. Using mathematics, he will unravel how much information, or partial information, is needed about a function’s frequencies in order to determine what the original function is.

Advancing fundamental mathematics

While his work centers on theory, there are a number of fields that can benefit from it.

“These problems interest me as basic questions in harmonic analysis,” a fundamental area of mathematics used for research in fields ranging from quantum mechanics to neuroscience, Jaye says, adding that “the specific forms I am interested in arose from work in probability theory — in particular, understanding the probability that a system is reliable over a long period of time.” 

This type of reliability analysis and probability theory plays a crucial role in predicting how safe equipment and processes are, and could lead to advancements in more reliable public transportation to safer planes.

Jaye also notes applications for partial differential equations, in particular “dampening” a wave function to ensure that energy is lost at a certain rate — a critical area of research for controlling and predicting waves, with applications in engineering, physics, and optics.

“I have had many amazing colleagues who have piqued my interest in these questions over the last ten years,” Jaye says. “The Simons Fellowship gives me an important opportunity to develop mathematical theories around them in a systematic way.”