BYU mathematics professor Tyler Jarvis: “I like the fact that mathematical tools aren’t just something to be used in the abstract. Yes, they are beautiful in their own right, but they can also be used to solve problems that many other people are interested in. They can tell us something deep about the nature of the universe.”

“When people say, ‘So what are you working on? Can you explain it?’ my wife just laughs. ‘No, he can’t. Sorry. You’ll never know what he does,’” joked mathematics professor Tyler Jarvis.

Jarvis’s latest research, which was recently accepted for publication in one of the most prestigious mathematics journals in the world—Annals of Mathematics, is a little complicated, but it’s making waves not only in the world of mathematicians but with physicists as well.

For many years, physicists have studied surfaces to try and understand how particles and quantum fields interact, but some aspects of their work lacked a solid mathematical foundation. They made rough arguments for why things should behave a certain way, but the mathematical tools to confirm whether their ideas were correct didn’t exist.

“Theoretical physicists conjectured that there should be four different ways of thinking about these interactions. Two of these theories are well known, like Gromov-Witten Theory and the Landau-Ginzberg ‘B-model.’ The other two, they postulated, should exist, but until recently, no one had any idea how to fill them in,” said Jarvis.

From 2001 to 2008, Jarvis and a team of mathematicians and physicists built the mathematical groundwork to change that. Their extensive research filled in one of these unknown theories with what is now called the Fan-Jarvis-Ruan-Witten Theory.

By establishing their theory, Jarvis and his collaborators formed the mathematical foundation necessary to begin studying the physics of singularities—defined by Stephen Hawking as “a point in space-time at which the space-time curvature becomes infinite,” much like the tip of a cone. This, in turn, will help physicists to further understand particle interaction.

“The hope is that [this] theory provides a simpler way of understanding aspects of quantum interactions. By clarifying how singularities and symmetries work, we made it easier to understand how particles and fields interact, which ultimately tells us something about a fundamental aspect of physics.”

This isn’t the first time that Jarvis has crossed disciplines to solve a problem. In fact, he has always enjoyed using geometry to find solutions to questions in physics. For Jarvis, part of the joy in math comes through applying it to other realms.

“I like the fact that mathematical tools aren’t just something to be used in the abstract. Yes, they are beautiful in their own right, but they can also be used to solve problems that many other people are interested in. They can tell us something deep about the nature of the universe.”