The UC Santa Cruz mathematics department has been put on the map with recent recognition from the American Mathematical Society (AMS), an organization devoted to mathematical research and education across the nation.
Richard Montgomery and Maria Schonbek, mathematics professors at UCSC, and Harold Widom, professor emeritus of mathematics at UCSC, were named AMS Fellows on Nov. 1.
According to the AMS website, Fellows are chosen based on their “outstanding contributions to the creation, exposition, advancement, communication and utilization of mathematics.”
“Personally, I’m delighted to see my colleagues in the math department recognized for their great service to mathematics,” said Martin Weissman, the undergraduate vice-chair of the UCSC mathematics department.
Montgomery, Schonbek and Widom were recognized for their multiple contributions of research to the larger field of mathematics.
Montgomery, a UCSC faculty member since 1990, is most well-known for his work on the centuries-old Three Body Problem.
“The Three Body Problem is how three planets or three stars move,” Montgomery said. “If they’re pulling each other by their own gravitation, then they move in complicated ways.”
Montgomery’s work on the Three Body Problem has not only influenced the field of mathematics, but also physics and astronomy.
“If everything’s kind of close together, same distance apart and all the masses are the same, then you get very complicated motions,” Montgomery said. “And what myself and a collaborator found is motion — where all three masses chase each other around in a figure eight shape.”
A small, new field called “choreographies” sprung from Montgomery’s work with this problem, Montgomery said. This field focuses on the ways in which celestial bodies — like those studied by Montgomery in the Three Body Problem — physically interact with one another.
“They’ll be five masses chasing each other around kind of a four leaf clover,” Montgomery said. “And complicated flower shaped arrangements where you can have any number of masses moving around in complicated ways.”
Widom, a UCSC faculty member since 1968, is most well-known for his work on Random Matrix Theory.
The Random Matrix Theory has been used to help explain certain aspects of atomic theory. Widom’s work has contributed to research in physics as well as mathematical progress.
“It would take more than a moment, maybe a year, [to explain] since it’s very technical,” Widom said.
Schonbek has been a UCSC faculty member since 1986. Her work involves Navier-Stokes equations, which were introduced in 1934.
“This was an open problem for over a half century,” Schonbek said, “And I was able to solve it. For this I introduced a technique which I called ‘Fourier splitting’.”
“Fourier splitting” is a technique developed by Schonbek used to study equations that model the behavior of fluids, Schonbek said.
“[Navier-Stokes equations] are fundamental in fluid dynamics,” Schonbek said. “They are used to model blood flow, ocean currents, weather and other physical phenomena.”
Schonbek’s work has an interdisciplinary focus.
“I have been extending my research in other directions,” Schonbek said. “Recently I have started to work on problems related to neurobiology.”
Montgomery said having three AMS Fellows gives UCSC mathematics much needed publicity.
“You’ve got to toot your own horn,” Montgomery said. “Mathematicians, we’re not good at tooting our own horns. The stereotype of the nerdy mathematician has some truth to it, and we just … sit in our office and do our work. For me, it’s good just to have some presence because we have a very good and very small math department. It’s nice to be recognized.”