Today at Brown

On a piece of paper, Mirjana Vuletic draws two cubes in a corner. Then she draws two more, so they’re stacked on each other. In a three-dimensional world, the stacked cubes have a certain shape, a defined pattern, she says.

Imagine that stack of cubes in the corner has mushroomed to some number approaching infinity. What would it look like in a three-dimensional setting?

Believe it or not, it would look like a curve gently sloping from the ceiling to the floor.

That’s a pattern, too, says Vuletic, an incoming assistant professor of mathematics.

Vuletic says what she studies is statistical physics. “I study the laws of physics on a large-scale to conclude whether there’s a pattern there,” she says.

The idea that patterns evolve, that there’s some natural order that objects will follow, was perhaps first recognized by the physicist Eugene Wigner in his Semicircle Law. Until recently, scholars used mainly probabilistic tools to show that random behavior disappears in the limit. Now, Vuletic said, the field appears to be merging with representation theory, algebraic geometry and number theory.

“No one would use representation theory to study probability,” the 31-year-old Serbian said, “and no one would use algebraic geometry to study probability. There was no connection between the two. They were like separated. People are seeing a connection, but they don’t know exactly why.”

Vuletic comes to Brown fresh from earning her Ph.D. in mathematics at the California Institute of Technology. She studied before that at the University of Novi Sad, about 40 miles northwest of the Serbian capital, Belgrade.

Vuletic said she has always loved math, and, like many others in the profession, the subject came easily — or logically — to her. But there’s more to it than a gift for solving equations that would baffle most others. Math has a beauty, an arresting simplicity to it, and it’s so much more than addition and subtraction.

“If it were just that, I’d never love math,” she said. “You take the most beautiful objects and study them, like an artist. I never had any doubts what I’d do.”

Math also led Vuletic to her husband, Viktor Rozgic, or vice versa. The two (who have a 1-year-old son, Luka) met in Serbia. Rozgic is on track to complete his Ph.D. this year in electrical engineering at the University of Southern California.

Vuletic is no stranger to leading a classroom. She has taught in Novi Sad, and she led large classes every quarter at Caltech. At Brown, she will teach an undergraduate course in calculus for science-oriented students and expects to teach a statistics class in the spring.

“That’s where my experience at Caltech will come in,” she said.