As Professor of Mathematics Dan Cristofaro-Gardiner prepares for one of his field’s biggest stages this summer, his recent string of honors reflects a career built on curiosity, collaboration and surprising connections.
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This summer, mathematicians from around the world will gather in Philadelphia for the International Congress of Mathematicians (ICM)—the largest and most prestigious conference on mathematics in the world. Meeting only once every four years, the ICM is often called the Olympics equivalent in the field of mathematics because it recognizes the most influential figures in the discipline.
In July, University of Maryland Professor of Mathematics Dan Cristofaro-Gardiner will take the stage as one of only a few handful of invited speakers, a distinction that puts him among a select group. For any mathematician, it’s a career-defining moment—but for Cristofaro-Gardiner, this opportunity marks another milestone in an extraordinary run.
In 2025, Cristofaro-Gardiner won the prestigious Michael Brin Prize in Dynamical Systems, an international award for outstanding contributions by early-career mathematicians. He also delivered the historic Marston Morse Lectures at the Institute for Advanced Study, a series of talks celebrating the 100th anniversary of groundbreaking work that helped shape modern mathematics.
For Cristofaro-Gardiner, this latest invitation to present at the ICM is even more meaningful because he won’t be the only Terp there; three other UMD mathematicians—Uri Bader, Dmitry Dolgopyat and Adam Kanigowski—were invited to present as well.
“Four of us will speak, which definitely puts UMD among the most in the world,” he said, noting that UMD’s representation at the event reflects the university’s considerable strength in the field. “I feel extremely excited and honored to be recognized alongside them.”
Unseen connections that changed everything
Ask Cristofaro-Gardiner how he arrived at this moment, and he’ll refer to his days as a Ph.D. student at the University of California, Berkeley. While searching for a research direction, he encountered a paper that seemed extremely surprising.
Mathematician Clifford Taubes had taken ideas from string theory and mathematical physics—fields that appeared to have nothing to do with planetary motion—and used them to solve a decades-old problem about periodic orbits, in a field going back centuries.
“Think of the solar system,” Cristofaro-Gardiner explained. “Planets move, interact through gravity, cycle through space. The question is whether there are configurations where the entire system returns to exactly the same state.”
Taubes found a cosmic reset button by using these unrelated tools, a discovery that inspired Cristofaro-Gardiner’s own research. His goal was to see if it was possible to find other kinds of periodic orbits.
The answer, it turned out, was yes—and then some. Using techniques from what’s called low-dimensional topology, Cristofaro-Gardiner and his collaborators showed that certain systems don’t just have a few periodic orbits, but a large number of them. His results revealed abundance where other mathematicians had searched without much success, leading to one of several breakthroughs recognized by the Brin Prize.
Cristofaro-Gardiner’s celebrated paper on the Simplicity Conjecture, published in the Annals of Mathematics with collaborators Vincent Humilière and Sobhan Seyfaddini, earned a Bourbaki seminar—one of the highest honors in mathematics—and was featured in a National Science Foundation article as solving “one of the mysteries of two-dimensional shapes.” Among the five papers by Cristofaro-Gardiner that were cited for the Brin prize, two focus on symmetries of the sphere and recovering volumes from periodic orbits, both showcasing his ability to bridge seemingly distant mathematical worlds.
Cristofaro-Gardiner is especially drawn to such surprises in math.
“For example, take four-dimensional space,” he said. “You might assume that as dimensions increase, things simply get more complicated; that four dimensions is harder than three, seven is harder than four and so on.”
But the truth is stranger, Cristofaro-Gardiner noted. In every dimension except the fourth, there’s fundamentally only one way to do calculus in standard space.
“Only in dimension four do you have infinitely many different ways of doing calculus,” he said. “Four dimensions is special, strange, uniquely rich. And it comes with another surprise: this fact actually connects directly to planetary motion and the kind of periodic orbits I study.”
For Cristofaro-Gardiner, these unexpected connections made his participation in the Marston Morse Lectures particularly meaningful to him. Morse was one of the first to theorize that there could be interesting relationships between geometry and dynamics.
“His work asked if you could deduce what shape you’re living on simply by studying functions defined on it. Can you tell you’re on a sphere just by measuring latitude, temperature or some other property at every point?” Cristofaro-Gardiner explained. “That’s also a fundamental theme in my own work and his ideas continue to generate new ones.”
Building a community
Since joining UMD in 2021 from the University of California, Santa Cruz, Cristofaro-Gardiner has built his work around collaboration, supervising three Ph.D. students, teaching reading courses with two others and co-organizing events like the Informal Geometric Analysis seminar.
“Research is interesting, particularly groundbreaking research, because you really have to push on the frontiers of human knowledge,” he reflected. “If I’m just sitting at my desk working alone—and of course, sometimes that is just what’s needed—my thinking can be isolated in my mind, like in a completely closed system. You never know which stray comment or unfamiliar technique can unlock your next breakthrough.”
Cristofaro-Gardiner believes that seminars, collaborations and even casual hallway conversations contribute to “a very rich intellectual environment.” He attends and helps organize multiple meetings across geometry and dynamics at UMD, welcoming new ideas that might not have entered his consciousness otherwise.
For students, these events serve another purpose: bridging the gap between settled knowledge and active research.
“Usually, what you will learn in a course is settled science,” he pointed out. “I’m teaching algebraic topology that was worked out 50 years ago, stuff that’s important and foundational but not what we’re grappling with today. Seminars can let students really learn what we’re doing in the field right now, putting faces to names, discovering which problems remain unsolved.”
As Cristofaro-Gardiner prepares for his talk in Philadelphia, he remains focused on his dual mission: advancing human knowledge and giving the next generation of mathematicians the resources they need to succeed.
“It’s wonderful to see UMD, a public university, so strong in my field,” he said. “I’d love to just do my part to make sure that our students have access to a world-class mathematical experience.”
Written by Georgia Jiang
