Pedro Sáenz is a mentor first, researcher second.

As a professor in the math department, he leads the Physical Mathematics Lab — a fully equipped experimental space where students dive into hands-on physics research. Here, they don’t just assist with projects; they design and run their own experiments, from forming a hypothesis to publishing their findings in academic journals.

“Getting involved in research early completely changes how students see science,” Sáenz shares. “In class, there’s usually a clear problem with a clear answer. But in the lab, it’s different. You face open-ended questions where no one knows the outcome.”

Sáenz’s field is deeply interdisciplinary, blending mathematics, physics, and engineering — which makes his research challenging because the problems are examined from very different angles. But for Sáenz, that’s where the magic happens.

“Students learn patience, persistence, and how to make progress through small, logical steps when the path isn’t obvious,” he explains. “They also learn that failure is part of the process. Experiments rarely work the first time — or even the second — and that’s okay. It’s how discovery happens.”

He adds: “Research makes them mature in so many ways. Seeing that transformation is one of the most rewarding parts of my job.”

Sáenz will be one of 26 participants at this year’s Research and Discovery Fair, part of University Research Week, on Wednesday, October 22 from 11 a.m. to 2 p.m. at the FPG Student Union. The event showcases active research spaces across campus — all offering opportunities for students to get involved.

UNC Research Stories sat down with Sáenz to learn more about his work and why student research experiences matter. 

What’s the main goal of your research?

We study seemingly simple systems — like a dish of liquid on a vibrating table — to uncover complex behaviors that reflect some of nature’s biggest mysteries. It’s about finding big ideas hiding in systems that at first seem almost trivial.

My team studies how tiny droplets “walk” across the surface by bouncing and creating waves that push them forward. These droplets behave in ways that resemble quantum particles — the fundamental building blocks of matter and energy, such as electrons and photons. This gives us a new way to explore the strange and fascinating world of quantum physics, but in a system we can actually see and measure.

What projects are you working on now?

Our main focus is how these “walking droplets” mimic quantum behaviors like tunneling and interference. One project looks at how many droplets move together, forming patterns that resemble a single wave — something we once thought only happened in certain quantum systems.

We’ve also discovered “galloping bubbles” that move in unexpected ways. Even though the mechanism is different from that of walking droplets, many of the underlying principles are the same. With this new way of making bubbles motile, we’re starting to explore potential engineering applications.

What are the biggest challenges in your research?

We’re often exploring phenomena that haven’t been studied before, so there’s no clear roadmap. That can feel daunting at times, but it’s also what makes the work exciting. We keep our setups simple and take small, logical steps to uncover the physics. We also approach problems from every angle — experiments, simulations, and theory — which takes time but leads to deeper understanding.

What’s the most surprising discovery your team has made recently?

We found that walking droplets can exhibit a behavior called Anderson localization, where droplets get trapped instead of spreading, even though they have enough energy to keep moving. This trapping arises from the waves the droplets themselves generate and until now we thought that this phenomenon was exclusive to quantum particles. Seeing this in a fluid system was unexpected and shows how rich and subtle these droplet behaviors can be.

If your research could solve one big problem, what would it be?

We would love to resolve the odd behaviors and paradoxes of quantum particles from a new perspective. Quantum mechanics is an extremely successful theory, but several of its foundational principles are very strange and difficult to accept. There are no complete explanations, and scientists are often asked to just accept them as they are. If our work could offer a new way to see and understand these mysteries, it could change how we think about physics.

What’s the coolest tool you use in the lab?

Our high-speed cameras let us slow down time and see what’s happening when droplets bounce, waves form, or bubbles deform. To the naked eye everything looks chaotic, but when you record thousands of frames per second you suddenly see a precise sequence of events and patterns that were hidden before.

Our custom vibrating tables are just as important because they give us unprecedented precision in how we drive the fluid. Even tiny changes in vibration can completely alter the dynamics, so having that level of control is what makes our experiments possible. Together, these tools let us reveal and measure behaviors that would otherwise remain invisible.

What do students gain from working with you?

They learn how to design experiments, use advanced equipment, and analyze data. They also usually pick up coding and simulation skills. Just as important, they learn how to tackle open-ended problems where there isn’t a clear answer and stick with a project from start to finish.

Most of our undergraduates end up coauthoring a paper, but it takes time and dedication. Along the way they learn the whole process, from preparing and submitting a manuscript to presenting their work orally at conferences or seminars. Those experiences give them a real taste of research and a set of skills they carry into whatever they do next.