An Accidental Advisor, a Serendipitous Direction - Profile Rodrigo Gonzalez Hernandez

When Rodrigo José González Hernández arrived at the Oden Institute for Computational Engineering and Sciences, he thought he knew his path. The son of a doctor and an administrator, he grew up in a household where education was highly valued. His parents introduced Rodrigo and his brother to as many science opportunities as they could find in his home country of Guatemala. “I knew I wanted to do science since I was very young,” said Rodrigo. 

His scientific world opened up at age ten when he and his brother joined the first cohort of a new astronomy program at a local university in Guatemala City. Classes met on weekends; they took exams and even wrote a small thesis. “As it turns out, I essentially completed my first year of undergraduate studies in astronomy as a 10-year-old – envision a kid giving a presentation to a university class full of adults!” he exclaimed. He wrote a thesis on measuring the orbits of Jupiter’s moons using Kepler’s laws and a backyard telescope. 

While in high school, he competed in Science Olympiads in math, physics, and biology. Those international trips and experiences led him to study in the US, where he received scholarships to Emory University. According to Rodrigo, seeking a Ph.D. in mathematics in his home country was not an option. “That doesn’t exist. If I wanted to do science, I had to leave,” he said.

During his years at Emory a professor guided him to specific coursework, and gave him an undergraduate thesis in cardiovascular mathematics that combined all his interests. “That’s when I really became involved in the research side of things,” said Rodrigo. He initially hoped to continue that research at the Oden Institute's Computational, Science, Engineering and Mathematics graduate program at The University of Texas at Austin. However, an initial pragmatic meeting meant to sort out first-year courses ended with something unexpected: a dissertation advisor.

“I went in to ask about tracks and classes, and came out with an advisor, which is a bit unusual for a first-year grad student,” he recalls, laughing. Though it altered his original research idea, Rodrigo said, "In the end, it turned out to be a great fit." His advisor, Professor Irene Gamba, is a renowned mathematician. “Dr. Gamba is phenomenal in many ways and in addition to being my advisor, she has also become a great friend,” he added.

Gamba’s work in kinetic theory would pull González’s interests into a new direction. For someone trained in pure and applied mathematics, with a long-standing love of physics and comfort in coding, the combination proved ideal. 

The shift meant letting go of his undergraduate cardiovascular project – something he doesn’t regret. “I’m happy where I am,” he says. “It’s different, but it’s the right kind of different.”

Discovering Structure Where None Was Expected

Working with Gamba’s research team with the Applied Mathematics Group, Rodrigo encountered a turning point on his research track. “Dr. Gamba handed me a 2018 paper on numerical approximations for the Boltzmann equation and asked the simplest kind of hard question: could the method extend to the Landau equation?”

In kinetic theory, the Boltzmann equation describes the statistical behavior of a dilute gas under short, isolated collisions; the Landau collision operator extends that framework to account for Coulomb (electrical) interactions, making it more appropriate for plasmas. González began to port the technique.

What happened next felt, in his words, “magical.” 

“I don’t think any of us were expecting the results we have achieved. When I implemented it for Landau, a very particular property emerged.” At first, he thought months of coding had gone wrong. “I was sure I’d broken something. It was just blank.”

That “blank” turned out to be the signature of deep mathematical structure. The sparsity wasn’t a bug; it was a feature that could be proved, generalized, and exploited to design significantly faster, more accurate solvers. Rodrigo, along with Professor Gamba and collaborators in Germany and beyond, chased the insight across variations of the problem, including the relativistic Landau equation (where particles approach the speed of light). Each extension revealed more architecture to leverage and more of the hidden mechanics within the equations.

“Philosophically, it taught me something,” he says. “You improve simulations by studying the structure, or the mathematics of the equations, and then translating that structure into algorithmic tools. That’s where you find both elegance and speed.”

Rodrigo emphasizes the collaborative nature of the breakthrough. “Through collaboration, everyone gave me pieces. I was just in the position to connect them for this research.”

Rodrigo’s describes kinetic theory as a probabilistic way of modeling systems with an enormous number of particles. Instead of tracking each particle exactly - a computational impossibility - kinetic theory describes the distribution of particles in phase space (a combination of position and velocity). That distribution evolves over time according to equations like Boltzmann, Landau, and Vlasov.

If “approximation” sounds abstract, “simulation” may be the more intuitive word. “I do simulations of plasmas in kinetic theory,” said Rodrigo. The nuance matters: plasmas, which are ionized gases of charged particles, interact through electromagnetic forces over multiple scales. The Vlasov equation describes the long-range, collective dynamics, while the Landau equation models localized, short-range (collisional) effects. Plasmas in fusion devices experience both, which is why decoupling and studying each in turn and then recombining them thoughtfully matters.

The practical upshot: better mathematical models and faster solvers mean researchers can predict plasma behavior more reliably and at larger scales. That’s crucial for designing and controlling confinement devices and for getting closer to the holy grail of fusion energy.

Last year, Rodrigo had two opportunities to delve deeper into research. The first, was a summer internship at Los Alamos National Laboratory. There, he worked on numerical methods for the Vlasov equation. The experience was markedly different from academia. “At a national lab, there’s more focus on a specific problem. You use similar tools of math and code, but the mindset is: here’s the problem, let’s get from A to B.” He continues to collaborate part-time with Los Alamos.

Last fall, he spent a semester at Simons Laufer Mathematical Sciences Institute (SLMath) in Berkeley, CA, where he was immersed in a program on kinetics. Rodrigo was awarded the Stephen Della Pietra Graduate, which is awarded to only one Ph.D. student per semester. The institute gathered leading mathematicians and postdocs from around the world. “It’s a niche field, but an important one. By the end, I felt like I’d met most of the big names,” he says. “For a Ph.D. student, that’s huge, especially when you’re thinking about your next steps.”

The Oden Effect: Interdisciplinary and Community

Before he gets to those next steps, Rodrigo is in his final year of his Ph.D. research at the Oden Institute – an environment that has helped him persist through the challenges “I love it here,” he says, noting the culture of collaboration which made the grueling first year survivable. “One of the best parts about my time at the Institute are my friends. We all come from different backgrounds and share ideas. Some of my best coding practices came not only from coursework, but also from friends in this community – they have literally contributed to my work in many ways,” Rodrigo said. The broader UT ecosystem has also provided support, where he’s developed relationships in the both the Math and Physics Departments as well as the Institute for Fusion Studies. “Being able to walk down the hall and talk to someone in pure math or in fusion physics - those perspectives sharpen the work.”

On the computational side, Rodrigo runs large-scale jobs on Lonestar6 at the Texas Advanced Computing Center (TACC), constructing and operating on the sparse “cubes” (tensors) that define his methods. “High-performance computing isn’t optional here, it’s foundational,” he stated.

Regarding his research, Rodrigo is careful to draw the line around his expertise. “I’m a computational scientist and mathematician, not an engineer,” he says. When it comes to fusion research, he understands the stakes. Fusion promises a safer, cleaner energy future: no greenhouse gases, no long-lived radioactive waste, and vastly better intrinsic safety than fission (if the plasma loses confinement, the reaction simply stops). Achieving it reliably on Earth, however, requires controlling a plasma hotter than the sun’s core while keeping the surrounding structures extremely cold - an engineering feat at the very edge of what’s possible.

Even on the math side, the problems are formidable. “We’re still doing baby, toy problems,” he admits. “These equations are incredibly complex. You can spend an entire Ph.D. just nudging the boundary forward.”

That he finds joy in the nudging is clear. “Those moments when you connect things, when the messiness crystallizes, are rare and wonderful,” he says. “They don’t usually come early in a career. I feel lucky. There aren’t many known Guatemalan scientists. I’m excited to have my name added to the list.”

Like most graduate students, Rodrigo’s inspiration ebbs and flows. “I’m not inspired all the time,” he says. “Enjoyment comes in seasons.” What keeps him steady is a love of challenge, and activities outside the lab. He weightlifts, trains for triathlon, plays guitar, and reads widely. “Exposure to many perspectives helps me make connections,” he says. “That’s true in reading as much as in research.”

Back to that astronomy program he took as a 10-year-old. Due to legal issues, Rodrigo waited eight years before being officially awarded the degree – he notes that the degree equivalency level is not the same as in the US, and said the program is still going and has expanded. Diego, the brother he referenced, is working on a Ph.D in astrophysics in California. “Our stories are intertwined,” he says, smiling.

He and Gamba are preparing a manuscript on the Landau extensions and related theory, which he hopes to submit by summer. As for life after the Ph.D., that story is still unfolding. For the immediate future, Rodrigo is entertaining two summer opportunities: one to return to Los Alamos Lab and another for an academic visit to Brown University.

Asked about a dream project, he returns to fusion. “If we can make it happen – fusion energy – I’d be happy to be part of it. It won’t be just me though. It will be generations of scientists. But being one of them? That would be enough."