Mathematics Assistant Professor Srivatsav Kunnawalkam Elayavalli discusses the surprising link between math, music and paragliding. 

By Jason P. Dinh

When Srivatsav Kunnawalkam Elayavalli plays the veena, he lets his mind roam. The four-foot-long Indian instrument resembles an oversized banjo with a basketball-sized resonator protruding from the top of its neck. Elayavalli plucks its strings like a bassist, bending them to warp the note as he sings a lilting melody. 

But Elayavalli doesn’t rely on sheet music to guide him. He plays ragas—ancient melodic frameworks refined over thousands of years of musical tradition—which, like jazz music, encourage exploration and improvisation. 

“Playing the veena is a form of meditation. It’s a form of yoga in South India,” said Elayavalli, an assistant professor of mathematics at the University of Maryland, who learned the instrument during graduate school at Vanderbilt University. “It opens up creativity; it opens up the brain to new possibilities.” 

While many may view music and mathematics as disparate interests, Elayavalli, who joined UMD in July 2025, sees a common pursuit. In both cases, he seeks beautiful ideas. These ideas may be easier to identify in musical motifs than mathematical theorems, but Elayavalli knows beautiful math when he sees it. Such ideas stand on tradition, he said, yet they push boundaries in unexpected ways and elegantly advance multiple disciplines.

At UMD, Elayavalli studies von Neumann algebras—the mathematical foundation of quantum mechanics, a field that produced several luminaries including two Fields medalists in the past half-century. He applies his expertise in this space to advance other fields of mathematics as well. Now, he plans to collaborate with some of UMD’s more than 200 quantum researchers, and he suspects his command of von Neumann algebras can advance both disciplines. 

Charting such vast terrain may seem daunting, and making interdisciplinary breakthroughs requires willpower, practice and exploration. Luckily, Elayavalli is well-equipped for the challenges, thanks to his experience on the veena.

“My musical training has really enhanced my research,” Elayavalli said. “It allows me to think in different directions without fear. The way I approach mathematics—the relationship I have with the unknown—it's much more affectionate because I work on that on a daily basis in music.”

Detective work on von Neumann algebras

To conceptualize von Neumann algebras, Elayavalli notes that you must first consider how you navigate the world. The 3D space you’re in and the 2D graph paper you use are considered Euclidean space, where you can measure lengths and angles the way you’re taught in geometry class. Euclidean spaces can be generalized into Hilbert spaces, which allow for more complexity—for instance, a space with infinite dimensions. 

Within Hilbert space, you can perform actions on objects and preserve their structure. For example, you can rotate or reflect a triangle around an axis, and it will still be a triangle. These actions are called bounded operators. Bounded operators can be combined into structures called operator algebras, and a special class of these that satisfy a property called the double commutant theorem is defined as von Neumann algebras. 

Elayavalli researches how to “classify” von Neumann algebras. He identifies subtle but important differences called invariants that distinguish them—a challenging task because operator algebras can have many components and structures. 

Elayavalli compares it to distinguishing two people who are buried under many layers of clothes that conceal their identities. He draws from ideas in dynamics, probability theory and geometry to strip back those layers and identify invariants. 

The impact of Elayavalli’s work stretches beyond his discipline. He says his key research accomplishment to date was applying his expertise in von Neumann algebras to solve long-standing problems in classifying a separate group of operator algebras called C*-algebras. 

For weeks on end, Elayavalli and his colleagues dedicated more than 12 hours per day to reading the literature and drawing up calculations on the board as they tried to push past the roadblocks that bested other mathematicians. They only realized they were on the precipice of a breakthrough after Elayavalli had a late-night epiphany while reading a paper at his home. 

“After that, I don’t think I slept for three weeks,” Elayavalli said. “Every night, my co-authors and I would have these multi-hour phone calls even at 1 a.m., day after day after day.” 

His research team of early-career researchers, consumed by its progress, finished the paper within three weeks and published it in the leading journal Inventiones mathematicae in October 2025. The findings quickly snowballed into another breakthrough in a mathematical logic challenge called the C*-algebraic Tarski problem, which is an operator algebraic analogue of the famous Tarski’s problem from 1945, concerning the notion of elementary equivalence. The findings led to rapid progress in the past year, with nearly 35 papers published on the topic by various teams of mathematicians around the world. 

“These were some of the best moments of my life,” he said. “The resolutions of these problems are some of  the key achievements of my career so far.” 

A life in search of beauty

It may not be so surprising that Elayavalli’s recent contributions lie outside of von Neumann algebras. For him, harmoniously integrating different disciplines is a key tenet of a beautiful mathematical idea. 

Now that he’s at UMD, Elayavalli spends much of his day cross-pollinating with other faculty members, students and postdocs in the mathematics department. Inspired by a recent paper on quantum physics that greatly influenced von Neumann algebras, Elayavalli plans to collaborate with the myriad quantum scientists around campus as well. 

As his career advances, Elayavalli continues to be guided by beauty—toward breakthrough mathematical ideas and entrancing performances on the veena, as well as flying high in Maryland’s natural world. 

He is a licensed paraglider, a hobby he picked up as a faculty member at the University of California San Diego. 

“In San Diego, my life was essentially three things: research, paragliding and music,” Elayavalli said, laughing. 

He is excited to get airborne in western Maryland’s mountains once the weather warms. Ironically, leaping off a cliff is, for him, a grounding experience.

“I don’t paraglide for adrenaline,” he explained. “I do it because it’s a liberating experience. When you’re in the air, you can’t think about anything other than paragliding. It brings me down to Earth and makes me focus on appreciating life.”