UMD mathematicians identified vaccination strategies that could completely eliminate HPV-related cancers. 

Cervical cancer is the fourth most common cancer for women in the world, with more than 660,000 new cases and nearly 350,000 deaths per year. Now, University of Maryland mathematicians have developed effective strategies to help contain and potentially eliminate the disease. The research, published last week in the journal Bulletin of Mathematical Biology, offers a new mathematical model that can help public health officials design effective vaccination and cancer screening policies.

Abba Gumel, a Distinguished University Professor of Mathematics and the Michael and Eugenia Brin Endowed E-Nnovate Chair in Mathematics at UMD, who holds joint appointments in the Institute for Health Computing and the Institute for Physical Science and Technology. Credit: Mark Sherwood

“The study provides a clear way of showing how science is influencing policy,” said study senior author Abba Gumel, a Distinguished University Professor of Mathematics at UMD who holds joint appointments in the Institute for Health Computing and the Institute for Physical Science and Technology. 

Nearly all cervical cancer cases are caused by human papillomavirus (HPV), which is considered the most common sexually transmitted infection in the world. HPV, a vaccine-preventable disease, is often asymptomatic and resolves naturally within two years in 90% of cases, but persistent infection in the remainder can lead to cancer.

HPV vaccines, which are already offered and recommended in 147 countries, can minimize disease spread and cancer risk. The UMD researchers developed a new mathematical model to assess the efficacy of various vaccination strategies, which they tested with a case study on South Korea. 

“Cervical cancer is one of the few cancers effectively prevented by vaccines,” said study lead author Soyoung Park, a Ph.D. candidate in applied mathematics & statistics, and scientific computation at UMD. “It was important to check if the recent government program for offering vaccines is going to be enough to effectively control the disease in Korea.”

Building a case study for South Korea

The model presented in the study incorporates previously published demographic and epidemiological data to predict how HPV transmits across a population. It stratifies people by sex, vaccination status, HPV infection and cancer progression, and it was calibrated using South Korean cancer data from 1999 to 2020. The model can be used to test how different vaccination strategies fare over time.

Simulations of the model revealed that current South Korean policies are insufficient to eliminate HPV and related cancers in the country. South Korea’s National Immunization Program (NIP), which started in 2016, currently vaccinates roughly 80% of the nation’s girls aged 12-17. Another 30,000 women aged 18-26 receive “catch-up vaccinations” annually. Additionally, the National Cancer Screening Program provides regular Pap tests to detect cancerous lesions for roughly 61% of Korean women older than 20. These existing efforts will reduce HPV-associated cancer burden over time, the authors found, but they will not eliminate the virus. 

“It’s achieving the objective of reducing cases of cervical cancer, but it’s not going to eliminate it,” said Gumel, who has collaborated with the modeling team of Merck Inc., the company that originally developed the HPV vaccine. “The objective is elimination.” 

South Korea could eliminate HPV by expanding vaccine access, the researchers found. The authors explored two scenarios where NIP could be improved. The first involved expanding vaccine access to cover 99% of females. Additionally, because the authors found that immunizing boys has a strong spillover effect of protecting females, the second scenario involved maintaining the current 80% female vaccination coverage while vaccinating 65% of boys aged 12-17. Model simulations suggest that these efforts would eliminate HPV-related cancers in South Korea within 60 and 70 years, respectively. 

Both vaccination strategies for expanded coverage are feasible in Korea given that national coverage for infant immunizations, such as measles, under NIP approaches 98%, Park said. She added that public buy-in for vaccination campaigns is high in South Korea. 

“There’s very low vaccine hesitancy,” she said. 

“Vaccinating boys reduces the pressure of having to vaccinate a large proportion of females,” added Gumel, who also holds the Michael and Eugenia Brin Endowed E-Nnovate Chair in Mathematics. “It makes elimination more realistically achievable.”

Applying the model around the world

The two solutions the researchers propose would achieve herd immunity, meaning that people who cannot be vaccinated—for example, the elderly or those allergic to the vaccine—would be protected against HPV and related cancers. 

“The way to protect them is to surround them with a sea of immunity,” Gumel said. 

The authors showed that while expanding Pap test coverage may only offer marginal benefits, strategies that promote safer sex practices, like condom use, would be very effective in curtailing the burden of HPV and related cancers in communities. 

Now, Park is tweaking the model to explicitly account for the contact dynamics of men who have sex with men, as well as other high-risk groups, such as female sex workers. 

At a conference talk last year in South Korea, Park connected with researchers who work closely with Korean public health agencies. They showed strong interest in sharing data and potentially using the study to improve NIP. She added that the findings are applicable around the world—including in the U.S. 

“We could use different data to compare the lessons learned about HPV to the U.S.,” Park said. “Can we do the same thing? Will the same set of intervention strategies work effectively here?” 

Gumel sees reason to try. He reckons that with the 95% effective Gardisil-9 vaccine offered in the U.S., around 70% coverage would be sufficient to achieve herd immunity.

“We do not have to be losing 350,000 people globally to cervical cancer each year,” Gumel said. “We can see an end to HPV and HPV-related cancers if we improve the vaccination coverage.”

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UMD mathematics Ph.D. candidate Hyunah Lim co-authored this article with Gumel and Park.

The paper, “Mathematical Assessment of the Roles of Vaccination and Pap Screening on the Burden of HPV and Related Cancers in Korea,” was published in Bulletin of Mathematical Biology on December 3, 2025.

This research was supported by the U.S. National Science Foundation. This article does not necessarily reflect the views of this organization.

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.”

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