A University of Utah - Department of Mathematics Publication | 2025
LETTER FROM THE CHAIR
DEAR FRIENDS,
MATH IS EVERYWHERE . It's not just confined to textbooks or classrooms; it's an integral part of our daily lives and the world around us. From the patterns in nature to the technology we use, math is fundamental to understanding and interacting with our environment.
It’s also foundational to artificial intelligence (AI). In fact, following the prompt of my opening sentence, AI generated the next two sentences in a matter of seconds, along with this one: Key mathematical areas like linear algebra, calculus, and probability are essential for developing algorithms, representing data, and enabling AI to learn and make predictions.
Our newest major, bioinformatics, is emblematic of how AI and machine learning are helping mathematicians and life science researchers advance their work as well as shaping their line of questioning.
Looking ahead, the department is prepared to lean into what’s next. We have hired six new faculty members, one of whom, our own alumnus Chris Miles PhD’18, will help “blaze a new trail” with the bioinformatics degree. You can read about him and the other new faculty in this issue of Aftermath, along with news about the many awards, fellowships, and scholarships with which our community has been recognized.
I hope you will enjoy our cover story featuring mathematicians Ken Golden and Jody Reimer’s trip to the Arctic to study sea ice, as well as our feature on student success and the innovative ways—including AI—that we are supporting it.
Currently, higher education is experiencing rapid change. While these shifts bring opportunity, they also bring challenges. Federal research dollars are being stripped away, and in Utah the state
legislature is requiring the U and other state-funded colleges and universities to cut budgets.
We want you, our friends, supporters, and alumni to know that math is not only integral to our daily lives but so are our institutions, including the U. College students are the future, and as graduation rates continue to rise, we know that these young individuals will be tomorrow’s leaders and innovators in our communities—all of which benefit the University FOR Utah.
These graduates secure highpaying, sustainable careers that are going to be the foundation of our economy, our reputation abroad as Americans, and our moral leadership globally. I hope you will consider a donation to the department in support of our operations, our student scholarships, and our faculty development.
At the recent AI Summit hosted by the John and Marcia Price College of Engineering, the tone was one of hopefulness and even wonder. While there are concerns and challenges related to this new AI-driven era – perhaps even as profound as the steam engine in the industrial revolution and
computers in the information age - there is also a great deal of excitement at the possibilities.
Our students embody that excitement and keep us motivated . . . as do you. Thank you for taking this journey with us.
RECOGNITION
UNIVERSITY OF UTAH
PRESIDENTIAL SCHOLAR
SEAN LAWLEY
SLOAN RESEARCH FELLOW
KURT VINHAGE
NSF CAREER GRANT
ANNA LITTLE
HAROLD BLUM
SIMONS FELLOWS
MLADEN BESTVINA
YEKATERINA EPHSTEYN
EARLY CAREER
TEACHING AWARD
PRIYAM PATEL
INTERNATIONAL CONGRESS OF MATHEMATICIANS
SRI IYENGAR
UU HEALTH CENTER FOR MEDICAL INNOVATION
- BENCH TO BEDSIDE COMPETITION
SPENCER MARX
USHE BOARD MEMBER
MUSKAN WALIA
GOLDWATER SCHOLAR
SYLVIA MESICEK
NSF GRADUATE
RESEARCH FELLOWSHIP
CONNOR SHRADER
ASSOCIATION FOR WOMEN IN MATHEMATICS WINNER
U OF U STUDENT CHAPTER, COMMUNITY OUTREACH
IN MEMORIAM
DON HARRELL TUCKER
Professor 1930 - 2025
DOMINGO TOLEDO
Professor | 1945 - 2025
FRANK STENGER
Professor | 1938 - 2024
KLAUS SCHMITT
Professor | 1940 - 2025
Sincerely, Chair Tommaso de Fernex
Cover: Nash Ward, an undergraduate student in mathematics, drilling his first sea ice core.
Credit: Nash Ward
Aftermath is the official magazine of the Department of Mathematics, University of Utah, published in partnership with Marketing & Communications, College of Science.
Associate Director of Marketing & Communications: Bianca Lyon
Writer & Editor: David Pace
Designer/Photographer: Todd Anderson
Follow us on social media @uofumath
Prefer only a digital version of Aftermath? Send us an email. office@math.utah.edu
by IZABELLA BOURLAND & MICHAEL JACOBSEN
UNDERSTANDING THE INTERSECTION OF MATHEMATICS, PHYSICS, BIOLOGY, AND ENVIRONMENTAL SCIENCE OFTEN REQUIRES STEPPING OUTSIDE OF THE CLASSROOM AND INTO THE NATURAL WORLD.
for students to develop a deeper understanding of polar research.
For Jody Reimer, assistant professor in the Department of Mathematics and the School of Biological Sciences, and Ken Golden, distinguished professor in the Department of mathematics and adjunct professor in the Department of Biomedical Engineering, this means venturing out into the Arctic where they can study how the physical environment affects life in and on the ice with the help of mathematical models.
In May of 2024, Golden and Reimer coled a field research trip to Utqiaġvik, Alaska. Though a fairly regular excursion, especially for Golden who has had 19 excursions to the frozen poles of our world, this one was special. The researchers were accompanied by a varied team of mathematics students ranging from high schoolers to PhD candidates, providing them invaluable hands-on experience in the unique and extreme conditions of the Arctic ecosystem. It was an opportunity to test mathematical models and field techniques. It was also a rare chance
Reimer focuses on how changes in sea ice impact polar bear and seal populations and how these animals respond to those changes. She is also fascinated by the microbes that inhabit the ice itself and the adaptations that allow them to survive in such a harsh environment. Golden’s research focuses on the complex multiscale physical properties of the ice, from modeling macroscale ice floe dynamics down to calculating the porosity and permeability of its microscale brine inclusions. Together, Reimer and Golden are exploring the complex interplay between physics and biology.
This interplay goes far deeper than one might expect, as Golden is able to make ties from astrobiology to military stealth technology and everything in between. He eagerly explains that “The math doesn’t care! It cross-pollinates all over the place. The same mathematics we use to analyze how algae get nutrients from the brine phase can be used to monitor the onset and progress of osteoporosis in human bone!”
This interdisciplinary work is why mathematics research is so critically important. It discovers patterns and correlations that ripple across the scientific community, providing the best possible tools to make new breakthroughs.
The 2024 outing was the largest field team ever led by Golden and Reimer’s first time leading a field research expedition. Because of this, organizing the trip proved to be both a complex task and a valuable learning experience. There was the logistical planning and coordination with university legal teams since students were being introduced to harsh conditions which necessitated
every safety protocol possible. The group also needed to acquire land use permits from the local Iñupiat groups of indigenous peoples. Students played a hands-on role in this process, packing equipment and troubleshooting issues in the field. Working with the Barrow Arctic Research Center (BARC), which provided accommodations and some logistical support, the stars were aligned to allow for a successful expedition.
Moving so much equipment across the ice had to be done carefully, especially with the occasional polar bear stopping by to say hello. Once out in the field, these mathematicians braved the Arctic cold in springtime— wind chill dropped to as low as 20° below 0 F on their first day—to carry out experiments linking their mathematical models to real-world observations.
Watching math students immerse themselves in field research was one of Reimer’s favorite parts of the trip. She has earlier explained that “Mathematics isn’t relegated to the realm of puzzles and isolated problems. There’s fundamental and deep connections that affect all regions of life.” Research like this perfectly demonstrates these connections, reinforcing her belief in the value of interdisciplinary integration as a crucial step in advancing applied mathematics.
relevant in the modern day with the advancement of technology which was a major feature of this trip as new programs and equipment could finally be tested. One such highlight was a tool called a PlanktoScope, an opensource and portable imaging device that allows researchers to analyze microbial life in sea ice samples.
More affordable than traditional flow microscopy equipment, this tool allows for broader access to high-quality image data collection. In Reimer’s lab, she and her students have since been analyzing the living organisms in the frozen samples
This integration is especially
they brought back from the Arctic. A few of these scientists are taking that technological integration a step further, processing the resulting images using AI-based tools that help sort and analyze thousands of microscopic snapshots of life hidden in the ice.
The trip’s success underscores the importance of hands-on fieldwork in mathematical research. Measurements that were collected align with the existing literature and will serve as pilot data for future projects and funding proposals. By blending mathematical modeling with empirical observation, students and faculty alike gain valuable insights
into complex environmental systems.
Golden and Reimer have been analyzing the data they collected in the Arctic for a year now and are well on their way planning the next expedition. “We’re laying the groundwork for a broader suite of physical measurements, and ramping up on the biological side of things,” says Golden. This expands on their findings and further explores the intricate relationships between ice, living beings, and the rapidly changing polar marine environment.
Funding for this trip was provided by the National Science Foundation through the Applied Math Research Training Grant. The agency provided funding for two trips with the second planned for next year. And, thanks to the work that’s been done so far, this follow-up expedition is shaping up to be something truly special. <
MODERNIZING MATH CLASSES FOR STUDENT SUCCESS
by ETHAN HOOD
A CORE TENET IN TEACHING MATHEMATICS IS CREATING AN ACCESSIBLE ENVIRONMENT FOR STUDENTS TO LEARN.
This applies to all resources available—whether it’s the support of an instructor, the materials used to foster learning, or additional services such as tutoring. It’s also fundamental to mitigating what’s called high DEWI (low or failing grade, withdrawal, incomplete) rates in math courses.
PHILOSOPHY OF TEACHING PRACTICES
A key consideration in teaching math is recognizing the diversity of the class and the uniqueness of each student. Some students thrive in group environments, while others are efficient independent thinkers. “Everyone's at a different level, so teaching for everyone is a difficult balance,” says faculty member Dalyana Guerra who outlines her strategy: “Assess your students' needs
by getting to know them, [and] asking questions. Walk around the classroom, and don't just stay up front. Physical proximity to students can make a big difference. If you just lecture, you'll never be able to adapt your teaching.”
Tactics such as these as well as connecting concepts to student’s reallife experiences can help lower math anxiety. “The best way to do that is to not take it so seriously,” adds Guerra. “If you asked my students about my teaching style, many would say it's casual, with lots of jokes and mistakes. When I make mistakes, I laugh about it. Math is a human experience.”
UPGRADES & STREAMLINING
A major departmental initiative supporting student success is the comprehensive redesign of Instructure Canvas course pages, an online learning platform that U instructors use for classroom management, sharing course materials, and communicating with students. In the new design, Canvas tools display information in multiple places, but it only needs to be updated in one place. With a single change, instructors can update the entire course page, ensuring synchronization and reducing errors. Additionally, familiar tools like Gradescope are incorporated to allow students to review assignments, request regrades, or seek clarification.
MyLab Math is also used, offering problem-specific tools tailored to different learning needs.
AI INTEGRATION
UBot, the U's friendly neighborhood virtual tutor, functions similarly to platforms like ChatGPT, but with a specific focus on the Socratic approach to tutoring. Rather than solving problems outright, it guides students through the learning process.
“We're in the early days of figuring out how to help our students use it effectively,” says faculty member Rebecca Noonan-Heale. “I often think about how we can encourage students to use it. What opportunities are there to incorporate it?” Common student uses include seeking step-bystep guides, reviewing prerequisite knowledge, creating reference materials, simplifying math notation, and reducing math anxiety.
Through a multifaceted approach that leverages interpersonal connections with refined course features and tools, the math department is steadily progressing toward greater student success. The professors in this enterprise are key. Says faculty member Aleksandra JovoanovicHacon, “I am always looking for new ways to help students succeed.” <
REMEMBERING DOMINGO TOLEDO
by JIM CARLSON
DOMINGO TOLEDO , A PROFOUNDLY INFLUENTIAL GEOMETER AND A BELOVED MENTOR, PASSED AWAY EARLIER THIS YEAR AFTER A LONG AND IMPACTFUL CAREER IN MATH.
He was known not only for his deep contributions to geometry and topology, but also for his clarity of thought, generosity of spirit, and dedication to his students and collaborators.
Toledo earned his PhD in mathematics from Cornell University in 1972 where he focused on the Atiyah–Bott fixed point formula which foreshadowed the depth and geometric intuition that would characterize his long career.
From 1974 to 1978, he served as a J. F. Ritt assistant professor at Columbia University, after which he joined the faculty at the University of Utah where he remained from 1986 onward as a professor of mathematics. There, he became known for his work in complex manifolds, algebraic topology, locally symmetric spaces, and complex hyperbolic geometry.
Toledo was awarded a Sloan Research Fellowship (1982–84) and was named a David P. Gardner Fellow in 1982. In 2016, he was elected a Fellow of
the American Mathematical Society for his fundamental contributions to complex and algebraic geometry and to the study of Kähler groups.
Toledo made pioneering use of harmonic maps to study the topology of complex projective varieties, with particular attention to rigidity phenomena. His 1993 paper in Publications Mathématiques de l’IHÉS gave the first explicit examples of compact projective varieties with nonresidually finite fundamental groups, answering a longstanding question posed by French mathematician JeanPierre Serre.
Equally notable was Toledo's collaboration with Larry Tong in the 1970s and 80s. Together, they developed the theory of twisting cochains and twisted complexes— innovative Čech-theoretic tools that enabled local, explicit constructions of characteristic classes and pushforward maps. These became foundational in analytic proofs of duality, the Lefschetz fixed-point formula, and Grothendieck–Riemann–Roch theorems in the holomorphic setting.
Toledo was also deeply engaged with moduli problems and the geometry of locally symmetric spaces. His 2011 work on the plurisubharmonicity of energy functions over Teichmüller space further bridged harmonic analysis and complex geometry.
His legacy endures not only in the theorems that bear his influence, but in the generations of students and colleagues who carry forward his love of geometry and his example of intellectual integrity. <
REMEMBERING DON TUCKER
“I AM NEITHER RETIRED, NOR ACCORDING TO MY COLLEAGUES, RETIRING,” THE LATE DON TUCKER ONCE SAID, “THOUGH MANY OF THEM WISH I WERE BOTH.”
Referring to his upbringing in Texas: “I’m told that I’m mean, ornery, and cussed. I guess I learned it from the horses I broke back in Throckmorton.”
A professor of mathematics at the U for over 64 years, Tucker focused his research on differential equations and functional analysis, authored over 40 papers and books in those areas, served as editor of compendia and was an organizer of mathematical conferences. Donations in his memory can be made to the Don H. Tucker Post Doctoral Fellowship. <
NEW FACULTY
JUNGLES AND GYMS
“A math contest is much like training in a gym,” says Daniel Sinambela, quoting an instructor who would become his PhD mentor. “You know what you are training for, you know the machines you’ll use. But math research is training in the jungle, where you have no idea what you’re about to run into.”
A structured environment vs. volatile and wholly unpredictable exploration is the difference between known solutions and research questions that may not even have an answer. It’s a fascinating contrast Sinambela looks back to at the onset of joining the U’s South Korean campus.
Throughout his education, Sinambela’s research has focused on the area of nonlinear partial differential equations, specifically those that govern the motions of fluids. In this field he’s using equations like freeboundary water waves, Euler and Navier-Stokes, and Stokes-transport. He is studying existence theory and the stability/instability of solutions of those equations.
While he’s eager to teach in his new
environment—to show students the ropes in these mathematics gyms— he hopes to show them the wonders of its jungle too. < ~Michael Jacobsen
BLAZING A NEW TRAIL
The new bioinformatics major is a trailblazing endeavor that new math faculty Chris Miles will soon be joining. Or perhaps “rejoining” would be the better word to use here as Miles is a Utah alumni. “It’s an exciting chance to build something new here; it’s a perfect project-based subject to design classes around.”
“In this field, you often have biological data from an experiment and have to figure out what to do with it. I want to expose students to that process, present data and encourage them to figure out how to use it. There’s no right answer!” That’s the beauty of a new degree, there’s no tradition that must be adhered to, so you truly get to design whatever works best.
Miles will also continue his research in mathematical biology, which includes the applications of modeling and AI with biological data. Machine learning allows researchers to survey all data in a set simultaneously and
find patterns or equations. In the study of cells, these equations work to help us understand why cells work so well despite being built by seemingly random and disorderly molecular building blocks.
Miles describes a field of two extremes where “some researchers will write equations for what they think is true of biology while others let AI decide. I think it's fun to walk between the two extremes and take the best aspects of both.” < ~Michael Jacobsen
COMMUNITY AND UTILITY
David Schwein’s research primarily deals with symmetry, using the Langlands program to study connections between the representation of p-adic groups, number theory and Galois theory. Across this educational arc he’s traveled to almost 20 countries, giving him a wide range of exposure to how math is approached across the globe.
He describes the international network of professional puzzle solvers who can (and usually need) to work together to pursue new breakthroughs. It’s an aspect of the field that often goes unnoticed in what he calls the stupor of
complicated lectures, which Schwein hopes to avoid.
“You’ve got to break students out of that stupor and get them communicating about ideas, coming up with examples,” he says. “It helps if they’re a little skeptical, questioning how something can be true. I’m looking forward to helping students see the beauty and structure of math, how it’s another science that tells us about the real world.” <
~Michael Jacobsen
KNOWING YOUR AUDIENCE
“When wearing the teacher’s hat and not the researcher’s,” says Uri Shapira, “I believe it is my job to give service. It’s an attitude that says, ‘Okay, let’s look and see what is best for this audience.’”
A biologist, he says, doesn’t need to understand the history of a formula or how it was developed. They just need to know how to use it as a tool. But a math major benefits from that history, understanding what the original problem was and how a new tool was created to solve it. By understanding that process—how such discoveries came to be—students will be better suited to make their own breakthroughs in the future.
of Jerusalem then spend his postdoc at ETH Zurich, which paved the way for a faculty position at TechnionIsrael Institute of Technology. He brings to the U a decade of teaching experience, paired with research into how questions in number theory can be approached with the tools of dynamical systems. <
~Michael Jacobsen
FINDING THE RIGHT QUESTIONS
For Petar Bakic , originally from Zagreb, Croatia, mathematics is about finding the right questions to ask rather than seeking the answers to them.
His work centers on representation theory—a field in mathematics that employs linear algebra concepts (such as matrices) for studying the symmetries of spaces. Though inherently abstract, it connects to other applicable fields including harmonic analysis, geometry, number theory, and physics.
FINDING THE PERFECT PITCH
Tim Tribone has a knack for finding new approaches to meet each student’s needs and interests, a skill he developed from his own educational journey. Originally a music major, he eventually shifted towards math following the guidance of a mentor. He would continue working his way to a PhD from Syracuse University before taking a postdoctoral researcher position here at the U.
Introduced to mathematics by his older brother, Shapira would go on to graduate from the Hebrew University
Abstract math researchers are often unheralded, as the complexity and nature of their research means it is not broadcasted to the general public to the same degree as other research fields. But Bakic is part of a broad research community that is conducting research at an unprecedented rate—helping to advance our collective understanding and to push the frontiers of mathematics. < ~Ethan Hood
Along the way, Tribone has learned the importance of helping students at the level they currently are. For his undergraduate researchers he’s learned from his music major experience to create an environment that shows them what a career in math is like. But for his students in business math, it’s far more important to treat math like a toolbox, focusing more on direct use and applications so a student can recognize, for example, why an Excel equation isn’t working.
This sort of teaching is Tim Tribone’s focus moving forward as he takes a faculty position at the U. Any student can learn and excel in mathematics, you just need to find the right level for them to do so. < ~Michael Jacobsen
COMPMATH MEETING
THE NATIONAL SCIENCE FOUNDATION MARKS ITS 75TH ANNIVERSARY THIS YEAR, AND TO CELEBRATE, COMPUTATIONAL MATHEMATICIANS GATHERED AT THE UNIVERSITY OF UTAH MAY 8-9 FOR THEIR ANNUAL MEETING.
The conference highlighted the latest advances in the field of computational mathematics, articulated and illustrated by approximately 250 attendees from across the nation.
Organized, with others, by the math department’s Yekaterina Epshteyn, the meeting featured diverse presentations—everything from the design of robust algorithms for various solutions of mathematical models to computational mathematics advances of data science and artificial intelligence.
“It was not only a wonderful and productive event for those who attended,” says Epshteyn of the event,
”it was a gratifying accomplishment for all the work supported by the NSF Division of Mathematical Sciences Computational Mathematics program, for the university and for the future of Utah.” <
2024 PRESIDENTIAL SCHOLAR FACULTY MEMBER
SEAN LAWLEY WAS NAMED A 2024 PRESIDENTIAL SCHOLAR, ONE OF FIVE ANNOUNCED BY U PRESIDENT TAYLOR RANDALL.
To hear Lawley talk about the power of math, you would think he was describing a magical tool that answers the unanswerable and predicts the future. To an extent, you’d be right.
Lawley has published more than 70 papers, many with undergraduate mentees—in less than 10 years— about the power of probabilistic models and analysis to answer questions in physiology and medicine. He uses stochastic math to answer questions like, Can a cryopreservation procedure delay menopause? If so, How much tissue and what age is needed to be most effective? What nutritional supplements can speed up arsenic detoxification of the body? What should you do if you miss a dose
of a prescription medication?
Through math, Lawley is able to answer questions that couldn’t be found in a lab or by any other means. “The equations become the laboratory from which you can explore and do experiments and solve some of these things,” Lawley says. “What I get really excited about and am passionate about is using mathematics to improve public health, to make an impact. I think mathematics is a very purposeful tool—a very big hammer.” < ~Amy Choate-Nielsen
CELEBRATING SIMONS FELLOWS
The Department of Mathematics celebrates the recognition of two professors on achieving a Simons Fellowship: Mladen Bestvina and Yekaterina Ephsteyn.
MLADEN BESTVINA
Originally from Croatia, Bestvina earned his undergraduate degree at the University of Zagreb before completing a PhD at the University of Tennessee in 1984. After beginning his academic career at UCLA, he joined the U in 1994. His research lies in topology, with a focus on geometric group theory—an area that explores algebraic structures
through geometric and topological methods. As a Simons Fellow, he values the honor and the opportunity to participate in programs at the Isaac Newton Institute in Cambridge and SLMath Sciences Institute in Berkeley.
YEKATERINA "KATYA"
EPHSTEYN
Ephsteyn earned her undergraduate degree in applied mathematics and physics from the Moscow Institute of Physics and Technology in 2000 before immigrating to the United States as a refugee. She completed her PhD in mathematics at the University of Pittsburgh in 2007, followed by an
EARLY CAREER TEACHING AWARD
Associate professor
Priyam Patel is a recipient of the U's 2024 Early Career Teaching Award. Regarding her innovative and impactful teaching, one student noted her use of
mastery-based grading for homework assignments. “This approach, coupled with metacognitive exercises, demonstrates her dedication to teaching students not only what to learn but also how to learn.” Patel believes in continually striving to “improve my teaching strategies to
NSF-RTG postdoctoral fellowship at Carnegie Mellon University.
Her current research focuses on two major areas: the development of mathematical and computational models for microstructure evolution in polycrystalline materials, and the design of robust, structure-preserving algorithms for hyperbolic balance laws and related systems with uncertainty. These efforts not only address fundamental mathematical challenges but also have wide-ranging applications in engineering and the physical sciences. This past May she helped organize and host the annual NSF CompMath meeting at the U. < ~Izabella Bourland
… ensure that all of my students can thrive as mathematicians in the classroom and beyond.”
Patel’s research lies in the fields of low-dimensional topology, hyperbolic geometry, and geometric group theory. <
SLOAN RESEARCH FELLOWSHIP
THE ALFRED P. SLOAN FOUNDATION ANNOUNCED THE WINNERS OF THE 2025 SLOAN RESEARCH FELLOW. AWARDED THIS YEAR TO 126 OF THE MOST INNOVATIVE YOUNG SCIENTISTS ACROSS THE U.S. AND CANADA, THE SLOAN RESEARCH FELLOWSHIPS ARE ONE OF THE MOST COMPETITIVE AND PRESTIGIOUS AWARDS AVAILABLE TO EARLY-CAREER SCHOLARS.
This year Kurt Vinhage, U assistant professor of mathematics, is a recipient. The award is often seen as a marker of the quality of an institution’s faculty success in attracting the most promising early-career researchers to its ranks. Since the first fellowships were awarded in 1955, 73 faculty from the U have received the award.
Vinhage works to understand classification questions in dynamical systems. “Any progress I have made,” says Vinhage, “is thanks to many hours of collaborative effort, and I would like to thank my co-authors and mentors, especially Anatole Katok and Ralf Spatzier, for their advice and encouragement throughout my journey.”
Vinhage’s research in part answers questions about when two flows commute with one another. “Suppose we have a flow A and a flow B,” explains Vinhage. “One could follow flow A for an amount of time, then flow B for an amount of time, or do it in the opposite order, B then A. The flows commute when we end up at the same place.” This special situation is not common and Vinhage’s work aims to describe under what conditions such flows belong to a limited family of constructions, or when they can be more “exotic.”
“There are several seemingly innocuous conditions one can put on the flows which force them to belong to a well-described and wellstudied class,” he continues. “Such phenomena fit into research programs called "higher-rank rigidity," "the Katok-Spatzier conjecture," and "the Zimmer program."
Says Jon Chaika, a colleague who nominated Vinhage for the Sloan
Fellowship, "Kurt shows how some natural assumptions on a system automatically imply it arises from a single family of beautiful constructions. Beyond this, he showed that if one weakens these restrictions there are more examples.” Chaika details some of Vinhage’s activities in the area of teaching, including a summer program Vinhage runs to introduce students to advanced mathematics immediately after calculus, a once-a-semester mini workshop with colleagues at nearby Brigham Young University and Utah Valley University, and multiple successful student seminars, one of which led to a paper.
Vinhage earned his PhD from Pennsylvania State University in 2010 followed by postdoctoral studies at the University of Chicago and Pennsylvania State before arriving at the U in 2021.
“We are thrilled that Kurt Vinhage has received the prestigious Sloan Fellowship,” says Tommaso de Fernex, chair of the Department of Mathematics at the U. “This award recognizes research accomplishments of the highest-caliber by early-career scientists.” De Fernex cites Kurt’s contributions to Dynamics which “exemplify the excellence of his scholarship and his potential as a future leader in the field. <
ICM-INVITED SPEAKER
THE INTERNATIONAL CONGRESS OF MATHEMATICIANS (ICM) IS THE MOST SIGNIFICANT GATHERING IN THE FIELD OF MATH, HELD EVERY FOUR YEARS AND BRINGING TOGETHER RESEARCHERS FROM AROUND THE WORLD.
Srikanth Iyengar, professor and director of graduate studies in the department, has been invited to
speak at next year’s ICM scheduled to take place this coming summer in Philadelphia. ICM serves as a central stage for presenting groundbreaking work, fostering international collaboration, and shaping the direction of future research. One of its highlights is the awarding of the Fields Medal and other distinguished prizes which recognize transformative contributions to mathematics.
Being invited to speak at the ICM is considered one of the highest honors in the profession, as it reflects the recognition of a mathematician’s work by the global community and places them among the leading figures in their field. <
LEADERSHIP TRANSITIONS
MATH FACULTY MEMBER
AKIL NARAYAN HAS BEEN APPOINTED ASSOCIATE DEAN FOR UNDERGRADUATE AND GRADUATE STUDIES IN THE COLLEGE OF SCIENCE.
As a member of the U's Scientific Computing and Imaging (SCI) Institute, Narayan has a broad research agenda at the forefront of computational innovation, machine learning, model reduction and uncertainty quantification, among others. He has previously held many departmental and university roles, including serving on an Academic Senate subcommittee and as a member
of the Executive Committee of the Department of Mathematics. In addition to Narayan, two other associate deans have been announced by Interim Dean Pearl Sandick: Lauren Birgenheier (Geology & Geophysics) for faculty affairs and Matthew S. Sigman (Chemistry) for research.
Additionally, College of Science
Dean Peter Trapa has accepted an offer to serve as the inaugural vice provost and senior dean of the Colleges and Schools of Liberal Arts and Sciences (LAS). As the first to hold this newly created position, Trapa will provide strategic advancement and management of the College
of Humanities, College of Science, College of Social and Behavioral Science and the School for Cultural & Social Transformation. Together, these units form the cornerstone of enrollment at the U, positioning Trapa to play a pivotal role in shaping the educational experience of students across disciplines.
Replacing Trapa in the College of Science as interim dean is Pearl Sandick , former associate dean in the College of Science and a theoretical particle physicist studying physics beyond the Standard Model, including possible explanations for the dark matter in the Universe. <
Iyengar at his chalkboard.
Credit: Matt Crawley
SPENCER MARX
APPLYING MATH SKILLS TO MEDICAL INNOVATION
by JULIA ST. ANDRE
A RECENT GRADUATE OF THE UNIVERSITY OF UTAH’S APPLIED MATHEMATICS PROGRAM, SPENCER MARX LED HIS TEAM TO SUCCESS AT THE U’S BENCH TO BEDSIDE COMPETITION, EARNING THE GRAND PRIZE FOR THEIR HANDHELD ULTRASOUND DEVICE NAMED ALOE.
The annual competition brings together students from different disciplines to design and prototype medical technologies.
Marx, who completed his degree in spring 2025, chose applied math over computer science after realizing the foundational role math plays in artificial intelligence. “Math is going to be more important in the future of AI,” he says. “The fundamentals all derive from calculus, linear algebra, and probability.”
His idea for Aloe dates back to high school when frequent medical visits
inspired him to imagine a portable imaging tool for home use. “I had a lot of medical issues myself,” he explains. “I thought, maybe there’s a way to automate this so people can do it at home.”
In college, Marx met electrical engineering student Nathaniel Fargo who had the technical expertise to help turn the vision into reality. Together, they built Aloe, a handheld ultrasound tool that uses AI to automate and interpret images. Their prototype focused on shoulder health, detecting signs of rotator cuff damage before serious injury occurs.
The team selected ultrasound for its portability and low cost compared to other imaging methods, with potential applications ranging from pregnancy monitoring to cancer screening. By using AI to analyze weekly scans, Aloe could make preventative care more accessible. “There are not nearly enough
technicians to look at one image per week for every person,” Marx says. “AI opens up new preventative medicine avenues because you can handle much higher volumes of data.”
Marx’s main role was developing the algorithms behind the device. To build a complete prototype, he and Fargo assembled an interdisciplinary team including electrical, biomedical, and mechanical engineers, as well as biology students. The group worked through challenges such as replacing traditional ultrasound gel with a more user-friendly hydrogel. With prize funding, the team continues refining Aloe with the long-term goal of securing FDA approval and developing a market-ready product.
For Marx, the project confirmed the practical power of mathematics across disciplines. “If you’re good at calculus and linear algebra, you can be incredibly useful in engineering or product development,” he says.
“Studying math can be as impactful as studying engineering or computer science—it just depends on how you apply it.” <
ABOVE THE NOISE
by MICHAEL JACOBSEN
IN THE CONSTANT CHAOTIC COMMUNICATION OF THE MODERN DAY IT IS VITALLY IMPORTANT TO FIND PROMISING INDIVIDUALS AND RAISE THEM ABOVE THE NOISE.
That is the role of the CAREER program, funded by the National Science Foundation (NSF): to find talented researchers and give them funding to catapult their work to new heights. Anna Little has earned her place amongst those recipients, receiving a grant of $550,000 to advance to the next stage of her career. Colleague Harold Blum also received the grant.
A Duke University alumna, Little received her PhD in mathematics there before moving on to a teaching position at Jacksonville University. In an ambitious gamble she left that tenure track position for a postdoctoral researcher appointment at Michigan State, which clearly paid dividends by setting the groundwork for research she’s being rewarded for today here at the U. Little’s work focuses on using geometric methods for highdimensional data analysis, a particularly useful subject. While current technology allows us to collect huge amounts of data, it is
often difficult to analyze that data in numerical form. But analyzing it geometrically can circumvent this issue, visually presenting shapes and patterns amongst the chaos. It is an approach that can be applied to many forms of data, and as Little describes, it really helps break up the “noise.”
“If you’re trying to take a picture of a molecule, you’re going to have a lot of noise in that data,” Little explains, defining that “by noise I mean measurement errors, random shifts or rotations. You’re trying to extract data from a complicated setting.” Noise of this kind is often unavoidable and can start corrupting data, but that’s where the math comes in to repair those gaps.
On top of this high dimensional analysis, Little is also interested in inverse problems and signal processing. In particular, the analysis of mathematical models inspired by biological applications such as cryoelectron microscopy.
When she isn’t looking for these patterns inside the noise, she often spends her time assisting others to take a break from their own noisy lives. In an initiative that was also supported by her award, she led a retreat for doctorate students and postdocs. In such a highly strenuous field like STEM it can be challenging to find time to take care of oneself, leading to unsustainable performance. Little explains that “It’s important to
work smart, to avoid burning out, and to understand one’s limits.”
Whether it is the noise of her research or the noise of life, Anna Little is taking the steps to both overcome it and help others do the same. And thanks to this award she’ll be able to continue to do so for many years to come.
HAROLD BLUM
The CAREER award is not Blum’s first connection with the NSF. Under the mentorship of Department Chair Tommaso de Fernex, he held an NSF Postdoctoral Fellowship at the U culminating in a position of assistant professor also at the U.
His research focuses on algebraic geometry, specifically in the area of higher dimensional shapes. A particular aim of his that the grant is financing is to develop theory for constructing parameter spaces of Calabi-Yau manifolds, a concept used heavily in string theory. Currently on leave from U, he has taken a position as assistant professor in the School of Mathematics at the Georgia Institute of Technology in Atlanta. <
Thank you for making Math students a priority! Generous and thoughtful alumni and donors like you are helping students succeed in Mathematics! To meet the demand for STEM graduates in Utah, our top priorities include Math Department Scholarships and other Areas of Greatest Need.
Scholarships and hands-on experiences are more important than ever for our students. Your support can help them stay enrolled, focus on their studies, graduate on time, and avoid burdening debt!
Our goal is to provide direct scholarship support to mathematics students and to increase the graduation rate of math majors.
Every donation is important— even $25, $50, or $100 will make a big difference. Will you help Math students today?
We appreciate all that you do for students here in the College of Science. Together, we can reach our goal to create a brighter future for science and math education in Utah.
For more information about giving to Mathematics, contact:
James "Jim" DeGooyer Associate Director of Development