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Goldwater Scholars 2024

Goldwater Scholars 2024

Two College of Science students awarded the prestigious Goldwater Scholarship for 2024-25

The Barry Goldwater Scholarship is a prestigious award given to undergraduate sophomores and juniors who intend to pursue research careers. Goldwater Scholars often go on to hold distinguished research and leadership positions across many disciplines. For the 2024-2025 academic year, 438 scholarships were awarded to college students across the country. At the University of Utah, two undergraduate students have earned the honor of becoming Goldwater Scholars: Muskan Walia and Nathan Patchen.

Nathen Patchen

“Biochemistry was a great way for me to combine my love of biology and chemistry and understand not only how things work, but why,” says Nathan Patchen about what motivated him to pursue research in that field. Patchen was awarded the Goldwater Scholarship for his work in Yang Liu’s lab, an assistant professor of biochemistry at the Spencer Fox Eccles School of Medicine

Patchen describes his research as broadly being focused on DNA damage repair. He says “[w]e have access to revolutionary gene editing tools that, when used in conjunction with advanced imaging techniques, allow us to explore how cancer cells undergo DNA damage repair as never seen before. Personally, I am doing this by implementing a modified CRISPR-Cas9 that allows us to capture time-resolved images after damage and then produce data about the kinetics of repair.” 

After graduating from the U, Patchen hopes to pursue an MD/PhD to practice medicine while continuing his research on gene editing and aging. Outside of his time in the lab, he enjoys being active through swimming, biking, and running as he trains for an IRONMAN 70.3 in St. George, Utah in May. 


Muskan Walia

“Mathematics is at the cusp of interdisciplinary research” says Muskan Walia. During the College of Science ACCESS Scholars research program, she reflected on her academic interests and goals. She explains, "I wasn’t interested in studying any discipline in a vacuum or in isolation. Rather, I wanted to work on mathematics research that centered justice and informed public policy.”

The majority of Walia’s undergraduate research sprouted from her time in ACCESS where with the help of Fred Adler in the mathematics department at the College of Science, she began to adapt an epidemiological SIR model to predict the number of cells infected with SARS-CoV-2. Since then, she has created other models to further answer her questions about disease. These include a “... model of disease progression within an infected individual, a model of an antigen test, and a model of symptoms to evaluate how testing can be used to limit the spread of infection.”

“Ultimately, I want to lead a team that utilizes mathematical principles to tackle the most pressing social justice related questions of our time.” Walia is one of 57 awardees honored this year who intend to pursue research in mathematics or computer science. Besides innovating mathematical models, Walia enjoys spending time outside bird watching with her mom and gardening with her grandmother.



By Lauren Wigod
Science Writer Intern




2024 Class of SIAM Fellows: Aaron L. Fogelson

2024 Class of SIAM Fellows: Aaron L. Fogelson

April 4, 2024

The Society for Industrial and Applied Mathematics (SIAM) has honored Aaron L. Fogelson's distinguished work with its fellows program.


This year's 26 esteemed fellows were nominated in recognition of their outstanding research and service to the community. Through their various contributions, SIAM Fellows form a crucial group of individuals helping to advance the fields of applied mathematics, computational science, and data science.

A professor of mathematics at the U, Fogelson, who lists his research interests as mathematical physiology, modeling of blood clotting, gels and viscoelastic fluids and numerical solution of partial differential equations (PDEs), is being recognized by SIAM for his pioneering work on mathematical modeling and numerical methods for platelet aggregation and blood clotting.

"Clotting is an extremely complex process with physical, chemical, and cell biological components which is essential to maintaining the integrity of our circulatory system," he writes on his faculty profile. "When it malfunctions the consequences can be dire, including heart attack and stroke. Clotting is subject to intense research by laboratory and medical scientists but its complexity makes it very difficult to think through how it works or to make predictions about how well medical interventions to treat clotting problems will work. That is where mathematics and the work I do comes in."

On his lab's website, Fogelson writes, "Because transmural pressure differences vary greatly in the circulatory system and because blood flowing at different speeds through vessels of widely varying diameter leads to great variation in shear stress, the challenges of forming a blood clot to stop the outflow of blood differ substantially in different vascular beds. The system that has evolved to cope with these disparate challenges involves the aggregation of cells (platelets) and the formation of fibrous protein gel (fibrin). In addition, there is a complex, powerful, and tightly regulated enzyme network (the coagulation system) involving reactions on the surfaces of activated platelets, that leads to production of an enzyme, thrombin, that is key both in activating platelets so they can cohere to one another and in forming the protein fibrin from which the fibrin mesh is constructed."

40 Years of Modeling Clotting

The Fogelson research group has been developing models of many of the disparate aspects of blood clotting for close to 40 years. "We have built and analyzed models based on PDEs, ODEs [ordinary differential equations], or SDEs [stochastic differential equations] and, as needed, we have developed novel numerical methods with which to study the PDE-based models," writes Fogelson.

Projects of current interest in this research space includes, first, developing ODE-based compartment models of platelet deposition and coagulation under flow that treat developing thrombi as porous materials and which can track resulting flow, the growth of aggregates, and the biochemistry of platelet signaling and coagulation from the initiation of clot formation through vessel occlusion. The goal is a high-throughput simulation tool that will allow extensive investigation of model behavior as model parameters and other inputs are varied to reflect different physiological situations and disease states.

A second project of interest is integrating the Fogelson lab's models of fibrin polymerization with models of platelet deposition and coagulation under flow during arterial thrombosis, to produce a more comprehensive model of the clot formation process.

Fogelson has been a faculty member at the U since 1986 after earning his PhD at the Courant Institute of Mathematical Sciences of New York University and working as a post doctoral researcher at first the University of California, Berkeley and then the Courant Institute. In addition to his faculty position in the U's Department of Mathematics, he is adjunct professor of biomedical engineering, and was Associate Dean for Research of the College of Science in the period 2014-17. His research has been supported by the National Science Foundation and/or the National Institutes of Health continuously since 1982.
Read about all 26 SIAM fellows announced here.

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Utah Symposium in Science & Literature

Utah Symposium in Science and Literature

March 27, 2024

Poet Claudia Rankine, physicist Brian Greene, and neuroscientist and artist Bevil Conway are the keynote speakers for this year’s Utah Symposium in Science and Literature, taking place from April 10-12 at the Eccles Alumni House on campus.

Claudia Rankine is the author of “Citizen: An American Lyric,” a New York Times bestseller, as well as four other books of poetry and three plays. She is the founder of The Racial Imaginary Institute, an NEA fellow, a former Chancellor of the Academy of American Poets, and a professor at NYU. Brian Greene is renowned for his groundbreaking discoveries in superstring theory and is known to the public through his books, “The Elegant Universe,” “The Fabric of the Cosmos,” and “The Hidden Reality,” which have collectively spent 65 weeks on the New York Times bestseller list and sold more than 2 million copies worldwide. He is a professor of physics and mathematics and the director of Columbia University’s Center for Theoretical Physics. Bevil Conway is a senior investigator at the National Eye Institute and the National Institute of Mental Health, and an expert on the neuroscience of color. His artwork is in the Boston Public Library, the Fogg University Art Rental Collection, the N.I.H. Building 35 Public Art Collection, and many private collections.

The Utah Symposium returns this year after a long Covid hiatus, and will feature the involvement of U professors and grad students from numerous departments and disciplines, from English to math to music to philosophy. The theme of this year’s Symposium is “Mere Beauty,” a topic arising from the reexaminations of beauty occurring not only in the arts and humanities, but also in biology, where dominant theories about the possible evolutionary purposes of beauty are being questioned.

Co-chairs Fred Adler, Professor of Biology and Mathematics, and Katharine Coles, Distinguished Professor of English, developed the Symposium’s theme together. Coles explains, “In some ways, the topic of Beauty as a topic of interdisciplinary discussion and examination seems very abstract. However, I think it has become my favorite Symposium topic so far. It seems to touch on every discipline and, in many ways, on every aspect of our lives. Nature seems to have built us to respond to beauty; it’s hard not to wonder why.”

Read the full article about the symposium in @TheU.

The Utah Symposium is free and open to the public. For more information, please visit

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U Fulbright Scholar Semi-Finalists 2024

Three Science Students selected as Fulbright SEMI-finalists

March 21, 2024

Nine U students selected as Fulbright finalists; three of them call the College of Science home.

The University of Utah is proud to announce that nine students have been selected as semi-finalists for the prestigious Fulbright U.S. Student Program. Three are affiliated with the College of Science in the Fulbright area of Research.

Sponsored by the U.S. Department of State’s Bureau of Educational and Cultural Affairs, this nationally competitive program supports academic exchanges between the United States and over 140 countries around the world. Selected program participants pursue graduate study, conduct research, or serve as English Teaching Assistants abroad. See

For 2024-2025, the University of Utah submitted 19 Fulbright applications. Its cohort of semi-finalists represents multiple schools and colleges, including the College of Education, College of Humanities, College of Science, College of Social and Behavioral Sciences, David Eccles School of Business, and the Honors College. The group includes two students who intend to enter graduate programs, three students who proposed research projects, and four students who aim to serve as English Teaching Assistants. Projected countries include Costa Rica, Denmark, France, Germany, Italy, South Korea, and Taiwan.

Making it to the semi-finalist round is a significant accomplishment for these students and means that their applications have been forwarded by the Fulbright National Screening Committee to the Fulbright Commission or U.S. Embassy in the host country for final review. Finalists will be notified later this spring, with the timing of notifications varying by country.

Below are the three finalists from the College of Science all in the category of Research.

Marina Gerton (B.S. in Biology and Chemistry, December 2023) aims to undertake a research project at the University of Costa Rica under the mentorship of Mario Espinoza that focuses on the secret life of snappers--insights from fish movements. Gerton got an early start in science. She graduated from West High School in Salt Lake City where she participated in the 2018 University of Utah Science and Engineering Fair with her project "Mucoadhesive HA-based film releasing metronidazole to treat bacterial vaginosis." Her ambition is to pursue a PhD in marine science, specifically focusing on conservation research.

"While I had a slightly different focus when I first started in the lab," she says, "I’m now working on using paper and plant waste products (think recycled paper, yard clippings, agricultural waste, etc.) as, essentially, a food source for this really interesting bacteria Teredinibacter turnerae." Currently working in Eric Schmidt's lab in the Department of Medicinal Chemistry, she says that "one of the most interesting aspects of her research is that the bacteria she works with live in symbiosis with another organism, shipworms, and actually grow within specialized host cells in the shipworms’ gill tissue." It’s especially interesting, she states, as we know this species produces various compounds of medicinal interest, and "we’re still able to see production of those compounds when it’s grown on these waste products."

Gerton loves boxing and swimming, but is quick to say that she loathes running "with a passion." She also claims that watching commercials for Best Friends or the WWF can make her cry. (She avoids them along with pineapple on her pizza.) Finally, what would she do if she had more time outside of academics? One word: bake.

Moses Samuelson-Lynn (HBS in Math, BA in German, Spring 2024) aims to research “A New Set of Efficient Initial Variables for Cluster Algebras of Finite Mutation Type” at the Max Plank Institute for Mathematics in the Sciences in Germany. His main interest is in pure mathematics, especially number theory, analysis, geometric graph theory, geometric group theory and algebraic geometry.

His undergraduate research has led him to multiple presentations at the Joint Mathematics Meetings. His ambition is to earn a PhD in pure mathematics with the goal of becoming a research professor.

Samuelson-Lynn lives in West Valley City and he enjoys playing piano, bicycle riding, chess, origami and programming. In addition to his Fulbright aspirations, he will be joining a research team in Germany over the summer of 2024 directly after graduation. He will be investigating applications of subatomic-scale sensitivity of nitrogen vacancy centers in ultra-pure diamond at GSI Helmholtz in Darmstadt, Germany. He is completing an honors thesis on the classification of surfaces and is a member of the university German club.  UPDATE (4/3/2024): Moses Samuelson-Lynn has been announced as a finalist and will now be participating in the program as Fulbright scholar. Congratulations!


Catherine Warner (HBS, Math'19; Ph.D. in Math, Spring 2025) is a graduate student in the mathematics department where she anticipates earning her PhD in 2025. She aims to undertake a research project titled “Semiduality Groups: An Analog of Duality Groups” at the University of Sannio in Italy.

Werner's path to mathematics wasn’t exactly obvious. "I began undergrad as a biomedical engineering student," she says. "And even before that I mostly played golf throughout my earlier schooling while secretly reading classical philosophy in my free time,"  She quickly realized that engineering wasn’t enough. "I realized that ever since my early reading as a child, I’m used to expecting some deeper structures to reality, some sort of a deeper meaning. I just didn’t know how to find it."

Following the completion of her undergraduate degree, and partly pushed by that curiosity "and partly for lack of anything better to do," she adds, "I signed on for abstract math. I did so with hesitation because it seemed to me to be airy, lacking contact with reality. But the more I pursued geometric group theory, the more I became fascinated. Because I realized something pretty fundamental: One of the ways of finding hidden structures of the world is math — the amazing pursuit of the human mind, attempting to penetrate and order reality by following the structure of the mind itself."  UPDATE (3/21/2024): Catherine Warner has been announced as a finalist and will now be participating in the program as Fulbright scholar. Congratulations!


Fulbright alumni from the United States and around the world have gone on to achieve distinction in government, science, the arts, business, philanthropy, and education. Among the ranks of Fulbright alumni are 62 Nobel Prize recipients, 78 MacArthur Foundation Fellows, 89 Pulitzer Prize winners, and 41 current or former heads of state or government.

Fulbright semi-finalists from the University of Utah were advised throughout the application process by the Office of Nationally Competitive Scholarships (ONCS) housed in the Honors College. ONCS staff members assist outstanding students and alumni in developing competitive applications, preparing for interviews, and securing University endorsements for a variety of prestigious nationally competitive scholarships, including Fulbright.

You can learn about all of the Fulbright semi-finalists at the U here.

The 2025-2026 Fulbright competition will open on April 2, 2024. To learn more, contact Alison Shimko, the University of Utah’s Fulbright Director and the Associate Director of ONCS, at or consult

Rhodes Scholar Finalist

Rhodes Scholar Finalist: Eliza Diggins

February 27, 2024 |

The University of Utah is proud to announce that Eliza Diggins, a senior Honors student double-majoring in physics and applied mathematics, was selected as a finalist for the 2024 Rhodes Scholarship.

One of the oldest and most celebrated awards for international study in the world, Rhodes Scholarships provide tuition and living expenses for two or three years of graduate study at the University of Oxford.  Along with “outstanding scholarly achievements,” Rhodes Scholars must demonstrate “character, commitment to others and to the common good, and the potential for leadership in whatever domains their careers may lead.”

Diggins, who hails from Sandy, Utah, is a cross-disciplinary researcher in astrophysics and epidemiology. She is completing an Honors thesis titled “Constraining Modified Gravity Using Galaxy Cluster Dynamics” and has worked throughout her undergraduate career to couple mathematical and computational skills with observational data and statistical method. She plans to carry these skills forward in a graduate program in astrophysics, where she intends to investigate the dynamics of galactic and extra-galactic systems and become a more holistically skilled researcher, capable in both theory and observation.

In addition to excelling in her coursework, Diggins has contributed to research projects and labs run by College of Science faculty, Daniel Wik, associate professor of physics and astronomy; Frederick Adler, professor of mathematics and director of the School of Biological Sciences; as well as Melodie Weller, assistant professor, School of Dentistry. These faculty members celebrated Diggins’ “drive, scientific curiosity and collaborative nature,” “the tremendous energy and enthusiasm” she brings to her academic work, and her “ability to convey mathematically intensive and innovative research.” Along with her selection as a Rhodes Scholarship finalist, Diggins received a nationally competitive Goldwater Scholarship, an Undergraduate Research Opportunity Program (UROP) award, a Wilkes Center Scholarship (awarded by the Wilkes Center for Climate Science and Policy in the College of Science) and a Thomas J. Parmley Scholarship for Outstanding Undergraduate Student from the Department of Physics & Astronomy. Finally, Diggins serves as the inaugural chair of the Physics & Astronomy Student Lecture Series and was selected to present her research at the American Society for Virology conference and to members of the Utah state government at Research on Capitol Hill (ROCH).

“Diggins’ research on the gravitational properties of X-Ray emitting intra-cluster medium and Modified Newtonian Dynamics (MOND), galaxy evolution, and plasma dynamics answers important galactic questions and will allow her to contribute to the scientific community in myriad ways, ensuring that she will contribute to the future of scholarship about not only our world, but our universe as well,” says Ginger Smoak, director of the Office of Nationally Competitive Scholarships. Smoak also celebrated Diggins’ community work and how it “aligned with Rhodes Scholarship values, including a commitment to others and to the common good.”

Diggins taught English to low-income immigrant adults through the Adult Education Program at Guadalupe School in Salt Lake City and facilitates a transgender friendship circle for Encircle, a local nonprofit committed to advancing the well-being of LGBTQ+ youth, young adults, and their families. Her community recommenders praised her as one of the “brightest, most authentic, and committed people” they had met and stated that “her dedication transformed lives.”

For Diggins, competing for the prestigious Rhodes Scholarship was “a difficult but illuminating experience.” She felt honored, she explained, “to meet and build relationships with the other Rhodes candidates, each of whom brought unique and interesting perspectives and qualifications.” Overall, she found the experience “instructive in forcing me to think very deeply about various aspects of my life.”

Per the Rhodes Trust, more than 2,500 students began the application process this year; 862 were ultimately endorsed by 249 different colleges and universities; 240 applicants from 90 different colleges and universities reached the finalist stage of the competition. Since 1904, the University of Utah has had 23 Rhodes Scholarship recipients, including Sabah Sial in 2023 (see

Diggins was advised throughout the Rhodes Scholarship application process by the University of Utah’s Office of Nationally Competitive Scholarships (ONCS) housed in the Honors College. ONCS staff members assist outstanding University of Utah students and recent alumni in developing competitive applications, preparing for interviews, and securing University endorsements for a variety of prestigious nationally competitive scholarships.

To learn more, see

This story originally appeared in @TheU.

Nash Ward Receives 2024 PME Speaker Award

Nash Ward Receives 2024 PME Speaker Award

Nash Ward has always wanted to visit all seven continents.  So, in high school when he saw that Professor Ken Golden made trips to Antarctica as part of his research on sea ice, he reached out to see if he could be a part of the team.


Nash’s undergraduate research on sea ice began his first semester as a freshman at the University of Utah.  Under Golden’s mentorship he has been working in mathematical geophysics, looking at the fractal dimension of the sea ice pack, with a primary focus on the brine microstructure.  He also looks at how these brine pathways are formed and what the fractal properties have to do with that.  On a larger scale, he looks at ice floes in the sea ice pack and how that geometry is formed.  The brine microstructure is responsible for a lot of the physical properties of sea ice, including electromagnetic, thermal, and fluid transport properties.  On a larger scale, the orientation of ice floes helps to protect the ice pack from surface waves that would break up the pack.  Understanding these structures is an important component in modeling the role sea ice plays in the bigger picture of climate change.

Nash had the opportunity to present his research at the Joint Mathematics Meetings (JMM) held in San Francisco, CA in January 2024.  There were over 5,500 participants registered, making this the world’s largest mathematics gathering.  Nash received a JMM 2024 Pi Mu Epsilon (PME) Speaker Award for his presentation there.  This award recognizes outstanding student speakers in the PME Paper Sessions.

Nash plans to become a professor one day.  He is excited to continue researching and is also interested in mentoring the next generation of scientists and researchers.  He’ll take the first step toward becoming a professor this fall when he begins a graduate program in Applied Mathematics.

Nash would advise any undergraduate who wants to get involved in research to start by sending emails.  He suggests finding a professor who is doing cool work, reading a few of their papers, and then emailing them to ask about it.  From there, he says, see if you can meet up to talk about what they’ve been working on.

It’s worked for him, and it should work for you!  You might even end up checking something off your bucket list . . . like traveling to the Arctic ice cap.

by Angie Gardiner

Originally appeared at



Ken Golden, Op-ed

Space Race? we can win the ‘Earth Race’ too

Alta Ski Resort, just outside of Salt Lake City, received a whopping 903 inches of snow last winter, delighting skiers with continuous fresh powder. But Utah’s snowpack and precipitation patterns are of interest not just to ski resorts; they are of critical importance to the state’s drinking water, agriculture, industry and the health of the Great Salt Lake.

Was this the start of a period of abundant precipitation for the state or an aberration — a last gasp before the climate here settles into a drier equilibrium?

There is a propensity on both sides of the political aisle to become entrenched in partisan policy approaches, making it difficult to navigate our way through an uncertain and rapidly changing environment. However, I see these challenges as an opportunity to spearhead new technologies, innovations and policies that balance current economics and investments with our shifting circumstances. What might seem to be a setback must instead be viewed as a launching pad for our next giant leap forward.

The last time the U.S. was presented with an opportunity on this scale, which also arose from a threat to our way of life and to national security, was the Space Race of the 1960s. Scientific and technological advances were ignited by the challenges that humans faced when we first set our sights on landing on the moon. Our government, partnering with federal agencies and academia, demonstrated its resolve to defeat the Soviet Union in a race to the lunar surface. This initiative triggered investment across our economy, in universities and in technological infrastructure, spawning new markets and industries, creating jobs and sparking revolutionary advances in STEM fields and beyond. American science was viewed with pride at home and abroad.

In this new “Earth Race,” we have an opportunity for incredible innovation and progress. We can work collaboratively to promote science-based approaches while ensuring that current economic engines have the resources to adapt to new realities. However, if we fail to act, we will be left behind as other countries take the lead in creating a sustainable and economically vibrant future.

We cannot afford not to use the full power of American ingenuity, entrepreneurship and the world’s best university system if we are to seize the historic moment that we are in to fuel potent change. By many metrics we are already losing this race, as well as the spoils that will go to the leader of the global-scale technological transition that is just getting started.

China, for example, has doubled funding for higher education and, by 2025, will be producing around 80,000 STEM Ph.D.s per year — twice as many as the U.S.

China’s spending on research and development has jumped to 2.56 percent of GDP, though some of that funding is coming from businesses; still, that is more than triple the U.S. federal investment of 0.7 percent, which has been in decline for over a decade. Furthermore, China recently overtook the U.S. in science and engineering publications, and in 2022 ranked No. 1 in contributions to the prestigious Nature group of science journals, surpassing us for the first time.

We can’t risk lagging behind for much longer. Let’s set the not-so-lofty goal of catching up over the next eight years to our principal global rival by tripling federal R&D investment in math, science and engineering, and doubling our STEM Ph.D.s.

Significantly increased funding and attention to STEM research and education can be the catalyst for the U.S. to win the Earth Race, as well as spawn breakthroughs on other critical fronts. It will accelerate advances important not only for climate solutions but to the future of our national economy and defense posture, in fields such as quantum computing, AI, data science, medicine, optimization, advanced materials, photonics and energy storage.

We’re all in the same boat: planet Earth! The sheer complexity, scope and highly interdisciplinary nature of climate issues necessitate that we work together, across ideological, academic, intellectual and political lines, to achieve big goals that will benefit all of us. These problems are solvable. We have the talent, the ingenuity and the motivation to succeed. Increased investment in STEM, with our sights set on winning the Earth Race, will jumpstart our economy through the development of new solutions and will pay substantial dividends as we sail forward.

Let us set the compass toward our highest aspirations: “through adversity to the stars.”

By Kenneth M. Golden




Kenneth M. Golden is a distinguished professor of mathematics and adjunct professor of biomedical engineering at the University of Utah.  This opinion piece originally appeared January 12, 2024 in The Hill, Washington D.C.

Ingredients for Data Science

Ingredients for Data Science


Data science is crucial — but can be faced with plenty of difficulties.

Posted November 16, 2023

“Sometimes [data science] can feel like alchemy,” Anna Little, Assistant Professor of Mathematics states. “Like we’re just stirring this big pile of math until the results look right.” Little was the featured speaker at the College of Science's Science at Breakfast speaker series on November 2 at the Natural History Museum of Utah. She titled her remarks Challenges of the Modern Data Era.

There are three key challenges today within the field of data science: Determining effective knowledge transfer, how to accomplish reliable data visualization and achieving physically meaningful machine learning.  All are issues that Anna Little’s research focuses on solving.

Effective knowledge transfer centers on what it means for two tasks to be similar. With so many different applications, it becomes difficult to accurately predict. “An alternative to assessing similarity is to think about distances depending on conditions in some underlying network, not just the individual points,” Little said, "investigating novel ways of measuring distance.”

Reliable data visualization deals with the patterns that we see when looking at data. Modern data tends to have a very large number of features, which makes it difficult to visualize the data as well as analyze it. Through a process called dimension reduction, one can take a large table and minimize it into a smaller table that’s easier to analyze. However, dimension reduction can also lead to patterns going undetected, or create false patterns, as well as the disappearance of outliers. Little’s research looks into the “best of both worlds” by using linear algorithms with better note properties for the data.

For the last challenge, Little reported that machine learning is currently unreliable when it comes to data science. “AI responses aren’t stable,” Little said. “We want a small change in input to lead to a small change in output, but it often leads to a big change in output, and that makes mathematicians very uncomfortable.” Machine learning has good performance, but it’s difficult for data scientists to understand why or how it comes up with a certain conclusion.

It’s important to design features of machine learning with the characteristics that one wants, and Little focuses on utilizing translation in variant features. This means the features all compute the same, regardless of whether the data has shifted in terms of location or interference.

Anna Little was born in Alabama, but spent a majority of her childhood in Europe. She received a bachelor’s in mathematics from Samford University before completing a PhD in mathematics at Duke University before arriving at the U in 2021. 

By CJ Siebeneck

Science @ Breakfast is a lecture series that features U faculty sharing their latest, cutting-edge research - while enjoying a meal. If you would like to be invited to our next Science @ Breakfast, please consider a donation to the College of Science at

Putting the ‘fun’ in commutative algebra

the ‘fun’ in commutative algebra


The word “fun” is a subjective one, but that is how Anne Fayolle describes mathematics as a discipline.

A graduate student in mathematics at the University of Utah, Fayolle is a recent recipient of a multi-year scholarship from The Natural Sciences and Engineering Research Council  (NSERC) which is Canada’s equivalent of the National Science Foundation’s Graduate Student Fellowship in the U.S.

Math credentials

As a Ph.D. student working with Professor Karl Schwede, Fayolle, who was born in France and grew up in Canada, clearly has her mathematics credentials. Before coming to the U, she studied first at McGill University, one of Canada's best-known institutions of higher learning and one of the leading universities in the world. There, she quickly developed an affinity for the independent learning model in which one is paired with a professor in a one-on-one setting and in which both determine together what textbooks and papers they will study together. This conversational model of learning proved to be better than the lecture-and-classroom-style model for Fayolle and helped solidify her desire to go to graduate school.

Following her bachelor’s degree, Fayolle returned to Europe at École Polytechnique Fédérale de Lausanne (EPFL), one of the most celebrated public universities in Europe. As a master’s student, Fayolle studied with Dr. Carvajal-Rojas in commutative algebra. This involves working in modular arithmetic, a type of arithmetic in which addition works similar to time on a clock: 5 + 10 = 3. “The numbers working differently,” she says, “means one cannot use the traditional tools of calculus to study polynomial equations and the shapes they define. "For instance, since the numbers work differently, we can't draw graphs exactly like we would over the real numbers. So our intuition derived from those graphs doesn't always work here. One has to rely on the underlying algebraic structures."

This algebraic abstraction and the understanding it brings is one of Fayolle’s favorite parts of doing math, and it may speak to what Fayolle identifies as the “weird” aspect in commutative algebra, followed closely by the feeling of it being “fun.” The appeal is also philosophical “You can get to the heart of why something works the way it does. I really enjoy the abstraction that comes with [commutative algebra]––trying to find the structure in abstract things.”

Part of her enjoyment in doing math is that singular moment when someone (or “some ones”) in the math sector solves a persistent problem. “It’s [only] ‘hard’ until someone comes along and finds the right object or point of view of how things are working,” she says of breakthrough findings. “It’s suddenly less ‘weird’ because it makes more sense.” She explains that she’s been working in this positive characteristic realm for the past few years and is now used to it. Fayolle is especially interested in studying singularity theory, she says, in positive and mixed characteristics and, fortunately, in Schwede has found a principal investigator/mentor at the U who “does cool math.” 

Everyone can do math

The multi-year NSERC fellowship will free up more of Fayolle’s time for research. ​​Her ambition is to continue in academics as a post-doctoral researcher and then as a faculty, if possible. “I like having stuff that has more world impact independent from [just the study of] math. I think that pure math is intrinsically valuable, hard to justify by linking it to real world applications, but still necessary. ” This includes teaching.  

“I think math is very scary to a lot of people.  I personally think that everyone can do math. Everyone struggles, and I think that’s very important to emphasize when you’re teaching. I struggle in math. I don’t think struggling in math should be a barrier to doing math.”

 In the meantime, Anne Fayolle continues in graduate school, sharing mathematics by organizing BIKES, the student commutative algebra seminar here at the U as well as co-organizing an Association for Women in Mathematics conference later this year. She also skis on the weekends. “I was skeptical,” the Montreal native says, “when I first saw the [Utah “Greatest Snow on Earth”] license plates. But after I went skiing, I agreed.” It helps, she says, that it doesn’t get too cold and is not too icy. 

“I think the license plates might be right.”

by David Pace

Nada Math Anxiety Here

Nada Math Anxiety with Ken Golden


At this point, we have all heard of STEM education, that is Science, Technology, Engineering and Math. And there’s also STEAM education which includes the Arts.

Why is specifically math so important in STEM education and subsequent careers?

Featured on KPCW's COOL SCIENCE RADIO podcast, Professor Ken Golden, Distinguished Professor of Mathematics at the University of Utah, talks about the importance of STEM careers in the U.S. to meet the needs of our climate and the economy.

Listen to the podcast at KPCW.