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.

A widely used instrument for monitoring black carbon in real time.

Black carbon sensor could fill massive monitoring gaps

Black carbon is the most dangerous air pollutant you’ve never heard of. Its two main sources, diesel exhaust and wood smoke from wildfires and household heating, produce ultrafine air particles that are up to 25 times more of a health hazard per unit compared to other types of particulate matter.


Despite its danger, black carbon is understudied due to a lack of monitoring equipment. Regulatory-standard sensors are wildly expensive to deploy and maintain, resulting in sparse coverage in regions infamous for poor air quality, such as the greater Salt Lake City metropolitan area in Utah.

A University of Utah-led study found that the AethLabs microAeth MA350, a portable, more affordable sensor, recorded black carbon concentrations as accurately as the Aerosol Magee Scientific AE33, the most widely used instrument for monitoring black carbon in real time. Researchers placed the portable technology next to an existing regulatory sensor at the Bountiful Utah Division of Air Quality site from Aug. 30, 2021-Aug. 8, 2022. The AethLabs technology recorded nearly identical quantities of black carbon at the daily, monthly and seasonal timescales. The authors also showed that the microAeth could distinguish between wildfire and traffic sources as well as the AE33 at longer timescales.

Because black carbon stays close to the source, equipment must be localized to yield accurate readings. The microAethsensor’s portability would allow monitoring at remote or inaccessible stationary sites, as well as for mobile use.


“Having a better idea of black carbon exposure across different areas is an environmental justice issue,” said Daniel Mendoza, research assistant professor of atmospheric sciences at the University of Utah and lead author of the study. “The Salt Lake Valley’s westside has some of the region’s worst air quality partly because it’s closest to pollution sources, but we lack the ability to measure black carbon concentrations accurately. Democratizing data with reliable and robust sensors is an important first step to safeguarding all communities from hazardous air pollution.”

The study was published on Feb. 1, 2024, in the journal Sensors.

In the dark

Black carbon pollutants are a type of fine particulate matter (PM2.5), a class of air particles small enough to be inhaled into the lungs and absorbed into the bloodstream. Black carbon is true soot, produced when hydrocarbons do not fully burn, and has been shown to migrate into the heart, brain, fetal tissue, and other biological systems.

“The combination of increasing wildfires driven by anthropogenic climate change and steady population growth along the Wasatch Front in coming decades will result in new pollution challenges that Utah will have to face,” said Erik Crosman, assistant professor of environmental sciences at West Texas A&M University and a co-author of the study.“The portable MA350 ‘micro’ aethalometer could be utilized in building a better spatial observational network of accurate but lower cost black carbon sensors across the region.”

Though research suggests exposure to black carbon is 10 to 25 times more hazardous to respiratory and cardiovascular health than other PM2.5, long-term health outcomes are largely unknown. An accurate observation network is the first step to establishing disease risk and creating effective public health policies. This study, funded by the Salt Lake City Corporation, aims to help regions with poor air quality establish a baseline of black carbon distribution.

“It’s crucial that we target our measurements to identify the largest and most relevant black carbon sources,” said Drew Hill, a study coauthor who leads data science and applied research work at AethLabs. “We’ve added a feature rooted in physical principles to provide real-time estimates of the amount of measured black carbon produced by fossil fuel burning versus wood burning to allow researchers and policy makers to triangulate such sources.”

Having established the portable sensor’s accuracy and regional relevance, the researchers are measuring black carbon levels around the Salt Lake Valley, including testing concentrations present inside school buildings.

“First, you need to get readings. In some neighborhoods you could look at air quality concentrations, then look at the cancer or other disease rate in that neighborhood,” said Mendoza, who is also an adjunct assistant professor in the Division of Pulmonary Medicine at University of Utah Health. “Getting measurements with a high degree of accuracy, now we can really think about health and policy avenues to really protect everyone’s lung health.”

Jeffrey Blair of AethLabs also contributed to the study, titled, “A long-term comparison between the AethLabs MA350 and Aerosol Magee Scientific AE22 Black Carbon Monitors in the Greater Salt Lake City Metropolitan Area.” Sensors 2024, 24 (3), 965;

Remembering John Warnock

REmembering John Warnock, 1941-2023


As a high school student at Olympus High in Salt Lake City, co-founder and former CEO of Adobe John Warnock, who passed away August 19th at age 82, found a mentor in math teacher George Barton. “His approach was really quite simple,” remembered Warnock.


“He instructed us to pick up a college-level textbook for algebra, solve every problem in the book, then move on to the next subject, trigonometry, and do the same. And after that, go on to analytic geometry. By following his advice and solving a lot of problems, my grades in math and all other classes improved, and I went from C’s to A’s and B’s.”

The auspicious career of Warnock and other brilliant University of Utah alumni who changed the world through computer science was in high relief last spring when a sampling of the scrappy and now legendary bunch assembled on campus to commemorate their roles as 3-D graphics pioneers. The occasion was a celebration of 50 years of the U.’s Kahlert School of Computing, and Warnock was presented with a IEEE Milestone award.

John Warnock receiving the IEEE Milestone award in March 2023 with wife Marva.

But before he was known as the co-founder with the late Charles Geschke of Adobe, Warnock was propelled by his high school teacher into the U’s math department where Warnock earned a BS and MS in mathematics in the College of Science before decamping to the College of Engineering where he earned a PhD in electrical engineering/computer science. It was an exciting time. The U was one of 15 renowned universities that had a contract with the Advanced Research Projects Agency, prompted by the worrisome launch of the Russian Sputnik satellite during the Eisenhower era. A node on the original internet known as ARAPNET, the U was the first university to offer online registration to its students, and Warnock, as part of his dissertation research was busy at work, days (and long nights), ahead of when the portal dropped, having developed the recursive subdivision algorithm for hidden surface elimination that made computer graphics possible and that would eventually carry his name.

Twenty-five years post Sputnik, Adobe appeared which, inarguably, lofted desktop publishing into the stratosphere with its soon-to-launch PostScript language. The information technology sector has never been the same since.

Commencement in the time of Covid-19

At the university’s first-ever virtual graduation ceremony due to the coronavirus pandemic, Warnock reported that in the previous half century he had witnessed advancements in informational technology that “have been totally unpredictable and quite frankly, mind-blowing. Things that were thought to be impossible have materialized over the years.” (To wit: today, the internet is 90,000 times faster than its ARAPNET prototype.)

“The changes over the coming years,” he continued, addressing the class of 2020, “will probably be much greater and even more consequential for all of our lives. To manage this evolution, the world needs an educated and informed populace. Today, you are being honored and have earned the right of becoming part of that group.” The brick-and-mortar corollary of the change Warnock anticipates, and the workforce that will be needed, is the Utah County-based 38-acre Adobe campus, arguably the anchor to what’s come to be known as Silicon Slopes. A recent addition to the spread, costing $90 million, appreciably expanded the Adobe's original 280,000-foot, four-story footprint.

Adobe’s physical presence in Utah brought an appropriate closing of a circle for Warnock, a native of the Beehive State. Known for developing what is now the ubiquitous Portable Document Format (PDF) as well as its Creative Suite, including PhotoShop software, the company, based in Lehi, engages with the community to build a STEM pipeline. It’s also widely known for its determination to diversify its employee base with, among other initiatives, true pay parity. "Your customers are diverse," Adobe CEO Shantanu Narayen said at the 2018 Silicon Slopes Tech Summit. "If anybody thinks that you can deliver great products to a diverse set of customers without having a diverse employee pool, you're in denial."

Tracing a trajectory

Upon learning of Warnock’s passing, Peter Trapa, dean of the College of Science said, "In tracing Warnock's trajectory at the U – first as undergraduate and master’s student in mathematics, and then as a PhD student in ECE – one can literally see the evolution of modern computer graphics. Many of the ideas in his famous PhD thesis are foreshadowed in his earlier work in mathematics.” He recommends reading the conclusions sections of Warnock’s dissertation which “is especially forward-looking.”

Likewise, Tommaso de Fernex, current chair of the Department of Mathematics and the inaugural Warnock Endowed Chair in mathematics expressed condolences, thanking the family for their support. “The Warnock Endowed Chair has been an invaluable recruitment tool that has allowed the Department to attract young faculty of outstanding quality. It is hard to overstate the impact that this has had, and will continue to have, on the growth and excellence of our Department.”

A member of the National Academy of Engineering and a fellow of the Association for Computing Machinery, Warnock in 2009 was awarded the prestigious National Medal of Technology and Innovation by President Barack Obama. In 2001 he was inducted into the College of Science’s Hall of Fame. Through his and his wife Marva’s largesse, the Warnocks have “paid it forward,” not only endowing the Warnock chair but donating millions to the U where an engineering building is named for them.

As commencement speaker, Warnock returned to the foundations of his career, not only at the U but as far back as high school in Holladay with his math teacher, George Barton.  “The whole experience taught me teachers have an enormous effect on their students. I hope in your educational experiences you have encountered great teachers and mentors.” He continued, determined to leave good advice to the 8,628 graduating students:

"The rest of your life is not a spectator sport. Your job in life is to be an active player, to make the world a better place.”

Warnock is survived by his wife and three children.


Read the remembrance of John Warnock from the The John & Marcia Price College of Engineering



How statistical physics illuminates sea ice

How statistical physics illuminates sea ice

Since he began studying polar sea ice at NASA in 1975, mathematician Ken Golden has helped document alarming changes in the seasonally shifting, thin veneers covering the Arctic and Antarctic oceans.

Ken Golden. Feature photo above: Arctic melt ponds. Credit: Donald Perovich

There’s now a lot less ice and the University of Utah scientist has since devoted much of his career to applying statistical mechanics—the physics of phase transitions and complex collective behavior in systems like gases and magnets—to better understand the role of climate change in the disappearance of our polar sea ice covers. The stakes couldn’t be higher as the impacts accelerate. In recent decades, according to Golden, the extent of Arctic sea ice has shrunk by about half.

“Not over the past million years, like on geophysical scales, not over a thousand years, but over the past 30 or 40 years. A couple of months ago, even in Antarctica, we just saw a new record low,” Golden said in his opening remarks at the May 17 Climate Summit hosted by the U College of Science’s Wilkes Center for Climate Science & Policy. “But just like throwing a rock into a pond, there are ripple effects, and the bigger the rock, the bigger the ripples and the further they go. The extent of sea ice we’ve lost in the Arctic is about two-thirds the area of the contiguous United States and is probably the largest change on Earth’s surface due to planetary warming. That’s a big rock.”

The part of Earth’s climate system featuring snow and ice, known as the cryosphere, is experiencing severe disruptions as the planet continues warming. Ice still covers 9% to 15% of Earth’s ocean surface, but the trends are ominous.

Read the full article by Brian Maffly in @TheU