Paul Watkins

Paul Watkins


As a boy growing up in Ogden, Utah, Paul Watkins attended summer programs at the U when he was in middle school. He enjoyed the experience and planned on attending the university because of its great reputation, affordability, and the fact that he could ride the express bus from Ogden to Salt Lake City.

When he began his freshman year at the U, Paul found that wanted to learn as much as possible to become a well-educated and well-rounded person. He was interested in so many subjects that it was difficult to declare a major.

At one point, he planned on a triple major in German, history, and philosophy, with an idea of going to graduate school in the humanities and teaching at either the high school or college level. In 1998, he graduated with a degree in German language and literature and a minor in history. He was one class shy of a completing a minor in philosophy, which he sometimes regrets not finishing.

Eventually, practical considerations set in, and Paul realized that he didn’t want to teach and that he needed to make a living. “Fortunately, I was good at math and physics, so this led me to the Electrical Engineering and Math Departments,” he said. He completed bachelor’s degrees in both mathematics and electrical engineering in 2003. He completed a master’s degree in electrical engineering in 2004. He worked on a Ph.D. in electrical engineering but did not complete the dissertation, opting for a job in industry instead.

Value of a U education

“My education at the U has made a huge difference in my life,” he said. “Without it, I wouldn’t have my career in electrical engineering. My studies in the humanities helped me to become a well-rounded individual, and my studies in the Math Department taught me to think critically. In my career, I have found that I’m constantly learning new things on the job, and I enjoy this. My education at the U gave me a solid foundation, which allows me to learn and understand a lot of technical content that I didn’t learn in a classroom.”

He was fortunate to receive departmental scholarships from the Math Department, which helped him complete his undergraduate degrees. “I’m very grateful to the Math Department. I try to contribute to the department’s Undergraduate Scholarships Fund every year to try to give back and pay it forward,” he said.

In graduate school, he won a National Science Foundation Graduate Research Fellowship. He believes that having a math degree, in addition to an electrical engineering degree, played a huge role in receiving a fellowship. He is also grateful to a number of math professors who wrote recommendation letters for him.

Favorite professors at the U

Paul enjoyed his math studies and admired a number of professors in the Math Department, including Davar Khoshnevisan, Lajos Horvath, Alexander Balk, Nicholas Korevaar, Misha Kapovich, and Fletcher Gross, noting that all of them are super smart, experts in their field, and great educators.

His favorite professor was Anne Roberts. “I took multiple statistics classes from her. She took the time to get to know me, gave me very good advice on multiple occasions, and wrote recommendation letters for me. I am very grateful to her,” he said.

Paul is also indebted to Professors Neil Cotter and Behrouz Farhang of the Electrical and Computer Engineering Department and Professor Emeritus Gerhard Knapp of the German and Comparative Literature Department for all their help and support.

When he wasn’t working on math or electrical engineering, he spent a lot of time studying in the library and playing chess. He took beginning racquetball and tennis classes and loved them, although he admits he was terrible at both.

Career highlights

His first job out of college was with a startup company, Slicex (short for Salt Lake Integrated Circuit Experts). The company had raised some venture capital and were trying to develop a product, and Paul found that his education at the U, especially his graduate work, had prepared him well. The work was very interesting, but the realities of being a startup also made the job stressful. A few times the company ran out of money. Eventually, the company failed.

Subsequently, he worked for several large companies, including T.D. Williamson, GE Healthcare, Moog Medical, and Cirtec Medical. While these companies proved more stable, they had other challenges. Often, they required significantly more paperwork than actual design work, particularly those companies in the medical field.

“My degrees in engineering and math have both been very helpful, and I’ve used statistics a lot in industry. My humanities degrees have also helped, as communication and writing skills are very important,” he said.

In his current position, he serves as principal engineer at Cirtec Medical, and the job is directly related to the work he was doing in graduate school. Paul works on medical implants for brain/computer interfaces and for neuromodulation, which refers to technology that acts directly upon nerves. Classes he took in graduate school that he never thought would be useful in industry, such as the physics of nuclear medicine and bioelectricity/electrophysiology, have come in handy.

Paul is still learning and his education at the U has benefited his family. “I share a lot of things I learned in college with my daughter,” he said. “We also spend a lot of time on campus, attending all kinds of events, like the Babcock Theatre, the Music Department’s Sundays@7 series, departmental open houses (the geology and chemistry departments put on great events!), the Physics Department’s star parties, and the Faraday Lecture series. These last two events have led directly to two science fair projects for my daughter. We are regular visitors of the Utah Museum of Fine Arts, the Natural History Museum of Utah (NHMU), and Red Butte Garden. We’re also season ticket holders for the women’s gymnastics team. I’d like to give special thanks to Christy Bills, the entomology curator at the NHMU, for mentoring my daughter.”

Advice to students

If Paul could revisit himself as a freshman, he would tell himself to plan better. “Come up with a plan to make it through college, and try to take a manageable number of classes at a time,” he said. “Taking classes because you’re interested in a topic is fine but also have a career path in mind. And remember that internships and industry experiences are extremely important to prepare you for your career and complement your coursework. One important thing is to allocate plenty of time during your senior year for a job search and/or graduate school applications.”

As an undergrad, Paul took a class on Career and Life Planning from the Educational Psychology Department. Students took personality tests and interest surveys and investigated careers that were a good fit. They also interviewed people currently working in those fields. Paul highly recommends that current students take this type of class.

“Critical thinking skills are among the most important things you can get from your college education, and they’ll serve you well for the rest of your life,” he said. “I would highly recommend reading the book How to Think About Weird Things: Critical Thinking for a New Age by Theodore Schick and Lewis Vaughn.”

Paul believes that engineering or computer science majors should take a lot of math classes, too. “A math degree, in addition to your engineering or computer science degree, will help you in industry and in graduate school,” he said. He remembers that Professor Ken Golden once told a class that when an engineer also has a math degree it’s like they are an engineer on steroids. Paul also recommends obtaining a master’s degree because graduate school gives students a chance to study fun and interesting topics, and the master’s degree will be useful in a career.

When Paul isn’t attending campus events, he spends time birdwatching and volunteering for both HawkWatch International and the Raptor Inventory Nest Survey, both based in Salt Lake City.

by Michele Swaner, first published @math.utah.edu

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Lauren Bustamante

Lauren Bustamante


 

Lauren Bustamante senior academic advisor, joined the Department of Mathematics in August 2021.

What was your previous job before you came to the Math Department?

I joined the U in 2020. Prior to my role here in the Math Department, I worked at the School of Medicine as the pre-medical laboratory science advisor. I have been working in higher education since 2016, and my first role as an academic advisor was in 2018 at Utah Valley University in the School of Arts.

What are your duties in your current position?

I advise all math majors in their academic planning. I am also a Bridge advisor with the U’s Academic Advising Center. This allows me to review general education exceptions for the College of Science undergrads, along with other responsibilities. Last but not least, I am on the curriculum, awards, and convocation committees.

What do you enjoy about working with students?

I enjoy interacting with students and seeing their drive and passion to succeed. I love helping and guiding students through all levels of their educational journey. Every student is unique, and working with each and every one of them presents a different challenge or obstacle to solve. The best part of advising is seeing my students grow and use the skills of self-efficacy—students recognizing that they have the ability to succeed at the tasks they take on. Advising students is more than telling them what classes to take—advising is guiding students to explore their wants, desires, and interests while attending the U. Helping students figure out who they are and what they are capable of brings joy to the work I do.

Hours and/or days when you can meet with students? Where are you located?

I meet with students Monday through Friday virtually at the moment; but, hopefully, one day I can meet with them in person. My hours vary but they are from 9 a.m. to 5 p.m. I’m located in LCB 212.

To get the most from an advising session, how should students prepare for a meeting with you?

I always advise my students to come prepared. When I mean prepared, it’s best if you have some questions ready to ask me or concerns you’d like to talk about. Every meeting is different, but an effective meeting is accomplished when a student has an idea of what they need.

What was your undergraduate degree? Where did you receive it?

I received a master’s degree in academic advising from Kansas State University in 2020. My bachelor’s degree was in psychology from the University of La Verne (in Southern California) in 2015.

- by Michele Swaner, first published at math.utah.edu

Biological Data

The Science of Biological Data


Fred Adler

In an age when cross-disciplinary collaboration has become a buzzterm, especially in academia, Fred Adler puts his mathematical models where his mouth is. Multi-disciplinary work—in which academic silos are breached in the search for truth—is the hallmark of what Adler, who has a joint appointment in mathematics and biology, does.

His is the kind of work that will be supported by the new science building recently announced by the College of Science, dedicated to applied and multi-disciplinary work, and where most STEM students at the U will eventually find themselves for a time.

As Director of the Center for Quantitative Biology, Adler and his team have applied their data-driven tool kit to everything from viruses to animal behavior, and from biodiversity to infectious diseases. Who else can claim a lab’s subject models as varied as aphid-tending ants, hantavirus, and the Southern Right Whale off the coast of Argentina?

Math in Nature

The Adler group’s approach to research is driven by basic questions about how biology works. To bring together several threads of research, the lab began a study of rhinoviruses, the most common cause of the common cold, and how they routinely and rapidly change. The study uses mathematical models based on known interactions in the immune system and genetic sequences. “We hope to build detailed evolutionary models of this rapidly change set of viruses,” Adler reports.

He and his team are now looking at cancer in humans. There are, of course, hypotheses of how cancer takes over cells in the body and grows. But too many of these hypotheses are based on assumptions that cells behave as they do with complete information and clever plans for the future instead of the confusing world of a real tissue.

“However useful some of these [current] models are,” says Adler, “they are not based on a realistic assumption.” In fact, a prime contribution of the mathematical modeler is “to make sense of things from the perspective of what you’re modeling.” What access to information does the cell or organism have, is a central, guiding question.

Muskan Walia and Emerson Arehart

Part of how cancer behaviors may be better scientifically “unpacked” is through game theory but expanded over time and space and placed in a context of incomplete information between constituent parts.

Mathematical models, or more accurately, an ensemble of models later aggregated like political polls or weather models to predict the future, may be the answer. “We usually don’t get a simple smoking gun,” says Adler referring to complicated questions in biology, whether developmental, behavioral-ecological, immuno- or micro-biological. “With nine or ten big mathematical models running all the time you have a [more robust] hypothesis,” he says.

“All thinking is done using modeling,” Adler reminds us, “whether it’s through language or, in my case, mathematics.” The strength of the latter is that when mathematical modeling is added to the classical biologist’s models, it is “perfectly explicit about its assumptions. When you do the math right (and we always do), the logic leading from assumptions to conclusions is airtight ‘true.’”

This is important because a mathematical argument can’t be controverted. “If conclusions in biological research are wrong, it’s the assumptions that are wrong,” and the researcher can then pivot on those assumptions.

Modeling of this kind, of course, has proven helpful, most recently, in the study of Sars-CoV-19, the virus that has propelled the world into a pandemic. The coronavirus does not operate in isolation, but with other components through the human immune system.

This kind of work is animated not just by its predictive character using statistics—as in the case of artificial intelligence or machine learning (“We aren’t all cyborgs, yet,” Adler says)—but, it is predictive in a mechanistic sense in that it cares deeply about the more nuanced and open-ended “how,” the foundation of the scientific method.

Adler started out at Harvard as a pure mathematician, but by the time he arrived at Cornell University as a graduate student, he had discovered that he really enjoyed talking and collaborating with biologists. Stanford-based Deborah Gordon, a renowned expert on ants, which as he puts it, “achieve a lot of stuff fairly robustly through simple rules,” was one of them. He also found himself with David Winkler in upstate New York in a bird blind and observing the breeding and offspring-raising behaviors of tree swallows. The complicated models he built based on that research were never published, but Adler was hooked on life sciences.

Whether it’s modeling the lungs of cystic fibrosis patients looking for a transplant, determining that the changesnin Covid-19 are driven not just by mutations in the virus but adaptations of human immune response, or other “bench to bedside” medical science, Fred Adler has found a home in the mechanistic aspects, the “how,” of basic science.

How to synthesize his research over the past thirty years is the next big question. For now he will continue with modeling biological systems, their signaling networks based on the body’s own network of “trust” between components, and determining how those systems are corrupted… and maybe how to fix them.

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Theory Meets Intuition

Theory Meets Intuition


Will Feldman

Will Feldman, Assistant Professor of Mathematics, joined the Department of Mathematics in 2020. He studies mathematical models of physics and thinks about the things most of us take for granted, for example, fluid flow, water droplets, and flame propagation. These models are often developed by engineers or physicists using basic assumptions, but the resulting equations can be difficult or impossible to solve exactly.

“I’m interested in proving mathematically rigorous results for these models,” said Feldman. In his research, the results sometimes show the limitations of the modeling assumptions used to derive the equations. Other times, they explain the behavior of all the solutions of the equation without relying on special formulae. “And sometimes, the results are used to justify numerical computations, which are meant to approximate solutions of these equations,” he said.

One particular type of problem Feldman has studied is called “homogenization”—the study of the physical properties of complicated heterogeneous materials. The idea is to “average” or “homogenize” the complicated small-scale inhomogeneities in the material to derive simpler effective equations to describe properties at larger scales. For example, the ideas of homogenization theory can be used to study the shapes of water droplets on surfaces that have microscopic roughness, such as a plant leaf, a piece of glass, or a table top.

Water droplet on fabric.

“I like to work out these kinds of questions because I get to use both physical intuition and theoretical mathematical tools,” he said.
Feldman wasn’t always interested in mathematics. As an undergraduate, he thought he wanted to study physics or history. He started taking math classes because math was useful in studying advanced physics. “I had a lot of amazing math professors, and I started to like math a lot,” he said. “Eventually, I realized I could maybe study math and also bring in my interest in applications (especially physics). Basically, that’s how I ended up studying partial differential equations.”

Like many undergrads who study math, Feldman was worried he would need a special talent to succeed at math, but he had supportive and encouraging mentors, so he never got too discouraged. “I hope the experience of having good mentors has taught me to be a good mentor, too, and show my students I believe in them and the many interesting possibilities available in a career in or related to mathematics,” he said.

Before joining the U, Feldman received his Ph.D. from UCLA in 2015 and was an L.E. Dickson Instructor at the University of Chicago from 2015-2019. He was also a member at the Institute for Advanced Study (IAS) from 2019-2020. The IAS is one of the world’s leading centers for curiosity-driven basic research, based in Princeton, NJ.

In 2019, Feldman was awarded the John E. and Marva M. Warnock Presidential Endowed Chair for Mathematics by the University of Utah. He will hold the chair for five years and anticipates the funding will provide new and interesting directions for his research. He hopes to have a positive impact by training, mentoring, and supporting a next generation of mathematicians. “It was a great honor to be offered the Warnock Chair,” said Feldman. “I am obviously very proud to receive the award and grateful to the Warnock family and the university.”

As he moves forward in his research, he’s been thinking about problems involving interfaces in heterogeneous media. He’s also been wondering about transport equations and models of grain boundary motion in polycrystalline materials. He’s looking forward to discussions and collaborations with his colleagues in the Math Department, especially in the applied and probability groups.
Feldman and his wife are in the midst of raising two young children. He enjoys the great hiking in Utah and is looking forward to relearning how to ski and maybe starting new outdoor activities, such as climbing and biking. He enjoys cooking and has become obsessed (during the pandemic) with making a great cup of coffee.

- by Michele Swaner, first published at math.utah.edu

Warnock Presidential Endowed Chair

“A Presidential Endowed Chair at the University of Utah is one of the highest honors that we can bestow on a faculty member.” —Dean Peter Trapa

Presidential Endowed Chairs are crucial for the recruitment and retainment of the most accomplished faculty members. Through these philanthropic gifts, the faculty are able to further support their cutting-edge research and explore new areas in their field.

John E. Warnock, BS’61, MS’64, PhD’69, and Marva M. Warnock created a Presidential Endowed Chair for Faculty Development in Mathematics in 2001 through a gift of Adobe Systems stock.

For more information on a establishing a Presidential Endowed Chair, or other named gift opportunities, please contact the development team at 801-581-6958, or visit science.utah.edu/giving.

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Arctic Adventures

The Science of Salty Ice


BBC StoryWorks

BBC StoryWorks and the International Science Council present "Unlocking Science," which showcases how science is helping to solve some of society's greatest collective challenges. The University of Utah is the only institution in North America represented in the series, which showcases how science is helping to solve some of society's greatest collective challenges.

Jody Reimer

Counting on Mathematicians to Help Save the Planet

On a brilliant white ice floe floating in the Arctic Ocean, a group of people in bulky coats adjust to the biting cold, having been dropped off by helicopter. “All of a sudden, I turn around and there’s a polar bear and it starts running at us,” says Jody Reimer, recounting a moment of panic. “Luckily, the helicopter swooped back in to scare the bear off, but I had the adrenaline shakes for the rest of the day,” she adds, laughing.

You might expect such a nail-biting anecdote to come from an explorer, but Dr Reimer is a mathematician and lecturer at the University of Utah, as well as being part of a community that has swapped cosy classrooms for some of the Earth’s most inhospitable wildernesses, in a bid to use numbers to understand global warming.

Their adventures enable them to observe first-hand the processes driving change in the polar regions and validate their mathematical theories of sea ice and its role as a critical component in the Earth’s climate system.

A complex problem
The thickness and extent of sea ice in the Arctic has declined quickly since satellite measurements were first taken in 1979.

Sea ice is the Earth’s refrigerator, reflecting sunlight back into space. Its enduring presence is important to our planet’s future because, as more ice melts, more dark water is exposed which absorbs more sunlight. This sun-warmed water melts more ice in a self-reinforcing cycle called ice albedo feedback.

While sea ice decline is perhaps one of the most visible large-scale changes connected to planetary warming on the Earth’s surface, analysing, modelling and predicting its behaviour and the response of the polar system it supports is incredibly difficult, but mathematicians can help.

Kenneth Golden, a distinguished professor of mathematics and adjunct professor of biomedical engineering at the University of Utah, has built a unique sea ice programme over 30 years. Its combination of mathematics research, climate modelling and exciting field expeditions, has attracted students and postdoctoral researchers, including Dr Reimer, who are focused on using this type of science to help tackle the pressing challenges of a rapidly changing climate.

Factoring in animals
Dr Reimer has studied how polar bears and seals respond to changes in their frozen environment. While she used mathematical models to understand the interactions between these creatures and their habitat, she also took measurements and samples from bears in the Arctic, which was something she never expected to do as a mathematician. “They’re not totally sleeping when they are tranquilised; they’re groggy,” she explains. “One of them freaked me out because it seemed like it could wake up at some point.”

Their shrinking habitat means polar bears are walking on thin ice, but it’s hoped that studies like Dr Reimer’s will help experts understand how to protect the majestic predators.

However, it is the “mind-blowing” microscopic world of bacteria and algae that live in salty water pockets inside the sea ice that now excites her. This biological community and its habitat are influenced by changes in temperature, salinity and light, making it difficult to model accurately. In her current work, Dr Reimer constructs models to understand how these factors interact to determine biological activity within the ice. “Understanding how processes on these small scales contribute to macro-level patterns is critical to modelling the impact of a warming climate on polar marine ecology,” she explains.

Crunching the numbers on salty ice
It is the challenge of understanding how the microscopic structure of sea ice affects the behaviour of massive expanses of ice that interests Prof Golden. He has visited the Earth’s polar regions 18 times, braving the westerly winds known as the “Roaring Forties” to reach Antarctica by ship and narrowly avoiding plunging into icy waters while measuring sea ice. “One time I was visited by a massive whale about eight feet away, who could easily have broken the thin floe I was on with a casual flick of its tail,” he says.

Ken Golden

Prof Golden studies the microstructure of sea ice to calculate how easily fluid can flow through it. “Sea ice is salty. It has a porous microstructure of brine inclusions which is very different from freshwater ice,” he says.

Prof Golden has led interdisciplinary teams to predict the critical temperature at which the brine inclusions connect up so that fluid can flow through sea ice, and to develop the first X-ray tomography technique to analyse how the geometry of the inclusions evolves with temperature. “Understanding how seawater percolates through sea ice is one of the keys to interpreting how climate change will play out in the polar marine environment,” he explains.

Discovering this “on-off switch” has helped scientists better understand processes such as how nutrients that feed algal communities living in the brine inclusions are replenished.

The brine in sea ice also affects its radar signature, which affects satellite measurements of parameters like ice thickness used to validate climate models. These models are important because they predict future changes to our climate and are used by world leaders and scientists to come up with mitigation strategies.

Coming in from the cold
The variety of ice presents a challenge, but diversity among researchers, teachers and students creates the perfect environment for fresh ideas. In the US, just one quarter of doctoral degrees in mathematics and computer sciences were awarded to women in 2015, but schemes such as the University of Utah’s ACCESS programme are nurturing talented female mathematicians by helping them unlock opportunities such as mentoring and hands-on research. Expeditions to the Arctic not only give students an elevated experience, but ensure mathematicians are involved in cutting-edge research and solutions, alongside climate scientists and engineers.

When they are not battling blizzards, Dr Reimer and Prof Golden work on collaborative, interdisciplinary projects and co-mentor female undergraduate students as part of the ACCESS programme. After refreshing the mathematics component in 2018 to include climate change, Prof Golden has seen roughly triple the number of ACCESS students interested in taking a maths major or research placement than before.

Rebecca Hardenbrook, who is one of Professor Golden’s PhD students, says: "focusing on pressing issues like climate change attracts more of the people we want into mathematics, which is everyone, but in particular, women, people of colour, queer people; anyone from an underrepresented background.”

Rebecca Hardenbrook

Pooling resources
Hardenbrook joined the ACCESS program ahead of her first year as an undergraduate, spending the summer in an astrophysics lab, which opened her eyes to the possibility of doing research. "It was really life changing," she says, not least because she further decided to pursue a PhD in mathematics with Prof Golden after studying thermal transport through sea ice as an undergraduate.

She now inspires younger students on the ACCESS scheme as a teaching assistant, as well as modelling melt ponds, which are pools of water on the Arctic sea ice. These ponds play a decisive role in determining the long-term melting rates of the Arctic sea ice cover by absorbing solar radiation instead of reflecting it. As they grow and join together, they undergo a transition in fractal geometry, effectively creating a never-ending pattern that can be modelled by mathematicians.

Hardenbrook is building upon a decade of work on melt ponds by Prof Golden and previous students and researchers at the university by adapting the classical Ising model, which was developed more than a century ago and explains how materials can gain or lose magnetism, to model melt pond geometry. “I hope to make the model for sea ice more physically precise so that it can be put into global climate models to create a more accurate approach of addressing melt ponds, which have a surprising effect on the albedo of the Arctic,” she explains.

Adding to the big picture
Mathematicians have already solved the conundrum of how to define the width of the undulating marginal sea ice zone, which extends from the dense inner core of pack ice to the outer fringes , where waves can break the floating ice.

Court Strong, who is an atmospheric scientist and one of Prof Golden’s colleagues at the University of Utah, drew inspiration from an unusual source: the cerebral cortex of a rat’s brain. He realised they could use the same mathematical method to measure the width of the marginal ice zone as they do for measuring the thickness of the rodent’s bumpy brain, which also has a lot of variation. With the aid of this simplified model, the team was able to demonstrate that the marginal ice zone has widened by around 40% as our climate has warmed.

The university of Utah’s ACCESS scheme, including its hands-on research, immerses students in an interdisciplinary environment where maths is part of a bigger picture. It encourages cross pollination, where methods and ideas from seemingly unrelated areas of science can be used to solve problems when the underlying mathematics is essentially the same.

“When you’re presented with an unusual situation, you need different kinds of minds to look at a problem clearly and come up with solutions,” says Prof Golden.

The loss of sea ice seen in the Arctic has happened over just a few decades and continues at an alarming pace.

“We need all the good brains and different ways of thinking that we can get, and we need them fast,” he says.

This article has been reviewed for the University of Utah, National Science Foundation and Office of Naval Research by Elvis Bahati Orlendo, International Foundation for Science, Stockholm and Dr Magdalena Stoeva, FIOMP, FIUPESM.

Originally published by BBC Storyworks
Interview of Jody Reimer and Ken Golden by Dean Peter Trapa - Video

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Be the Light

Be the light in your community


On July 14-16, 2021, students of the American Indian Services (AIS) Pre-Freshman Engineering Program (AIS PREP) came to the University of Utah to celebrate the completion of their 2021 AIS PREP, co-hosted by the College of Science. AIS PREP is a free program for Native American students to take advanced science, technology, engineering and mathematics (STEM) courses for six weeks for three consecutive summers. At the end of the program, the students earn scholarships to any higher education institution that they choose and continue to receive financial assistance. The 2021 AIS PREP group included 113 students from different Native American tribes: Navajo (Diné), Hopi, Oglala Sioux (Lakota), Shoshone/Bannock, Zuni, Crow, Paiute, and Cheyenne. AIS PREP is focused on making the curriculum culturally sensitive to the Native American students they serve. They bring a unique opportunity to keep the students close to their homes.

“We’re the only non-profit that has taken on such a big program like this. Some of these tribal communities are in rural areas—resources are scarce,” said Meredith Little Lam, project and program manager at AIS and AIS scholarship alumnus. “The whole point of AIS PREP is that we want to make sure we give our Native American students STEM resources that will allow them to succeed in high school.”

The students traveled to the U on July 14 to stay in campus dorms, meet PREP students from other AIS PREP sites, and hear presentations from U staff and College of Science faculty to celebrate the completion of the program. The week ended with a keynote address from the architect, inventor and entrepreneur Alice Min Soo Chun, during which she shared her inspiring story of changing the world by inventing a durable, portable, collapsible solar light.

“These students come from some of the poorest reservations in the United States. This really is a trip of a lifetime for them,” said Little Lam, “Some come from areas where there’s no running water, no electricity. We live in the United States and it’s just appalling that we can’t figure out ways to help these communities. And so, I think that this is a proactive way of getting these students involved in STEM to let them know, ‘You can change your tribal communities. You have it within yourself to be that leader.’”

“The College of Science is honored to have taken part in celebrating this incredible accomplishment of completing AIS PREP,” said Cassie Slattery, director of special projects of the college. “We would be lucky to have any one of these exceptional students pursue science here at the U.”

Anyone can be a scientist


On Thursday, the students learned about a diverse array of topics from speakers, including Donna Eldridge (Navajo/Diné), program manager of Tribal outreach for Health Equity, Diversity, & Inclusion, Amy Sibul of the School of Biological Sciences, Paul Ricketts of the South Physics Observatory, Julie Callahan (Little Shell Tribe of Chippewa) of ASPIRE, and Kyle Ethelbah (Western Apache), director of the U’s TRIO programs. One of the day’s highlights was an explosive presentation from chemist Ryan Stolley. He threw balls of fire, inhaled sulfur hexafluoride to give himself a funny low voice, and had the students freeze flowers with liquid nitrogen and smash them to bits. In between the chemistry magic, Stolley shared his personal story.

“I was a Native American student, of the Choctaw Nation of Oklahoma. When I was young, school was not my focus—I was just getting into trouble. But I got a lucky break and met some chemists who really changed my life,” said Stolley. “Native students are severely underrepresented in STEM disciplines. I love any opportunity to show them that it’s possible to pursue science. I mean, I’m covered in tattoos. Anybody can be a scientist. You just have to be curious.”

Stolley spoke to the students about attending Fort Lewis College, a university in Colorado that offers free tuition to Native American students. He received a doctoral degree in organic chemistry from the U and was a postdoctoral research assistant at the Pacific Northwest National Laboratory. He returned to Salt Lake City as a research assistant professor first in the Department of Chemistry and now in the College of Science, as well as part owner of a local chemical company.

“Part of what my company does is to make products that help clean contaminants out of water across the Colorado Plateau, especially on Tribal lands,” Stolley said, “I want to get these students thinking about how we can take our science and turn it around to help our Native communities.”

Creating positive memories on campus is part of how AIS PREP helps plant the seed to pursue higher education.

“We’re excited to be partnering with the U and having the ability to connect these students with faculty and current student volunteers who are Native American so that they can instill in their minds that it’s not an impossible dream,” said Little Lam. “Maybe they’ll be teachers and maybe they’ll be researchers, but wherever they may be, they can contribute to their Tribal communities. AIS doesn’t just stop with them after they graduate. We give them financial resources, but also say, ‘Hey, we’re here for you. Even after you finish this program.’”

A problem is an opportunity in disguise

This is the first year that AIS invited a keynote speaker to address the students during their program completion celebration. For Little Lam, Alice Min Soo Chun was the perfect choice. Chun, founder and CEO of Solight Designs, Inc. invented the Solar Puff, a portable, collapsible, self-inflating light powered by the sun. Little Lam met Chun while at Navajo Strong, through which Chun donated Solar Puff lights to families on the Navajo Nation without access to electricity.

“Every problem is an opportunity in disguise,” Chun, who is also a professor at Columbia University, told the AIS PREP graduates. “By doing research and observing, anybody can do this.”

Chun’s passion for solar energy began when her son was diagnosed with asthma, a condition that was aggravated by New York City’s poor air quality. Chun was inspired to find energy solutions that would reduce air pollution and its impacts on respiratory health. She realized that her son’s respiratory issues were global; without access to electricity, millions of people are forced to burn kerosene lanterns for lighting that produce noxious fumes. She saw a need for solar lights that were durable and collapsible, but the only ones available had to be inflated, leaving users vulnerable to bacterial infections. So, she invented a foldable design that drew from her childhood.

“I’m Korean. When I was a little girl, my mother taught me origami when I was young. Origami is an incredibly powerful tool,” she said. “Paper on its own can’t stand up. Fold it once, you have a corner, you have structure.”

Through the “Give a Light” program, Solight Designs has supplied Solar Puffs to Haiti, Puerto Rico, The Florida Keys, Ghana, Ecuador, Miami and more after natural disasters left people without power. During her keynote address, Chun passed out Solar Puff lights to everyone in attendance and turned off the lights. Everyone switched on their solar lanterns, eliciting ooo’s and aww’s. The lights illuminated the entire auditorium, demonstrating the invention’s power.

“I used to get beat up a lot for looking different. So, I became a fighter—not with my fists, but with the light of my heart and mind. You are all light warriors,” Chun said. “My hope is that you leave understanding how powerful you are and that you have the ability to change the world.”

by Lisa Potter - originally published in @theU

NSF CAREER Award

NSF CAREER Award


Priyam Patel receives National Science Foundation CAREER Award.

Priyam Patel, assistant professor of mathematics at the U, has received a National Science Foundation CAREER Award. The National Science Foundation's CAREER Award is the most prestigious NSF award for faculty members early in their careers as researchers and educators. It recognizes junior faculty members who successfully integrate education and research within their organizations. The award comes with a federal grant for research and education activities for five consecutive years.

Priyam Patel

“I'm thrilled to receive the award, and I'm very excited to have the ability to pursue the research and educational projects the grant will afford,” said Patel. “The award also recognizes the support the Math Department and the University of Utah provide to faculty.”

Patel works in geometry and topology. The two areas differ in that geometry focuses on rigid objects where there is a notion of distance, while topological objects are much more fluid. In her research, Patel’s goals are to study and understand curves on surfaces, symmetries of surfaces, and objects called hyperbolic manifolds and their finite covering spaces. Topology and geometry are used in a variety of fields, including data analysis, neuroscience, and facial recognition technology. Patel’s research doesn’t focus on these applications directly since she works in pure mathematics.

She is currently working on problems concerning groups of symmetries of certain surfaces. Specifically, she has been studying the mapping class groups of infinite-type surfaces, which is a new and quickly growing field of topology. “It’s quite exciting to be at the forefront of it. I would like to tackle some of the biggest open problems in this area in the next few years, such as producing a Nielsen-Thurston type classification for infinite-type surfaces,” she said. She is also interested in the work of Ian Agol, professor of mathematics at Berkeley, who won a Breakthrough Prize in 2012 for solving an open problem in low-dimensional topology. Patel would like to build on Agol’s work in proving a quantitative version of his results. Other areas she’d like to explore are the combinatorics of 3-manifolds and the theory of translation surfaces.

Patel joined the Math Department in 2019.

by Michele Swaner, first published @ math.utah.edu

Patterns in Sound

Fernando Guevara Vasquez


U mathematicians create quasiperiodic patterns using sound waves.

Mathematicians and engineers at the University of Utah have teamed up to show how ultrasound waves can organize carbon particles in water into a sort of pattern that never repeats. The results, they say, could result in materials called “quasicrystals” with custom magnetic or electrical properties.

The research is published in Physical Review Letters.

“Quasicrystals are interesting to study because they have properties that crystals do not have,” says Fernando Guevara Vasquez, associate professor of mathematics. “They have been shown to be stiffer than similar periodic or disordered materials. They can also conduct electricity, or scatter waves in ways that are different from crystals.”

Quasiperiodic two-dimensional pattern by Fernando Guevara Vasquez

Non-pattern patterns

Picture a checkerboard. You can take a two-by-two square of two black tiles and two white (or red) tiles and copy and paste to obtain the whole checkerboard. Such “periodic” structures, with patterns that do repeat, naturally occur in crystals. Take, for example, a grain of salt. At the atomic level, it is a grid-like lattice of sodium and chloride atoms. You could copy and paste the lattice from one part of the crystal and find a match in any other part.

But a quasiperiodic structure is deceiving. One example is the pattern called Penrose tiling. At first glance, the geometric diamond-shaped tiles appear to be in a regular pattern. But you can’t copy and paste this pattern. It won’t repeat.

The discovery of quasiperiodic structures in some metal alloys by materials scientist Dan Schechtman earned a 2011 Nobel Prize in Chemistry and opened up the study of quasicrystals.

Since 2012, Guevara and Bart Raeymaekers, associate professor of mechanical engineering, have been collaborating on designing materials with custom-designed structures at the microscale. They weren’t initially looking to create quasiperiodic materials—in fact, their first theoretical experiments, led by mathematics doctoral student China Mauck, were focused on periodic materials and what patterns of particles might be possible to achieve by using ultrasound waves. In each dimensional plane, they found that two pairs of parallel ultrasound transducers suffice to arrange particles in a periodic structure.

But what would happen if they had one more pair of transducers? To find out, Raeymaekers and graduate student Milo Prisbrey (now at Los Alamos National Laboratory) provided the experimental instruments, and mathematics professor Elena Cherkaev provided experience with the mathematical theory of quasicrystals. Guevara and Mauck conducted theoretical calculations to predict the patterns that the ultrasound transducers would create.

Creating the quasiperiodic patterns

Cherkaev says that quasiperiodic patterns can be thought of as using, instead of a cut-and-paste approach, a “cut-and-project” technique.

If you use cut-and-project to design quasiperiodic patterns on a line, you start with a square grid on a plane.  Then you draw or cut a line so that it passes through only one grid node. This can be done by drawing the line at an irrational angle, using an irrational number like pi, an infinite series of numbers that never repeats. Then you can project the nearest grid nodes on the line and can be sure that the patterns of the distances between the points on the line never repeats. They are quasiperiodic.

The approach is similar in a two-dimensional plane. “We start with a grid or a periodic function in higher-dimensional space,” Cherkaev says. “We cut a plane through this space and follow a similar procedure of restricting the periodic function to an irrational 2-D slice.” When using ultrasound transducers, as in this study, the transducers generate periodic signals in that higher-dimensional space.

The researchers set up four pairs of ultrasound transducers in an octagonal stop sign arrangement. “We knew that this would be the simplest setup where we could demonstrate quasiperiodic particle arrangements,” Guevara says. “We also had limited control on what signals to use to drive the ultrasound transducers; we could essentially use only the signal or its negative.”

Into this octagonal setup, the team placed small carbon nanoparticles, suspended in water. Once the transducers turned on, the ultrasound waves guided the carbon particles into place, creating a quasiperiodic pattern similar to a Penrose tiling.

“Once the experiments were performed, we compared the results to the theoretical predictions and we got a very good agreement,” Guevara says.

Custom materials

The next step would be to actually fabricate a material with a quasiperiodic pattern arrangement. This wouldn’t be difficult, Guevara says, if the particles were suspended in a polymer instead of water that could be cured or hardened once the particles were in position.

“Crucially, with this method, we can create quasiperiodic materials that are either 2-D or 3-D and that can have essentially any of the common quasiperiodic symmetries by choosing how we arrange the ultrasound transducers and how we drive them,” Guevara says.

It’s yet to be seen what those materials might be able to do, but one eventual application might be to create materials that can manipulate electromagnetic waves like those that 5G cellular technology uses today. Other already-known applications of quasiperiodic materials include nonstick coatings, due to their low friction coefficient, and coatings insulating against heat transfer, Cherkaev says.

Yet another example is the hardening of stainless steel by embedding small quasicrystalline particles. The press release for the 2011 Nobel Prize in Chemistry mentions that quasicrystals can “reinforce the material like armor.”

So, the researchers say, we can hope for many new exciting applications of these novel quasiperiodic structures created by ultrasound particle assembly.

Find the full study here.

 

by Paul Gabrielsen, first published in @theU

Amanda Cangelosi

Amanda Cangelosi receives U's Early Career Teaching Award


Amanda Cangelosi, instructor (lecturer) in the Mathematics Department, has received the 2021 Early Career Teaching Award from the University of Utah. The award is given to outstanding young faculty members who have made significant contributions to teaching at the university. Specifically, the University Teaching Committee looks for a faculty member who has distinguished her or himself through the development of new and innovative teaching methods, effectiveness in the curriculum and classroom, as well as commitment to enhancing student learning.

“I’m honored to receive this award and recognition from the university,” said Cangelosi. “Since my work focuses on the preparation of future Utah K-12 teachers, which intersects with social justice goals in a foundational way, this award means that the U cares about dismantling systemic oppression. There is nothing more systemic than K-12 education, and thus no more impactful space to invest one’s energy.”

In her approach to teaching, Cangelosi believes it's important for children to have math teachers who are skillfully trained to break the unhealthy and dangerous cycle of students who make value judgments about their self-worth based upon their achievement (or lack of) in math. “Issues of mathematical status and power between students in a math classroom need to be recognized and attended to by teachers so children don’t label themselves as “stupid” or, equally-dangerously, as “smart” relative to each other,” she said.

To overcome social divisions and stratifications within the classroom, Cangelosi believes teachers need to focus on creating productive, collaborative, and student-centered learning activities, implementing culturally relevant lessons, using multiple approaches to teaching math, and embracing unconventional approaches. Implementing these strategies require teachers to engage in challenging identity work, understanding the history of education in the U.S., embracing heterogeneous classrooms, and engaging in anti-bias and anti-racist training within mathematical contexts.

In her own teaching, Cangelosi draws heavily from the mainstream math education literature. For example, several of her students were personally affected from watching and reflecting upon Danny Martin's Taking a Knee in Mathematics Education talk from the 2018 annual conference of the National Council of Teachers of Mathematics.

Cangelosi’s teaching contributions include the following:

  • She taught a math lab class at Bryant Middle School for the 2019-2020 academic year to deepen productive collaborations between the U and local schools, thereby creating a seamless practicum space for undergraduate Math Teaching majors, while providing long-term outreach to the local community.
  • Inspired by Utah State University’s teaching practicum, in 2011 she established the current innovative structure of the Math 4095 course—including funding (often out of her own pocket) for mentor teachers, which resulted in onsite, fully-contained classrooms at local schools for University of Utah teaching majors.
  • During the pandemic, she created a sustainable and equitable virtual after-school tutoring program that allowed local high school students to meet with math undergraduates for homework support.
  • She created sanitized manipulatives kits to be distributed to her students for use in online synchronous lectures and labs, to help maintain the integrity of her hands-on collaborative Math 2000/4010/4020 classes during the COVID-19 pandemic.
  • She helped develop course curricula for Math 2000, Math 1010, and Math 4090/4095, introducing and modifying resources from her previous work as a secondary math teacher at The Urban School of San Francisco, bringing what are now mainstream practices to the University of Utah.
  • She has made numerous community, school-district-level, and Utah State Board of Education (USBE) contributions, such as diverse teacher recruitment, committees, and professional development.

“I love approaching old concepts in new, nontraditional ways, because we so often confound our understanding of concepts with the arbitrary conventions that we use to communicate them,” she said. “This often challenges student perceptions of classroom status and power in productive ways, often flipping the previously conditioned dynamic on its head and inviting students to rewrite their mathematical identities in a positive light.”

Cangelosi received her Bachelor of Science degree in Mathematics Education, as well as a Master’s of Statistics degree from Utah State University. She also has a post-baccalaureate degree in mathematics from Smith College. She joined the U’s Math Department in 2011.

 

by Michele Swaner - first published @ math.utah.edu

2021 Churchill Scholar

Six in a Row!


Isaac Martin brings home the U's sixth straight Churchill Scholarship.

For the sixth consecutive year a College of Science student has received the prestigious Churchill Scholarship to study at the University of Cambridge in the United Kingdom. Isaac Martin, a senior honors student majoring in mathematics and physics, is one of only 17 students nationally to receive the award this year.

Martin’s designation ties Harvard’s six-year run of consecutive Churchill Scholars (1987-1992) and is second only to Princeton’s seven-year streak (1994-2000).

“Isaac’s recognition as a Churchill Scholar is the result of years of remarkable discipline and dedication to a field of study that he loves,” said Dan Reed, senior vice president for Academic Affairs.

Martin decided to apply for a Churchill Scholarship as a freshman, after meeting for lunch with Michael Zhao, a 2017 Churchill Scholar who unexpectedly passed away in 2018.

“I am positively delighted and quite flabbergasted to receive the scholarship,” Martin says, “but I wish I could phone Michael to thank him for making the opportunity known to me. His legacy lives on in the undergraduate program of the math department here at Utah, where many others like me have greatly benefited from the example he set.”

Martin, a recipient of an Eccles Scholarship and a 2020 Barry Goldwater Scholarship, remembers as a kindergartener trying to write down the biggest number in existence and, as an eighth grader, suddenly understanding trigonometry after hours of reading on Wikipedia.

“That sensation of understanding, the feeling that some tiny secret of the universe was suddenly laid bare before me – that’s something I’ve only felt while studying math and physics, and it’s a high I will continue to chase for the rest of my life,” he says.

Books by Carl Sagan and Jim Baggott also kindled his love of math and physics, and after several years of self-directed study in middle and high school and a year at Salt Lake Community College, Martin enrolled at the U as a mathematics and physics double major.

After early undergraduate experiences in the research labs of physics professors Vikram Deshpande and Yue Zhao, Martin found himself gravitating more toward mathematics. He completed a Research Experience for Undergraduates (REU) at UC Santa Barbara studying almost Abelian Lie groups, which have applications in cosmology and crystallography, under Zhirayr Avetisyan. This experience resulted in Martin’s first research paper. He later completed another REU at the University of Chicago.

“This research was incredibly rewarding because while it applied to physics, the work itself was firmly rooted in the realm of pure math.” Martin says.

Returning to Utah, Martin worked with professors Karl Schwede and Thomas Polstra to study F-singularities, and developed this work into a single-author paper and his currently-in-progress honors thesis with professor Anurag Singh.

“I would not be where I am today without the incredible faculty at Utah and their willingness to devote time to undergraduates,” Martin says.

At Cambridge, Martin hopes to study algebraic geometry, number theory and representation theory (“in that order,” he says) in pursuit of a master’s degree in pure mathematics.

“I’m particularly interested in learning as much as I can about mirror symmetry, which I intend to make my essay topic,” he adds. “I also plan to drink a lot of tea and to buy one of those Sherlock Holmes coats. I will also begrudgingly begin using the term ‘maths’ but I promise to stop the instant I board a plane back to the U.S. in 2022.”

After he returns from Cambridge, Martin plans to earn a doctoral degree in pure mathematics and enter academia, using his experiences in many different educational systems including U.S. and British public schools, homeschooling and online learning, to broaden opportunities for students from a diversity of backgrounds.

“My past has molded me into who I am today,” he says, “and I hope I can use my experiences to create programs in STEM for opportunity-starved students, whether they are held back due to non-traditional schooling or to socio-economic factors.”

 

by Paul Gabrielsen - First Published in @theU

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