Aftermath - Spring 2022

Spring 2022 | Volume 21, Issue 2

Awards recognize department excellence Page 2

In this issue Message from the Chair. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Awards recognize department excellence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Priyam Patel receives U Faculty Fellow Award. . . . . . . . . . . . . . . . . . . . . . . . 2 Jon Chaika wins U’s Distinguished Research Award. . . . . . . . . . . . . . . . . . . . 3 Kevin Wortman honored with MAA Teaching Award. . . . . . . . . . . . . . . . . . 4 Eamon Quinlan-Gallego and Alex Rasmussen awarded NSF Fellowships. . . 4 Samantha Linn and Kaitlin O’Dell receive NSF-GRF Awards. . . . . . . . . . . . . 7 Sanghoon Kwak wins U Graduate Research Fellowship. . . . . . . . . . . . . . . . . 9 Seungsu Lee receives U Teaching Assistantship Award . . . . . . . . . . . . . . . . 10 Muskan Walia Named Public Service Scholar by Phi Beta Kappa Society. . 11 Eli Counterman wins CoS University Student Researchers Award. . . . . . . 12 Ken Golden Named U Presidential Societal Impact Scholar . . . . . . . . . . . . 13 Sloan Fellowship recipient Li-Cheng Tsai joins Math Department in July . . . 14 Summary of Mathematics Department awards. . . . . . . . . . . . . . . . . . . . . . . . 16

Message from the Chair During the semester, we continued to hold in-person classes while ensuring a

healthy and safe campus. Slowly but surely, we appear to be returning to campus life and the activities we enjoyed before the pandemic. It truly was wonderful to see students, their families, and guests at our convocation and hooding ceremonies in May. We want to recognize the achievements of our undergraduate and graduate students in completing their degree requirements. Obtaining a math degree or a Ph.D. takes hard work and commitment. We have enjoyed teaching and working with our students, and we wish them the best as they move forward in their lives and careers.

This spring the Department of Mathematics received many awards and recognitions for our amazing and talented faculty, postdocs, and graduate and undergraduate students, and staff. The quality and quantity of the awards are a testament to the reputation of the department in having a world-class research and teaching faculty committed to a strong educational and mentoring program. Since 2019, our faculty has received 11 National Science Foundation awards, with the majority received in 2021-2022. We remain focused on our commitment to excellence in research and teaching at both the graduate and undergraduate levels. We are very proud of the accomplishments of all those in our Department of Mathematics community, our faculty, postdocs, and students.

As always, thank you for your support and generosity. We depend on your interest in advancing our mission of excellence, teaching, mentoring, and research.

Davar Khoshnevisan

Best regards,

Davar Khoshnevisan Professor and Chair Department of Mathematics

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Awards recognize department excellence At the end of each academic year, the University of Utah, the College of Science, the Department of Mathematics, and national and international organizations recognize excellence in faculty, postdocs, graduate and undergraduate students, and staff through the presentation of awards. In this section of Aftermath, we highlight some of the members of our Mathematics academic community who received distinctions in the 2021-2022 academic year. For a complete list of recipients, please see the summary on pages 16 and 17.

FACULTY AWARD

Priyam Patel receives U Faculty Fellow Award Priyam Patel, Assistant Professor of mathematics, has received a Faculty Fellow Award from the University of Utah.

Faculty Fellow Awards provide a semester of full release time from teaching and administrative tasks at full salary to tenure-line faculty for scholarly and creative projects. The funding can also be used to support pilot studies for external funding proposal submissions.

“Receiving this award is such an honor, and I am thankful for the time it will afford me to build on the momentum in my current research program,” said Patel.

Patel studies curves on surfaces, symmetries of surfaces, and objects called hyperbolic manifolds and their finite covering spaces. Surfaces come in two types: finite or infinite. Traditionally, finite-type surfaces have been studied more extensively; however, infinite-type surfaces are the focus of a quickly growing, new subfield of geometry and topology. One of the biggest unsolved problems in mathematics is to classify the symmetries of infinite-type surfaces.

Patel plans to use the award to further her research in this area.

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Priyam Patel In 2021, she received a National Science Foundation (NSF) CAREER Award, which is considered the most prestigious NSF award for faculty members early in their careers as researchers and educators.

Patel joined the Math Department in 2019.

FACULTY AWARD

Jon Chaika wins U’s Distinguished Research Award Jon Chaika, Associate Professor in the Department

of Mathematics, has been awarded the Distinguished Research Award (DRA) from the University of Utah.

The DRA recognizes outstanding achievements in research by University of Utah faculty. Up to three awards for outstanding achievements in research are awarded to university faculty each year. This prestigious research award provides a faculty member with a $10,000 grant to pursue research and/or creative pursuits, as well as recognition at the university’s commencement exercises.

“It’s a big honor to receive the DRA, and it adds to my excitement to continue working on the problems that I have been pursuing,” he said.

The funds from the award will allow Chaika to meet with other colleagues on his research. “The type of mathematics I do doesn’t need labs or expensive machinery, but it does rely heavily on interactions with other people,” he said. “This award will allow me to work with my collaborators, domestically and abroad.”

Chaika’s research is in the field of dynamical systems, which seeks to understand a space and a map by following individual points. The map could represent the passage of time in a physical system. Ergodic theory is a sub-branch of dynamical systems that uses an idea called a measure to do this. A measure is an abstraction of the idea of length or area (or volume). One of the families of systems Chaika studies is billiards in polygons. In these systems, a point travels in a straight line inside a polygon until it hits one of the sides.

Once it hits a side, it obeys the law of elastic collision, bouncing off the side the same way a billiard ball would off the side of a pool table. It then continues to travel in a straight line until it hits the next side, where it again has an elastic collision. Chaika and Giovanni Forni, a mathematician at the University of Maryland,

Jon Chaika have been able to show there are billiards in polygons in which the flow in different directions is usually uncorrelated.

In July 2022, Chaika will give an invited lecture at the prestigious International Congress of Mathematicians (ICM), the largest and most significant conference on pure and applied mathematics, as well as one of the world’s oldest scientific congresses. Originally scheduled to be held in St. Petersburg, Russia, the conference now will be held remotely. Chaika will present jointly with Barak Weiss, Professor of Mathematics at Tel Aviv University. Invited lectures are organized into sections, and Professors Chaika and Weiss will present within the “Dynamics” section. The U’s Department of Mathematics will have outstanding representation at the ICM. In addition to Chaika, Mladen Bestvina, Distinguished Professor of Mathematics, will give a plenary lecture at the event.

In 2020, Chaika received a Simons Fellows Award in Mathematics. He obtained a Ph.D. in mathematics in 2010 from Rice University and joined the University of Utah in 2013.

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FACULTY AWARD

Kevin Wortman honored with MAA Teaching Award Kevin Wortman, an Associate Professor and Director of Undergradu-

ate Studies in the University of Utah Department of Mathematics, has been honored with the 2022 Mathematical Association of America (MAA) Distinguished Teaching Award for the Intermountain Region.

Kevin Wortman

The award honors professors of mathematics whose efforts have been recognized as influential beyond their own institutions. Since 2004, Wortman is the fifth U mathematics faculty member to receive this honor. Previous U math faculty recipients include Don Tucker, Nicholas Korevaar, Peter Alfeld, and Anne Roberts. Wortman joined the U’s Math Department in 2007.

The Mathematical Association of America, with more than 25,000 members, is the primary professional organization for teachers of undergraduate mathematics. The MAA Intermountain Region includes all colleges and universities in Utah and southern Idaho.

POSTDOC AWARDS

NSF Fellowships awarded to Eamon Quinlan-Gallego and Alex Rasmussen Two professors in the Department of Mathematics have each received a Mathematical Sciences Postdoctoral Research Fellowship from the National Science Foundation. The three-year fellowship is awarded to support future leaders in mathematics and statistics by helping them participate in postdoctoral research that will enhance their development.

Eamon Quinlan-Gallego Eamon Quinlan-Gallego, who joined the department in 2021, serves as an Assistant Professor (Lecturer). “Receiving this fellowship is an incredible honor, and it will allow me to dedicate myself to research full-time for four semesters and extend my stay in Utah for an extra year. It will also give me funds to travel to conferences and visit collaborators,” he said.

Quinlan-Gallego studies solutions to polynomial equations and their singularities. For example, in pre-calculus, the equation y = x^2 defines a parabola in the plane. This parabola is smooth—it doesn’t have any sharp corners; however, occasionally, polynomial equations can fail to be smooth. These non-smooth points, called singularities, are ubiquitous across mathematics, and their study is a fundamental problem.

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Typically, Quinlan-Gallego uses two different techniques to study these singularities. First, he can associate certain differential equations to them whose behavior allows them to be classified in different ways.

Second, he can study singularities using “modulo-p.”

He fixes a prime number (usually denoted by p, but in this case, for example, we could use p = 5). Working “modulo-5” means that when he looks at a polynomial equation, like y^3 = x^2, instead of thinking about it in the real-number system (as you would in pre-calculus), he thinks of it in clock arithmetic. This means that he does all of the algebra using a clock with 5 hours. For example, if our clocks had 5 hours, and it was 4 o’clock and 2 hours pass, it is 1 o’clock. In clock arithmetic, we would say that 4 + 2 = 1. Similarly, 4 x 2 is usually 8 but in our clock, we have 4 x 2 = 3.

“By working in this clock arithmetic, we lose all of the ‘geometry,’ but we gain a host of other tools we can use, and the hope is that as the prime p selected gets larger and larger, the behavior of the singularity modulo-p approaches the real behavior,” he said. He also likes to combine these two techniques and think about differential equations modulo-p.

He was good at math as a kid but until he was a senior in high school, he thought he would become a biologist. Then two things happened. First, he realized he only wanted to study biology because the idea of going to remote islands to look at creatures no one had seen before sounded cool, but learning about all the chemical reactions going on in the mitochondria wasn’t so exciting. Second, he read Stephen Hawking’s book A Brief History of Time and became fascinated by how mathematics is used to learn about things that are far away in space and time. At that point, he switched from studying biology to physics. The jump from physics to mathematics was much more straightforward when he realized he was enjoying his math classes more than experimental physics.

Quinlan-Gallego was raised in Spain—his mother is Spanish and his father is American. After high school, he left Spain to study in Scotland at the University of Glasgow. “There was this great program for citizens of the European Union that allowed me to study in Scotland for free,” he said. “I had a wonderful time in Glasgow, and I was given so many amazing opportunities.” During his undergraduate years, he also

Eamon Quinlan-Gallego participated in an exchange program at the National University of Singapore for a year.

Once he completed his bachelor’s degree, he knew he wanted to come to the U.S. for graduate school. He was accepted to the University of Michigan and began working under Professor Karen Smith, who serves as the William Fulton Distinguished University Professor of Mathematics. He also spent more than a year in Tokyo, again as an exchange graduate student, at the University of Tokyo.

He’s looking forward to continuing his work at the U. “The department has many experts in modulo-p methods and a host of other very interesting topics, so I’m looking forward to learning as much as possible from them and moving forward in my research,” he said.

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Alex Rasmussen Rasmussen is a Research Assistant Professor in the department. “I’m very grateful to be recognized for my research and to the people who helped me along the way, including my advisors, collaborators, mentors, and teachers,” he said. “The award will allow me to devote more time to my research program. In addition, it will enable me to take on more activities to serve the math community, such as mentoring undergraduates and organizing conferences.”

Rasmussen’s work focuses on symmetries of geometric objects. Specifically, he’s interested in symmetries of spaces that are “negatively curved.” “The geometry of negatively curved spaces is quite unlike that of our own space, and it makes them exotic and also very beautiful,” he said.

A bunch of symmetries form a group, and a group can be thought of as symmetries of many different negatively curved spaces at the same time. A large part of Rasmussen’s research is spent on classifying the different spaces associated to one group. He finds the subject interesting because it allows him to draw pictures, engage his creative and aesthetic senses, and use tools from other fields, such as commutative algebra.

In high school, Rasmussen wasn’t especially interested in math. He did well at it but found it somewhat dry and mechanical. His first math class at Colby College was a multivariable calculus class taught by Scott Taylor, Associate Professor and Department Chair. Taylor used pictures of curves and surfaces in his teaching.

This was a revelation to Rasmussen, who began to discover the beauty, depth, and creativity of math. From that point on, he took more math classes.

He received a bachelor’s degree in mathematics and began a graduate program at the University of California Santa Barbara, where he received a master’s degree. He obtained a Ph.D. in mathematics from Yale University in 2020.

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Alex Rasmussen He has a few research goals he’d like to work on over the next few years. These include classifying hyperbolic actions of metabelian groups and classifying geodesic laminations on infinite type surfaces. Metabelian groups are a wide class of relatively simple groups that can still have complicated hyperbolic actions. Geodesic laminations are 1-dimensional objects on surfaces consisting of long straight lines interacting in complicated ways. “These are pretty hard problems that will keep me busy for a while. Along the way, many other related problems will pop up naturally,” he said.

GRADUATE STUDENT AWARDS

Samantha Linn and Kaitlin O’Dell receive NSF Graduate Research Fellowships Two graduate students in the Department of Mathematics each have been awarded a Graduate Research Fellowship from the National Science Foundation (NSF). The fellowship provides three years of support over a five-year fellowship period for individuals working on a graduate degree who have demonstrated potential for significant research achievements in STEM or STEM education.

Samantha Linn “Recognition from the NSF feels like a pat on the back from one of your greatest role models,” said Linn. “It means ‘well done,’ but it also means, ‘keep up the good work.’ I am grateful because the fellowship gives me more freedom to focus on research and continue my participation in organizations that I care a lot about, such as the Association for Women in Mathematics, the Prison Mathematics Project, and the Living Room Exchange of Mathematics.”

Linn’s research focuses on understanding randomness in various biological processes. In particular, she has spent time thinking about what is known as the “redundancy principle,” which is about the need of many copies of the same entity (think cells, molecules, or ions, for example) to fulfill a biological function. The redundancy principle states that while these copies may seem energetically wasteful, this redundancy is necessary for certain tasks to occur sufficiently fast.

Such a task might be neurotransmitters, which we think of as random searchers, looking for postsynaptic receptors, which we think of as targets.

Linn has been working on characterizing what might be expected from the fastest searcher. “One advantage of my work is that the application doesn’t need to be solely centered on biology,” she said. “In fact, the questions I ask are often relevant to many areas of physics, chemistry, and sociology. There are many more questions to be asked, with specific applications in mind, so I’m sure this work will keep me busy for a while!”

Samantha Linn Linn grew up loving math, and she spent a lot of her free time doing sudoku puzzles and other math games.

It wasn’t until halfway through college that she became aware of the possibility of pursuing a career in mathematics.

Before moving to Utah for graduate school, she studied biomedical engineering at the University of Minnesota. She had planned to study medicine but became concerned by the lack of math in her pre-med classes.

With the help of mentors, she realized that she would be happier pursuing a Ph.D. in mathematics.

She wasn’t sure where she wanted to go for graduate school—she had flights booked for graduate program visits, but everything was canceled at the last minute with the start of the COVID pandemic in March Continued on page 8

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Continued from page 7 2020. After participating in Zoom calls with at least 50 graduate students and faculty at various programs, she decided that the people in Utah were the happiest.

She had never been to Salt Lake City until the day she moved here, but it has worked out well. Linn likes the graduate program, finds it fun, and she’s very happy she made the decision to come to the U. After graduate school, she hopes to continue her research as a postdoc and, ultimately, have a career in academia as a full professor.

Kaitlin O’Dell “I feel so honored to receive such a prestigious award,” said O’Dell. “I never imagined I would receive the amazing feedback I got while I was applying for the fellowship. The research I plan on doing is groundbreaking work in numerical methods, so to have that recognized is beyond exciting! The fellowship is really going to allow me to focus on my research and hopefully give not only the numerical community—but the science and engineering community—a great way to model high-dimensional equations.”

O’Dell’s work is primarily focused on the numerical modeling of high-dimensional partial differential equations. She and her team specifically are developing a particle method that will preserve the energy dissipation structure of the physical systems. Once the actual numerical procedure is developed and analyzed for validity, the team hopes to test it on many physical models to gain a better understanding of these higher-order systems. These physical models can range from materials science to fluids, mechanics, and engineering.

She excelled at math as a kid, but it wasn’t until she began doing research as an undergrad that she realized how much she enjoys math. “I was able to do research on engineering topics that I was already familiar with and combine them with my two favorite subjects—numerical analysis and ordinary differential equations,” she said. “This really opened my eyes as to what I could be doing in the field of math and the broad range of research I could perform as an applied mathematician.”

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Kaitlin O’Dell O’Dell started out studying engineering at the University of New Mexico (UNM) because of her love for space and science. She enjoyed internships and had the opportunity to work at NASA Ames Research Center. However, she began to find that she was enjoying the math modelling aspect of engineering more than the actual engineering. She decided to switch her major to applied math during her senior year, and she began doing research with Professor Emeritus Deborah Sulsky on beam theory (a way of calculating the load-bearing and deflection characteristics of beams) as part of her honors thesis.

“Dr. Sulsky is an amazing mentor, and she’s very much the reason that I’m now doing a Ph.D. in mathematics,” O’Dell said. After O’Dell graduated from UNM in 2020, with honors from the university and honors in mathematics, she decided to apply to the U because of the reputation of the Math Department and the fact that the graduate students seemed happy. “At the time I wasn’t sure what I would research, but I found a project that I absolutely fell in love with, and now I couldn’t be happier,” she said. After she obtains her Ph.D., O’Dell would like to stay in academia, but she can also envision working in industry. “I’ll most likely apply to a wide variety of things and choose what I think will be the best fit for me,” she said.

GRADUATE STUDENT AWARD

Sanghoon Kwak wins U Graduate Research Fellowship Sanghoon Kwak, a third-year Ph.D. candidate in

the Department of Mathematics, has been awarded a Graduate Research Fellowship (GRF) from the University of Utah. The purpose of the GRF is to provide graduate students with an opportunity to do full-time research during an academic year. Recipients are selected and evaluated on the quality and impact of their research or creative project, their achievements, and their potential for success.

“I am tremendously honored and humbled to receive a GRF,” said Kwak. “It’s a huge affirmation of the work I’ve done for the last three years and an encouraging nod to my future work. The fellowship will allow me to have more solid blocks of time to dedicate to my research. I also want to recognize the support, trust, and patience I’ve received from my advisors, Distinguished Professor Mladen Bestvina and Assistant Professor Priyam Patel.”

Kwak studies geometric group theory, which is an area of mathematics devoted to studying groups, endowing them with a metric, and treating them as geometric objects. Geometric group theory is a relatively new area of mathematics, providing a variety of applications to geometry, topology, group theory, number theory, and graph theory. Many junior researchers have been drawn to this field, and the Math Department at the university has one of the leading groups.

In his research, Kwak works on the group of symmetries of infinite graphs that correspond to infinite-type surfaces. In the fall of 2021, Dr. Bestvina and Dr. Yael Algom-Kfir, a lecturer at the University of Haifa in Israel who received her Ph.D. in mathematics from the U in 2010, conducted a pioneering study on the symmetry group of infinite-type graphs. Based on this study, Kwak and other colleagues in the Math Department were able to develop a complete classification of which infinite-type graphs have symmetry groups with “interesting” geometry. The GRF will allow him to continue his work in this area.

Sanghoon Kwak Kwak has always enjoyed the beauty, simplicity, and universality of math. “One of the things I like about mathematics, compared to the other sciences, is that mathematical knowledge has no expiration date,” he said. “An established fact in mathematics, as long as it is rigorously proved, rests forever. For me, publishing a paper is like putting a small stone out there that will last. The stone could be a part of a cornerstone of a castle to build on; it could be placed on top of a pyramid of stones; or it could serve as a kind of Rosetta Stone that unlocks understanding between different fields; or it could contribute to a mosaic of stones that helps us understand a larger piece of a picture.”

He received a bachelor’s degree in mathematics from the Korea Advanced Institute of Science and Technology (KAIST) in South Korea. During his undergraduate education, Dr. Bestvina visited KAIST and gave a lecture on geometric group theory. Kwak attended his presentation and wanted to learn more about the correspondence between surfaces and graphs. Following graduation, Kwak was accepted to the U for graduate school. After he receives his Ph.D., he hopes to continue his research and teach at a university.

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GRADUATE STUDENT AWARD

Seungsu Lee receives U Teaching Assistantship Award Graduate student Seungsu Lee has received a Teaching Assistantship Award from the University of Utah. The award is designed to bolster undergraduate education while providing graduate students with experience teaching in undergraduate environments. The opportunity is for full-time graduate teaching assistants.

“Receiving the award means a lot to me in different ways,” said Lee. “It tells me that my proposal is effective and will help many people who study math. Also, the award ensures support from the department and my mentor in implementing my proposal into an actual class. In terms of my career, the award confirms my teaching skills. I learned English as a second language, and I have a strong Korean accent, so receiving the award proves that one can develop communication and teaching skills to teach mathematics efficiently across cultures regardless of one’s background.”

Lee will be teaching an asynchronous online class for Math 2270—Linear Algebra—and will have responsibility for creating lecture videos for the department website. Asynchronous learning allows an instructor flexibility in creating a learning environment that will allow for different kinds of learners and learning styles. Lee’s academic advisor is Professor Karl Schwede, and his mentor for the project is Assistant Professor (Lecturer) Matt Cecil.

Seungsu Lee

“I like to chat about mathematics with other people,” said Lee. “When I teach, I love to communicate with students, tell them what they’re doing correctly, and teach them how to do mathematical reasoning. In particular, I like the moment when students understand what I’m teaching about a mathematical concept and I can see the ‘aha’ moment in their faces.”

When Lee was a child, his father showed him the magic square. The magic square is a square array of numbers in which all the rows, columns, and diagonals add up to the same sum, which is called the magic constant. This is the fun part in working through the square—you get the same number when you add numbers for each row, column, or even diagonals. “As far as I can remember, the magic square marked the first time that I ever saw a mathematical puzzle,” said Lee. He was very interested in the algorithm to solve the magic square. As he got older, he started to do more and more math. When he was in high school, he had a great math teacher who showed him rigorous ways to think about calculus by using epsilon and delta. This was a turning point for Lee that made him decide to forge a career in math.

He completed his undergraduate degree at Yonsei University in South Korea. “I got interested in algebraic geometry when I was an undergraduate,” he said. “Unfortunately, my university’s graduate school didn’t focus on this area of math, so I searched online and was excited to see that the U’s Math Department has a huge research group in algebraic geometry. I was so happy to be accepted to the department’s program.”

After he earns a Ph.D., he plans to seek a research position.

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STUDENT AWARD

Muskan Walia Named Public Service Scholar

by Phi Beta Kappa Society Muskan Walia, a second-year student at the Uni-

versity of Utah Honors College studying math and philosophy, has been named a Key into Public Service Scholar by the Phi Beta Kappa Society. The Society is the nation’s most prestigious academic honor society, and the Key into Public Service award highlights specific pathways for arts and sciences graduates to launch public sector careers.

Chosen from nearly 900 applicants attending Phi Beta Kappa chapter institutions across the nation, the Key into Public Service Scholars hail from 17 states. These are high-achieving college sophomores and juniors who display notable breadth and depth in their academic interests.

“I am extremely grateful and honored to be receiving this award from Phi Beta Kappa,” said Walia. “My community here at the University of Utah has provided me with a prodigious liberal arts and sciences education and has nurtured my interest in exploring the dynamics between science, society, and the public sector.

I am excited for the incredible opportunity to further explore this interest this summer.”

Walia is an ACCESS Scholar and undergraduate researcher working with Dr. Fred Adler, Professor of Biology and of Mathematics. In her research, Walia adapted an epidemiological SIR model for spread of disease to model the number of cells infected with SARS-CoV-2 in order to predict when different types of tests will produce false positives or false negatives.

“My summer in the ACCESS Scholars program sparked an interest and motivation to pursue a career in public service,” she said. “Being taught by faculty across the University of Utah in diverse disciplines, I learned about the intersections of science, communication, and policy and how scientists can practice the art of advocacy.

Muskan Walia “Working under the mentorship of Dr. Fred Adler has been invaluable. I wanted to be engaged in mathematics research that centered on justice and informed public policy. There was truly no better pairing than with Dr. Adler. He has wholeheartedly supported and encouraged my curiosity and passion to utilize mathematics principles to tackle the most pressing social justice related questions of our time.”

In addition to her studies, Walia currently serves as the ASUU student government Senate Chair and works as a youth environmental organizer in the Salt Lake City area. She founded a campaign to commit her local school district to a 100% clean electricity transition by 2030, and she has assisted with the expansion of local clean energy campaigns in Utah school districts.

She is also a leader and mentor at Utah Youth Environmental Solutions Network (UYES), where she supports the development of a new youth-based climate justice curriculum. Her experiences have cultivated a passion and commitment to community building, climate education, and environmental justice.

Each Key into Public Service Scholar will receive a $5,000 undergraduate scholarship and take part in a conference in late June in Washington, D.C. to provide them with training, mentoring, and reflection on pathways into active citizenship.

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STUDENT AWARD

Eli Counterman wins CoS University Student Researchers Award Elijah (Eli) Counterman

has been recognized

for his excellence in research by winning the College of Science University Student Researchers Award.

“This is a great honor for me and comes with significant recognition for my mentor’s work and the work I’ve been fortunate to do with him,” said Counterman.

“I feel extremely grateful to receive such an award!”

Under the guidance of Sean Lawley, Associate Professor in the Department of Mathematics, Counterman has been working on answers to some fundamental questions in the area of pharmacokinetics, the branch of pharmacology concerned with the movement of drugs within the body. Counterman has focused on the following question: if a patient misses a dose of medication, and they realize it the following day, should they take one pill or two to compensate for the missed dose?

“The mathematical models are interesting because of their direct implication to medicine and the health and well-being of a patient,” said Counterman. “These models use random variables to mimic the unpredictability and forgetfulness of human beings.” The models Counterman used were developed from some of the work of renowned Hungarian mathematician Paul Erdős and others in the 1930s.

“I’m interested in the research because I plan to graduate from the U next spring and attend medical school in the fall of 2023,” said Counterman. “Questions such as these—where math and medicine/biology overlap—are extremely applicable and interesting. I want to make an impact in the math world as a physician researcher. Mathematics seems to be one of the least utilized, yet potentially revolutionary fields, in the developing world of medical research.”

Counterman says he has always enjoyed studying math. He excelled in the subject in middle school,

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Elijah Counterman which allowed him to take undergraduate math classes at the U as a sophomore in high school. By the time he graduated from Highland High School in Salt Lake City, he was more than halfway through the coursework needed to obtain a bachelor’s degree in mathematics. “I love math because of its magnificently wide range of applications as well as its ability to answer fundamental questions,” he said.

Counterman has praise for the Math Department, noting that the professors are supportive, approachable, and easy to talk to. He has enjoyed the relatively small class size and the different teaching styles. He is impressed with the department’s research opportunities, teaching excellence, and reputation of the faculty.

Outside of math, he makes the time to play violin and guitar. He is very involved with his local faith organization and in serving the community.

Ken Golden Named U Presidential Societal Impact Scholar President Taylor R. Randall has named Ken Golden, Distinguished Professor of Mathematics, as an inaugural recipient of the University of Utah Presidential Societal Impact Scholar Award.

Dr. Golden and four other scholars are a select group of faculty. Recognized as experts in their respective fields and disciplines, they share and translate their scholarship, research, creative activities and ideas with opinion leaders, policy makers, the public and other audiences outside the university and in ways that can transform society.

The 2022 cohort of impact scholars are:

Kenneth Golden, Distinguished Professor, Department of Mathematics RonNell Andersen Jones, Professor, College of Law Michelle Litchman, Assistant Professor, College of Nursing Susie Porter, Professor, College of Humanities and the School for Cultural and Social Transformation

Paisley Rekdal, Distinguished Professor, Department of English Golden is a brilliant expositor and a passionate advocate for public awareness of our changing climate and the critical role of mathematics in climate modeling. He has given more than 40 invited public lectures since 2008 and more than 500 invited lectures since 1984. His public lectures emphasize the rapid and significant loss of Arctic sea ice and how mathematics is helping us predict the future of the Earth’s polar marine environment. Dr. Golden is among the rare group of top-level mathematical scientists who is able to reach to the broader public about one of the central issues of our time.

Ken Golden

From tackling the social determinants of health and wellness, to addressing the underlying causes of crime and poverty, to designing interventions to curb poor air and water quality, to helping better inform public debate on society’s most pressing issues, these scholars’ works have a positive impact on people and institutions and help make our world a better, more equitable, and more enjoyable place in which to live.

The Presidential Societal Impact Scholar Award was conceived by and is supported by a gift from University of Utah Professor Randy Dryer, the Presidential Honors Professor in the Honors College and a Professor of Law (Lecturer) at the S. J. Quinney College of Law.

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Sloan Fellowship Recipient Li-Cheng Tsai Joins Math Department in July In July, the Department of Mathematics will welcome Assistant Professor pus and Utah.

Li-Cheng Tsai to the U cam-

Tsai, who recently received a Sloan Research Fellowship, is currently teaching and doing research at Rutgers University, New Brunswick. The Sloan Fellowship is awarded to outstanding early-career researchers in scientific and technical fields. Tsai is one of 118 in the U.S. and Canada to receive the two-year fellowship from the Alfred P. Sloan Foundation.

“I’m deeply honored to receive this prestigious award,” said Tsai. “The fellowship will provide me with the resources to further my research, which I plan to continue in Utah.”

Tsai is looking forward to joining the U. “The Math Department has a really rich research portfolio, and the research directions of the probability group are well aligned with my own,” he said. “I look forward to fruitful interactions with my future colleagues in the department’s vibrant research environment.”

Probability and stochastic analysis Tsai’s research is about understanding unexpected universal patterns in stochastic systems. It turns out that systems that are random and governed by very different underlying rules can exhibit similar patterns.

For example, consider two lists of numbers: the first list is the populations of U.S. counties. The second list is the height of the 1,000 tallest structures in the world in meters. These two lists of numbers should have nothing in common, but, surprisingly, the leading digit of each number follows the same distribution on both lists.

“One might think that maybe the distribution of the leading digit just follows a uniform distribution (where 1, 2, 3, … 9 all have the same frequency of

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Li-Cheng Tsai occurrence), but that’s not the case,” said Tsai. In fact, the probability of the leading digit being 1 is about 30%, and the probability of being 9 is under 5%. This is known as Benford’s Law, or the first-digit law, and it occurs in a wide range of data sets: bills, taxes, and stock prices to name a few. In fact, the pattern is so universal that it is used as a standard test to see if a data set has been manipulated.

Tsai looks for these kinds of universal patterns, but in systems that are related to rough interfaces, such as the edge of a coffee stain, the front of a burning paper, or a randomly played tetris game. Despite having very different underlying physical mechanisms, the interfaces in these systems all share the same statistical pattern, and the pattern defies the standard law (or Gaussian) in probability textbooks. This universal phenomenon was discovered in the 1980s by physicists and has since grown into an active area of research in math and physics. Tsai’s work focuses on developing and applying a strand of mathematical tools called stochastic analysis to understand the universal pattern in these systems.

“I like this subject because it keeps me in contact with physics, my past academic interest, and because it touches on a wide spectrum of math,” he said. “For example, stochastic analysis and algebraic combinatorics are two very different kinds of math, sitting on the opposite ends of the spectrum, but both are very relevant to this subfield. My expertise lies in stochastic analysis, and it makes up the bulk of my research. At the same time, I have the opportunity to interact with and learn from experts in algebraic combinatorics.

This kind of interaction is very stimulating. Some of my recent work made me stretch quite a distance from my math comfort zone.”

Tsai’s research in stochastic analysis is widely used in science and engineering, as well as in finance, such as tracking the evolution of stock prices.

Initial interest in physics Before going to college, Tsai wasn’t terribly interested in math and planned to major in physics. That changed in his first year while taking a calculus class. His professor was passionate about calculus, taught interesting things about and beyond calculus, and always strived to inspire his students. “I still remember that he began the first lecture by shattering many of our math misconceptions,” said Tsai. After taking the class, Tsai became interested in mathematics. He received his bachelor’s degree in physics, with a minor in mathematics, from the National Taiwan University.

After college, he applied to a research-training program at the Institute of Mathematics of Academia Sinica in Taipei City, Taiwan, and had a productive year under the mentorship of Professor Emeritus Tai-Ping Liu. Initially, doing math research for a living had seemed rather odd to Tsai, but his experience at Sinica made him more confident about this path.

After the research training program, he decided to pursue a career in math research and applied to math Ph.D. programs. He received his Ph.D. degree in mathematics from Stanford University, working with Amir Dembo, the Marjorie Mhoon Fair Professor in Quantitative Science and Professor of Mathematics and Statistics. Dr. Dembo introduced Tsai to the subject of his current research. Tsai did post-doctoral research at Columbia University.

Other awards In addition to receiving a Sloan Research Fellowship, Tsai has received other honors, including a 2020 Bernoulli Society New Researcher Award, which recognizes the work of outstanding young researchers in the fields of mathematical statistics and probability. Tsai was named a junior fellow of the Simons Society of Fellows from 2016 to 2019. Founded in 2014, the Simons Society of Fellows is a community of scholars that encourages intellectual interactions across disciplines and across research centers in the New York City area. During this fellowship, Tsai conducted research at Columbia University under the guidance of Professor Ivan Corwin.

Future research Recently, Tsai has started to explore an aspect of stochastic systems called large deviations. Broadly speaking, the theory of large deviations is one of the pillars of probability theory, so understanding how it manifests in different stochastic systems becomes a meaningful and important task for mathematicians.

He started to study the large deviations of rough interfaces and related systems a few years ago, and he’s been intrigued by their behavior, many of which remain conjectural and only partially understood. He hopes to contribute to furthering the understanding of this area of probability.

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Mathematics Department Awards Students receiving a Ph.D. in spring or summer 2022: Amanda Alexander Xuesong Bai Donald Chacon-Taylor You-Cheng Chou Dihan Dai Ryan Dickmann George Domat Chengyu Du Rebekah Eichberg Kyle Gaffney Hannah Hoganson Junpeng Jiao Kristen Lee Zexin Liu Ryleigh Moore Thuong Hoai Nguyen Vaibhav Pandey Marin Petkovic Nathan Willis Yiming Xu Ryeongkyung Yoon

UNIVERSITY FACULTY AWARDS University of Utah Distinguished Research Award Jonathan Chaika University of Utah Faculty Fellow Award Priyam Patel University Teaching Assistantship Seungsu Lee University Graduate Student Fellowship Sanghoon Kwak

OTHER AWARDS University of Utah Presidential Societal Impact Scholar Ken Golden NSF Mathematical Sciences Postdoctoral Research Fellowship Eamon Quinlan-Gallego Alex Rasmussen NSF Graduate Fellowship Samantha Linn Kaitlin O’Dell MAA Math Teacher of the Year (Intermountain Sectional Region) Kevin Wortman

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College of Science Excellence in Research Award Kenneth Bromberg RTG Summer Research Fellowship Michael Kopreski Peter McDonald Summer Research Fellowship Samantha Linn Kees McGahan Qixian Zhao Phi Beta Kappa Society Key Into Public Service Scholar Muskan Walia

College of Science Awards University Student Researchers Award Eli Counterman Dean’s Scholarship Eli Counterman Andrew Nichols Crawford Taylor Maya Wagner American Indian Housing Scholarship Mason Burden Promising Scholarship Benvin Lozada Joseph T. Crockett M.D. Memorial Scholarship Andrew Nichols Crawford Taylor Mia Rossmango Crocker Science House Scholar Grant Daniels Sahana Kargi Toshi Mowery Nash Ward

Incoming Freshman Awards Sandra Bromley Scholarship Jordyn Wilder Freshman Scholarship in Science & Mathematics Liza Roberts Percy Stetich

Mathematics Department Awards

Undergraduate Problem-Solving Contest

UNDERGRADUATE AWARDS

Fall Semester Top-Problem Solver & Spring Semester Undergraduate Facilitator Conrad Morris

Calvin H. Wilcox Memorial Scholarship Eli Counterman Junius John Hayes Diversity Scholarship Savannah Romney Junius John Hayes Endowed Scholarship Maya Wagner Nash Ward The Golden Scholarship Mason Burden Nicole Forrester D. Keith Reed Memorial Scholarship Benvin Lozada Michael Zhao Memorial Scholarship Guang Yang Susan C. Christiansen Memorial Scholarship Moses Samuelson-Lynn Thomas Andrew Hurd Mathematics Scholarship Avalon Blaser Tom and Cathy Saxton Scholarship Ben Huenemann C. Bryant and Clara C. Copely Scholarship Toshi Mowery Continuing Department Scholarship Ocean Armstrong Ian Chang Jude Horsley Erik Merrell Cassandra Shultz Tyler Trotter Mathematics Department Scholarship Audrey Glende Kiyanna Porter J. L. Gibson Senior Award Matthew Gordon Peter Maughan Darshan Shimpi Caleb Walker

Fall Semester Undergraduate Facilitator & Spring Semester Top-Problem Solver Emil Geisler Pi Mu Epsilon Benvin Lozada Brennan Richardson Moses Samuelson-Lynn Anna Tang Guang Yang

GRADUATE AND DEPARTMENT AWARDS Math Department Outstanding Thesis Award George Domat Yiming Xu T. Benny Rushing and Gail T. Rushing Fellowship Alex Beams Outstanding Graduate Student Award Justin Baker Sean Groathouse Hannah Hoganson

FACULTY AND STAFF AWARDS Don H. Tucker Postdoctoral Fellow Award Joshua Pollitz Outstanding Postdoc Award Peter Bakic Faculty Undergraduate Teaching Award Aleksandra Jovanovic-Hacon Michael van Opstall Anurag Singh Outstanding Staff Award Lauren McComber Michele Swaner

Undergraduate Award for Excellence in Graduate Courses Daniel Koizumi Maxwell Plummer Putnam Award Emil Geisler

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