AfterMath - Fall 2022

Message from the Chair

This semester has marked a return to normal academic life . Classes are in person, and it’s wonderful to have lectures and events on campus again.

As usual, our faculty and grad students are doing interesting research. You can read the cover story about the adventures of two of our grad students at Sea Ice School in the Canadian Arctic.

In July, Distinguished Professor Christopher Hacon was reappointed as the Trevor James McMinn Professor in the Department of Mathematics. Distinguished Professor Hacon held the inaugural McMinn Chair for five years, a term that ended last June. His work has been groundbreaking, and he is recognized internationally as a mathematical scientist of the highest caliber, whose work has motivated and impacted the next generation of brilliant algebraic geometers. We are thrilled that he has been reappointed to the position.

Mathematicians in the department have found that they can design a range of composite materials from moiré patterns created by rotating and stretching one lattice relative to another. According to Distinguished Professor Ken Golden, the mathematics and physics of these twisted lattices apply to a wide variety of material properties. You can read more about moiré patterns on page 6.

Each fall we announce our year-end campaign. As always, we are grateful and honored to have alumni and friends of the department support our efforts. This year, we are asking for donations to student scholarships. For more information, please see the article on page 12.

Best regards,

Davar Khoshnevisan Professor and Chair Department of Mathematics

Davar Khoshnevisan

Adventures in the Canadian Arctic: Sea Ice School

Last May, mathematics graduate students

Rebecca Hardenbrook and Julie Sherman participated in Sea Ice School at the Canadian High Arctic Research Station in Cambridge Bay, Canada .

Rebecca Hardenbrook and Julie Sherman, both graduate students in the Department of Mathematics, participated in the Biogeochemical Exchange Process at Sea Ice Interfaces (BEPSII) Sea Ice School May 14-23, 2022, at the Canadian High Arctic Research Station (CHARS) in Cambridge Bay, Canada.

The purpose of the BEPSII program is to provide early-career polar researchers an opportunity to learn fieldwork methods for understanding and analyzing polar sea ice firsthand, as well as building a community in the sea ice research world. Acceptance in the program is competitive—nearly 100 applications were received for 30 spots.

The U Department of Mathematics asked Hardenbrook and Sherman about their adventures in the Canadian High Arctic. Below is an edited compilation of their responses. Find the full interview with Hardenbrook in the news archives on the Math Department website.

How did you become interested in sea ice research?

Hardenbrook:

I started my college-level educational journey at the U as an undergrad in 2014. I knew that I wanted to pursue a career that would allow me to do something related to studying climate change in some way, but I also found my passion in studying math. I began working with [Distinguished Professor of mathematics] Ken Golden in my junior year. He works right in that intersection of climate change, specifically sea ice and math. I was lucky enough to be accepted to the U for my Ph.D., which I am grateful for because being able to continue in this research direction has opened my eyes to a lot of really important research questions about things—such as the fact that all living things depend on sea ice to survive, including humans.

Sherman:

I wanted to study how math can be applied to climate as soon as I began my studies as an undergraduate at the University of Minnesota. I became interested in sea ice after meeting with Ken Golden. He had been a part of the NSF’s Mathematics and Climate Research Network that I was also involved in. Dr. Golden’s projects are very interesting and definitely relevant to my interests in climate change.

How did you travel to Cambridge Bay?

Sherman:

We had four flights total. First a flight from Salt Lake City to Seattle and then to Edmonton, Alberta. We spent the night in Edmonton because there is only one flight a day to Cambridge Bay. The next day we flew out, had a short stop to Yellowknife, and then to Cambridge Bay.

Hardenbrook:

On all of our flights, I couldn’t stop looking outside the window on the plane as the landscape changed slowly from the familiarity of the Wasatch mountains to the flattened landscape surrounding Edmonton to the frozen lakes and dense woods surrounding Yellowknife to the endless snowy and icy terrain of the Canadian High Arctic, which includes the area in the Northwest Territories, Yukon, and Nunavut.

What was it like meeting the other fellow scientists and colleagues?

Hardenbrook:

Meeting other blooming scientists was equally as exciting as actually getting to be on the sea ice for the first time. I now have 30 friends all around the world who are working on exciting and relevant problems relating to polar sea ice, who I can potentially work with in the future. I certainly have never had that sort of network before! The relationships I made with other early-career researchers at the BEPSII Sea Ice School left me with a renewed passion for my own work and for asking questions I haven’t thought of before.

Sherman:

It was amazing to meet all these people. It seemed like a really friendly community. There was a COVID outbreak among the group, so many had to quarantine. Especially before [the outbreak], there was tons of energy and ideas for collaboration. Everyone was really cool! I’m really happy to have made these connections.

What was a typical day like?

Sherman:

We would wake up around 8 a.m. with breakfast in our flat—the groceries were provided by the staff. Lectures would start at 9 a.m. and last until noon. There were usually two different lectures, with several short breaks in between. Lunch was served at 12:30 p.m., followed by hands-on activities around 2 p.m. Some days it was field work and other days lab work or modeling. Our last day was group work. The work continued until 6 p.m. At 7:00, we had dinner, followed by free time. Some would watch hockey—one night we did a pub quiz, or sometimes we might all watch movies together.

Flying to Cambridge Bay.

Julie Sherman.

Hardenbrook:

The activities really varied day by day, but we did have several lectures from experienced polar researchers that ranged among topics. For example, we heard from experts studying biophysical processes of the ecosystems and organisms living within the Arctic Sea ice. The researchers are investigating the movement and transport of critical nutrients and trace metals in the Chukchi Sea, the optical properties of sea ice, and how snow on the surface comes into play.

We did have a few days of fieldwork; the first two primarily were practice days for learning how to drill ice cores, dig snow pits, take snow hardness measurements, make sack holes, and more. We had a lot of free time to explore the area surrounding Cambridge Bay, although we didn’t venture too far away from the town itself. You only have to go out 3/4 of a mile or so before you really understand how remote the area is.

Sherman:

We did go into the town of Cambridge Bay—the folks were friendly, and they invited us to some of their summer festivities—called frolicks. These were activities like snowmobile races, music, and dancing. Unfortunately, because of the COVID outbreak, we couldn’t attend any of them, but the culture of the town seemed pretty fascinating.

What were your living quarters like? What about your meals?

Hardenbrook:

We lived in apartments of eight people each, and within the apartments, we shared a room with one person. Our apartments were part of the Canadian High Arctic Research Station (CHARS) campus, and they were very nice. Because the sun was out for most of the day (or for several hours the entire day), our apartments were pretty warm despite the outside temperature being below freezing.

Sherman:

Meals were catered, and the food was surprisingly good and diverse! I didn’t expect much given that it’s nearly impossible to grow food that far north, but there were fresh fruits and veggies. Each meal came with dessert, so that was nice, too. I’m sure it was expensive—someone said that a watermelon cost $75!

What did you enjoy most about the experience? What was the environment like?

Hardenbrook:

I truly enjoyed the entire experience, but I think selfishly finally getting to be able to walk on the sea ice, see the algae at the bottom of the ice core we took, feel the cold summer Arctic air on my face, and experience that environment was life-changing for me. I did get a little emotional when I first stepped out onto the ice because I’ve wanted to be able to do that now for the last six years.

Endless sunset at Cambridge Bay–photo taken about 11 p.m.

A sea ice vista.

Hardenbrook doing research with colleagues.

I am also so grateful to be able to make the friends that I did. The people I met there are so passionate about their work, and that drives me to continue doing research in this field. The environment was like nothing I’ve experienced before, and it’s kind of hard to put into words.

The air was incredibly dry despite us being right near the ocean—I mean it’s technically a desert up there—so I think the cold felt a little less intense unless it was windy (which it often was). I think the most notable thing for me was just how quiet and flat it is. I could see many miles on a clear day.

There is an Inuit legend about a family of giants who died while crossing Victoria Island looking for food. These giants are the three eskers (a ridge of stratified sand and gravel, deposited by meltwater from a retreating glacier or ice sheet) nine miles outside of Cambridge Bay. They are named Uvayuq (after the father), Amaaqtuq (after the mother, who was pregnant), and Inuuhuktu (after the son). It is so flat that you can see Uvayuq clearly from the town. In fact, some of us actually considered running to it, but we got too nervous about potentially meeting a bear on our way, so we didn’t do it.

Luckily, we didn’t see any bears (polar or grizzly), but we heard that there was a polar bear 30 miles out from the town somewhere. We did see a few Arctic foxes, which was really exciting because early on in our time there, their fur was completely white and they are hard to see. As time went on, we saw Arctic foxes that were starting to shed their winter coats. Their summer fur is short and black, so they’re much more visible. We also saw a few Arctic hare, but they are very good at hiding so we didn’t see too many. There were also a lot of birds—unfortunately, I’m not much of a birder at the moment so I couldn’t identify them.

Sherman:

The environment was definitely cold and pretty barren, everything still covered in snow. The first couple of days it was sunny and warm (like 30F!), so that was a nice treat. One of the coolest things was watching the sun not set. A few nights I stayed up late and became obsessed with watching it never go down. I’d go out every 30 minutes and watch it travel across the sky, but it never set. Of course, the sun would dip down to the horizon, but it wouldn’t cross it, so it was like a continuous sunset from 10:30 p.m. to 2 a.m.

What are your plans after you receive your Ph . D . ?

Sherman:

I hope to stay in academia studying math as it applies to climate.

Hardenbrook:

I am hoping to get a postdoctoral research and teaching position at a college or university. I love my research, and I also love teaching undergraduate students about math, sea ice, and the environments around us. A life where I can continue on with both of my passions would be a good one, and so I hope to do that.

Hardenbrook and colleagues running at Cambridge Bay.

Julie Sherman (left) and Rebecca Hardenbrook.

Moiré patterns have potential technological applications.

Moiré magic

Highly tunable composite materials—with a twist

By Paul Gabrielsen, science writer, University of Utah

Moiré (pronounced mwar-AY) effects—created by two sets of lines offset from each other—are optical illusions that simulate movement and sometime bedevil photographers and videographers. But researchers in the U’s Department of Mathematics are finding potential technological applications related to moiré patterns. At the atomic scale, when one sheet of atoms arranged in a lattice is slightly offset from another sheet, these moiré patterns can create some exciting and important physics with interesting and unusual electronic properties.

Mathematicians at the University of Utah have found that they can design a range of composite materials from moiré patterns created by rotating and stretching one lattice relative to another. Their electrical and other physical properties can change—sometimes quite abruptly, depending on whether the resulting moiré patterns are regularly repeating or non-repeating. Their findings are published in Communications Physics

The mathematics and physics of these twisted lattices apply to a wide variety of material properties, said Kenneth Golden, Distinguished Professor of mathematics. “The underlying theory also holds for materials on a large range of length scales, from nanometers to kilometers, demonstrating just how broad the scope is for potential technological applications of our findings,” he said.

With a twist

To understand the new findings, Golden said it’s helpful to understand the history of two important concepts: aperiodic geometry and twistronics.

Aperiodic geometry means patterns that don’t repeat. An example is the Penrose tiling pattern of rhombuses. If you draw a box around a part of the pattern and start sliding it in any direction, without rotating it, you’ll never find a part of the pattern that matches it.

“We observe a geometry-driven localization transition that has nothing to do with wave scattering or interference effects, which is a surprising and unexpected discovery . ”

—Ken Golden

Ken Golden, Distinguished Professor

Aperiodic patterns designed over 1,000 years ago appeared in Girih tilings used in Islamic architecture, Golden said. More recently, in the early 1980s, materials scientist Dan Shechtman discovered a crystal with an aperiodic atomic structure. This revolutionized crystallography, since the classic definition of a crystal includes only regularly repeating atomic patterns, and earned Shechtman the 2011 Nobel Prize in Chemistry.

Twistronics is a field that also has a recent Nobel in its lineage. In 2010, Andre Geim and Konstantin Novoselov won the Nobel Prize in Physics for discovering graphene, a material that’s made of a single layer of carbon atoms in a lattice that looks like chicken wire. Graphene itself has its own suite of interesting properties, but in recent years physicists have found that when you stack two layers of graphene and turn one slightly, the resulting material becomes a superconductor that also happens to be extraordinarily strong. This field of study of the electronic properties of twisted bilayer graphene is called “twistronics,” Golden said.

Two-phase composites

In the new study, Golden and his colleagues imagined something different. It’s like twistronics, but instead of two layers of atoms, the moiré patterns formed from interfering lattices determine how two different material components, such as a good conductor and a bad one, are arranged geometrically into a composite material. They call the new material a “twisted bilayer composite,” since one of the lattices is twisted and/or stretched relative to the other. Exploring the mathematics of such a material, they found that moiré patterns produced some surprising properties.

“As the twist angle and scale parameters vary, these patterns yield myriad microgeometries, with very small changes in the parameters causing very large changes in the material properties,” says Ben Murphy, co-author of the paper and Adjunct Assistant Professor of mathematics.

Twisting one lattice just two degrees, for example, can cause the moiré patterns to go from regularly repeating to non-repeating—and even appear to be randomly

disordered, although all the patterns are non-random. If the pattern is ordered and periodic, the material can conduct electrical current very well or not at all, displaying on/off behavior similar to semiconductors used in computer chips. But for the aperiodic, disordered-looking patterns, the material can be a current-squashing insulator, “similar to the rubber on the handle of a tool that helps to eliminate electrical shock,” says David Morison, lead author of the study who recently finished his Ph.D. in Physics at the University of Utah under Golden’s supervision.

This kind of abrupt transition from electrical conductor to insulator reminded the researchers of yet another Nobel-winning discovery: the Anderson localization transition for quantum conductors. That discovery, which won the 1977 Nobel Prize in Physics, explains how an electron can move freely through a material (a conductor) or get trapped or localized (an insulator), using the mathematics of wave scattering and interference. But Golden said the quantum wave equations Anderson used don’t work on the scale of these twisted bilayer composites, so there must be something else going on to create this conductor/insulator effect. “We observe a geometry-driven localization transition that has nothing to do with wave scattering or interference effects, which is a surprising and unexpected discovery,” Golden said.

The electromagnetic properties of these new materials vary so much with just tiny changes in the twist angle that engineers may someday use that variation to precisely tune a material’s properties and select, for example, the visible frequencies of light (a.k.a. colors) that the material will allow to pass through and the frequencies it will block.

“Moreover, our mathematical framework applies to tuning other properties of these materials, such as magnetic, diffusive and thermal, as well as optical and electrical,” said Professor of mathematics and study co-author Elena Cherkaev, “and points toward the possibility of similar behavior in acoustic and other mechanical analogues.”

Find the full study in Communications Physics 5, Article number: 148 (2022).

Christopher Hacon appointed to McMinn

Chair in Mathematics

Last July, University of Utah President Taylor Randall reappointed Distinguished Professor Christopher Hacon as the Trevor James McMinn Professor in the Department of Mathematics. Hacon held the inaugural McMinn Chair for five years, a term that ended last June.

The McMinn Chair is a five-year appointment. Only one faculty member in the department may hold the appointment at a time, and in exceptional cases, the current professorship holder may be considered for reappointment.

Christopher Hacon, Distinguished Professor

Born in England and raised in Italy, Hacon arrived at the U as a postdoctoral scholar in 1998 and came back as a Professor in 2002. He is particularly interested in objects that exist in more than three dimensions. He and his colleagues have applied studies of these objects to extend the “minimal model program”—a foundational principle of algebraic geometry—into higher dimensions. The American Mathematical Society has lauded their work as “a watershed in algebraic geometry.”

Hacon has been honored with numerous prestigious distinctions, including his 2019 election to The Royal Society of London; the 2018 Breakthrough Prize in Mathematics; the 2016 EH Moore Research Article Prize; the 2015 Distinguished Scholarly and Creative Research Award from the University of Utah; the 2011 Antonio Feltrinelli Prize in Mathematics, Mechanics, and Applications; the 2009 Frank Nelson Cole Prize in Algebra; and the 2007 Clay Research Award. He is a member of the American Academy of Arts and Sciences, a fellow of the American Mathematical Society, and a member of the National Academy of Sciences.

“Distinguished Professor Hacon’s work has been groundbreaking, and he is recognized internationally as a mathematical scientist of the highest caliber, whose work has motivated and impacted the next generation of brilliant algebraic geometers .”

— Davar Khoshnevisan, Chair, Department of Mathematics

Annie Giokas

I started as an international transfer student from Georgia, a country in the Caucasus. I was nervous about adjusting to a new environment and, in addition, the pandemic started during my first semester at the University of Utah. Thankfully, understanding professors in the Department of Mathematics encouraged me, and the friendly attitudes of my peers helped motivate me.

Many say the easiest way to get into research as an undergraduate is ask their instructors for research opportunities. Unfortunately, transfer students get limited time to interact with their professors. I knew I had to make use of resources offered by the Math Department to the fullest. The turning point for me was during an independent study on the topic of commutative algebra. I knew then and there I wanted to pursue graduate studies on that topic. This led me to my Undergraduate Research Opportunities Program (UROP)-funded thesis and another research project supported by a Research Training Grant. Participating in undergraduate research helped me gain skills as an independent thinker and the courage to improve at public speaking after presenting at multiple conferences.

I started the Math Club at the U to establish a space for undergrads to discuss mathematics and have a platform for presenting topics they are passionate about. The pandemic made it hard to organize large-scale in-person events, which is why the organizing committee made an online platform for students to connect. It was fulfilling to see people connect with others whom they don’t usually interact with.

I continued my funded research project last summer, then I began my Ph.D. at Purdue University. I have been very privileged to get the chance to work with amazing people. The University of Utah gave me the skills and support that I needed to succeed in my chosen career.

Annie Giokas, Class of 2022, H.B.S. in Mathematics, College of Science, founder, Math Club

“Participating in undergraduate research helped me gain skills as an independent thinker and the courage to improve at public speaking after presenting at multiple conferences .”

—Annie Giokas

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 he 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 decide on 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 completing a minor in philosophy, which he sometimes regrets not finishing.

Eventually, Paul realized he didn’t want to teach in the humanities. “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 his having received the 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 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 says 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 was 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.

“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 Physics & Astronomy 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 to 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 Distinguished 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.

Support Mathematics Students

Donor funded scholarships allow the Department of Mathematics to provide life-changing educational and research experiences at an exceptional value . For a limited time, the University is offering some matching incentives for new multi-year scholarship pledges and/or new endowed scholarships .

Please consider helping our students through a scholarship contribution today. Online gifts can be made at: giving.utah.edu/math

For more details about the matching incentive please contactTJ McMullin at travis .mcmullin@utah .edu or 801-581-4414 .

If you have ever considered naming a permanent scholarship to support mathematics students, now is the perfect time to do so.

We support Mathematics

In recognition of your dedication to the Department of Mathematics, every person listed is an honorary member of the Crimson Laureate Society for the designated period .

Our members are advocates for science, making their voices heard on campus, in the community, and elsewhere to help create and support new science programs . We encourage all alumni and friends of the department to join today

Founders Club $50,000 - $99,999

Howard Hughes Medical Institute

Alfred P. Sloan Foundation

Presidents Circle $10,000 - $24,999

Renaissance Charitable Foundation, Inc.

Gail T. Rushing

Presidents Club $2,500 - $9,999

Scott Carter

Charitable Flex Fund

John Haslam, Ph.D.,* and Gale Haslam

Susan Rushing, JD

Jia Wang, Ph.D., and Xiaodong Jiang, Ph.D.

Deans Circle $1,000 - $2,499

Reid F. Barton

Berton Earnshaw, Ph.D., and Tiraje Earnshaw

Kenneth Golden, Ph.D.

Brent Hawker

Noel Marquis

Thomas McMillan, Ph.D., and Linda McMillan

Eric and Lora Newman

Chris and Nico T. Waters

Deans Club $500 - $999

Richard Easton, Ph.D. and Linda Easton

Daniel Lundberg

Cameron J. Soelberg

John and Tracy Wood

Collegiate Club $250 - $499

Andrej Cherkaev, Ph.D., and Elena Cherkaev, Ph.D.

Christopher Hacon, Ph.D., and Aleksandra

Jovanovic-Hacon

Sanghoon Kwak

David and Gloria Pehrson

Eric Weeks

Century Club $100 - $249

Frederick Adler, Ph.D., and Anne Collopy

Glenn Allinger, Ph.D., and Lee Allinger

Alexander Balk, Ph.D.

Aaron Bertram, Ph.D.

Gary and Shanna Blake

Michael B. Bockelie, Ph.D., and Nanci Bockelie, JD

Carmen Buhler and William Wilson

Yu-Hsing Chiu, Ph.D., and Pea Chiu

Tony Chow

John Dallon, Ph.D., and Laurie Dallon

Tommaso de Fernex, Ph.D.

Christopher Erskine

Brian and Mary Haan

Christopher House

Hsiang-Ping Huang, Ph.D., and Yuanping Lee

Jeffrey and Sherry Jasperson

Aurora and Richard Jensen

James Keener, Ph.D., and Kristine Keener

Sandor Kovacs, Ph.D., and Timea Tihanyl

Kerry Lee, Ph.D., and Ann J. Lee

Mary Levine

Xing Lin, Ph.D.

Walter McKnight, USAF (Ret.), and Carol McKnight

Graeme Milton, Ph.D, and John Patton

Keith Olson, Ph.D., and Patricia Olson

Octavio Pimentel

Michele Swaner and Tom Vitelli

Domingo Toledo, Ph.D., and Paula Schnitzer

Robert Van Kirk, Ph.D., and Sheryl Hill

Christian and Laura Ulmer

Thomas and Linda Wilkinson

David and Olivia Worthen

Timothy Zajic, Ph.D., and Rocio Zajic

Jingyi Zhu, Ph.D.

This list represents gifts of at least $100 made to the Department of Mathematics between October 1, 2021 and October 1, 2022. Standard University of Utah group designations are used. We are extremely grateful for these and all of our generous donors.

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Crimson Laureate Society

Join the Crimson Laureate Society at the College of Science! Society members advocate for science, gain exclusive benefits, and drive the future of research and education at the University of Utah. Your annual membership will start today with any gift of $100 or more to any department or program in the College. For more information, contact the College of Science at 801-581-6958, or visit www.science.utah.edu/giving.