Biannual Newsletter | Spring 2018 | Volume 17, Issue 2

In This Issue Breakthrough Math with Christopher Hacon . . . . . . . . . . . . . . . . 2 The Secret World of Math. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Modeling Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Jรกnos Kollรกr Endows Lecturer in Mathematics. . . . . . . . . . . . . . . . 8 Frederick Adler Honored with Ecology Award. . . . . . . . . . . . . . . 9 Dr. Henryk Hecht Wins 2018 Hatch Prize in Teaching . . . . . . . . . 9 Alumni Profile on Ray Greer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 New Development Coordinator for Math Department . . . . . . . 11 Scott Neville Receives Churchill Scholarship. . . . . . . . . . . . . . . . 12 Awards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

The Crocker Science Center is housed in the historic and newly renovated George Thomas Building. The center serves as a world-class facility for science education through the addition of state-of-the-art teaching laboratories and flexible classroom spaces combined with integrated advising and tutoring centers.

Message from the Chair We take pride in noting that the University of Utah Department of Mathematics continues to be ranked among the top universities in the U.S. for excellence in teaching and research at both the undergraduate and graduate levels. As a department, our goal is to ensure that every student, regardless of his or her major, benefits from a rigorous and effective mathematical education that enhances skills within mathematics or in other fields. During the 2017-2018 academic year, our faculty has continued to excel in teaching, research, and training, and their efforts and accomplishments have been recognized by numerous awards and distinctions, which are highlighted in this newsletter. I want to thank each and every member of our faculty and staff for their efforts and dedication in making this a great department.

Davar Khoshnevisan

The new Crocker Science Center (CSC) on Presidents Circle began serving students, faculty, and staff in January and was formally dedicated in April. The building has been completely renovated to provide a world-class math and science educational facility with flexible classroom spaces combined with integrated advising and tutoring centers. The Crimson Laureate Society (CLS) was established by the College of Science in May 2017. The goal of the Society is to build a community of alumni and friends who are passionate about advancing scientific research and education at the University of Utah, which includes mathematics, biology, chemistry, and physics and astronomy. For more information on how to support the Math Department through the Society, please contact the College of Science at 801-581-6958 or visit https://science.utah.edu/cls/. Best,

Davar Khoshnevisan Professor and Chair Department of Mathematics

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Breakthrough Math with Christopher Hacon

Christopher Hacon, distinguished professor of mathematics

at the U, has been interested in math for as long as he can remember. As a child, he loved playing with numbers and would spend hours on a calculator trying to count and figure out thingsâ€” such as how much all the books in his house cost, or the number of seconds in a year or a lifetime. He particularly enjoyed figuring out patterns and seeing the relationships among numbers. When he got to college, Hacon thought he would study physics and engineering, but when he was accepted into a prestigious math program, he ran with it and never looked back.

Awards and Recognition Christopher Hacon

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Today Hacon has carved out a career as one of the worldâ€™s top mathematicians and has been recognized with numerous awards for teaching and research. In December 2017, he was awarded a 2018 Breakthrough Prize in mathematics at a star-studded event in Silicon Valley. The Breakthrough Prize recognizes achievements in fundamental physics, life sciences, and mathematics and is one of the most generous prizes given in science. Hacon shares the award with his collaborator and colleague, James McKernan, professor of mathematics at the University of California San Diego.

In addition to the Breakthrough Prize, Hacon recently was named the first recipient of the McMinn Presidential Endowed Chair in Mathematics at the U, which will allow him to continue his research for the next five years. In May Hacon was elected as a member of the National Academy of Sciences. He is among 84 U.S. scientist-scholars and 21 foreign associates from 15 countries who were elected at the Academy’s annual meeting in Washington, D.C. Hacon’s research is in algebraic geometry, the field that studies geometric objects defined by polynomial equations. Algebraic geometry connects and elevates algebra, which solves polynomial equations, and geometry, which describes the shapes that arise from those equations. “I am extremely honored and humbled to receive the Breakthrough Prize and to be awarded the McMinn Chair,” said Hacon. “The work I’ve done and am doing is the culmination of sustained efforts by many brilliant mathematicians. It is very exciting that the field of birational algebraic geometry and the University of Utah are receiving this kind of recognition.”

Early Life in Italy Hacon was born in England but moved with his parents to Italy when he was three. His father was a mathematician, too, and served as a postdoctoral scholar in the math department at the University of Pisa. Hacon graduated from the same university and then moved to the United States at age 23 to pursue a Ph.D. in mathematics at the University of California Los Angeles. “Italy was a great place to grow up, and I visit when I can,” he said. “Unfortunately, it’s never as often as I’d like.” He arrived at the U as a postdoctoral scholar in 1998 and returned as a professor in 2002.

“One of the things I love about math is that it allows me to find patterns and explain the reasons behind a certain behavior,” said Hacon. “This is really the essence of scientific discovery. All of these patterns are described by numbers. I’m fascinated by them, regardless of their origin. I’m constantly surprised by the power of math and abstract thought in general. It is truly amazing to read a mathematical proof dating back decades or centuries, which is still correct and interesting— both today and in the future.”

Mentors and Teaching Hacon credits his mentors with providing inspiration and helping him move forward in his career. “While I have been inspired by many people, I have four mentors who have really made a difference in my life. They are Fabrizio Catanese and Fabio Bardelli at the University of Pisa, Robert Lazarsfeld at UCLA, and János Kollár, my postdoctoral advisor at the University of Utah, who now teaches at Princeton.” Hacon enjoys teaching students at the U and finds the Department of Mathematics is a good place to work. He and his wife, Aleksandra Jovanovic-Hacon, who is a math instructor at the U, are busy raising their six children. They like the outdoors, especially rock climbing, hiking, and skiing. “Working as a mathematician has been great,” said Hacon. “The academic freedom to pursue my own research goals is one of the biggest rewards I have, as well as working with students and other researchers.” Hacon hopes to continue his research, while inspiring the next generation of mathematicians. He would love to see his students surpass his efforts and continue to make strides in further exploring and expanding our understanding of algebraic geometry.

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The Secret World of Math Anna Romanova, who will receive a Ph.D. in mathematics in May, always enjoyed math classes in her early school years, but admits that she didn’t really understand what math was until late in her senior year of college. She took a point set topology class where the goal was to classify all compact topological surfaces. Instead of just stating the theorem and proving it, her professor guided the class through a process of “discovery,” whereby the students figured out what the answer had to be and then constructed the proof together. “This was the first time that math had felt like an exploration,” said Romanova, “and it was incredibly appealing to me. This is still what appeals to me about math—doing math feels like I’m uncovering a secret world. And representation theory is an especially beautiful world to uncover—it’s full of patterns and surprising connections with other fields of math.” Anna Romanova

Research and Teaching In doing research, Romanova classifies herself as being under the umbrella of “geometric representation theory,” which means that she looks at representation theory problems using tools from geometry. In studying the representation theory of Lie groups, she borrows tools from algebraic geometry. By using a technique that mathematicians developed in the early 1980s, it’s possible to translate questions about representation theory of Lie groups into questions about differential equations. “These differential equations live on certain nice geometric shapes called varieties,” said Romanova. “The power in this translation is that it allows us to use a whole new set of tools developed by algebraic geometers to tackle our representation theory problems, and often these tools are more effective.” In addition to her research, Romanova has taught a wide range of undergraduate courses at the U, including college algebra, pre-calculus, linear algebra, and discrete math. She recently taught a class on representation theory techniques in quantum physics. “Like most things, math is much more satisfying when you can share the experience, and this is how I see my role as a teacher,” she said. “I am there to share the delight of learning new math with my students and to guide them through the process so that it can be a positive and enriching experience for all of them.” Raised in northern Nevada, she received two bachelor’s degrees from Colorado State University. She obtained a Bachelor of Science in mathematics and a Bachelor of Arts in

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Spanish language, literature, and culture. For the past six years, she has worked with Dragan Miličić, professor of mathematics, at the U. “I feel so lucky to have had the opportunity to work with Dragan,” she said. “He has generously shared his wealth of mathematical knowledge with me. Learning about his perspective on representation theory and watching his intuition with problems has been a very valuable experience.”

Diversity and Inclusion Romanova feels strongly about the fact that certain groups are underrepresented within mathematics. “I find the contrast between the homogeneity of most math departments and the diversity of our country (and world) to be deeply disturbing. On one hand, this means that we are missing out on all of the ideas that these missing people could contribute to mathematics. But more importantly, it seems to reflect the power imbalance of our country, where only certain people have access to the social benefits of higher education. These issues are complicated and unlikely to be solved anytime soon, but I think that talking about them is an important first step.” While at the U, Romanova has been involved in the Association for Women in Mathematics (AWM).

“DOING MATH FEELS LIKE UNCOVERING A SECRET WORLD— IT’S FULL OF PATTERNS AND SURPRISING CONNECTIONS.” —Anna Romanova

Recently, Romanova was awarded a National Science Foundation postdoctoral research fellowship to work with Professor Geordie Williamson at the University of Sydney. In addition, she received the “Best Graduate Student Research Poster” award for the AWM’s poster competition at the Joint Mathematics meetings held in San Diego in January. Following graduation, Romanova will relocate to work at the University of Sydney in Australia.

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Modeling Fluid Dynamics Originally, Christel Hohenegger, assistant professor of mathematics, had wanted to study chemistry because she thought that reaction equations were beautiful. But she didn’t like doing the lab work and decided instead to study mathematics, without a clear idea of what a mathematician does—she just knew that she liked structure and order. Later, as an undergraduate at the renowned Eidgenössische Technische Hochschule Zürich (ETH Zurich), she took a course in the history of math and learned about all of the famous mathematicians who taught at the ETH. “I found it fascinating to learn that they were trying to answer both math and physics questions,” said Hohenegger. After graduating from the ETH, she earned a Ph.D. from the Georgia Institute of Technology.

Practical Applications Hohenegger’s research focuses on questions concerning fluid dynamics that can be solved using different mathematical tools from modeling and analysis to simulations and predictions. “I study how solid objects and liquids interact in a fashion that is counterintuitive,” said Hohenegger. “For example, I look at models of swimming organisms in water, where reciprocal swimming results in zero net displacement. Or I’m interested in how the stickiness and gooeyness of a liquid can affect how far an object moves.” Brownian motion is used to describe the random motion of particles suspended in a fluid resulting from their collision with other fast-moving molecules in the fluid. In a complex fluid with memory, such as ketchup or mucus, the particle motion is different. Hohenegger, along with colleague Scott McKinley, associate professor of mathematics at Tulane University, developed a framework to model these kinds of interactions. Her research has practical applications in many industries, such as pharmaceuticals and aerospace. “Understanding how particles diffuse in a complex fluid or knowing how much time it takes a sphere to traverse a layer has potential application in drug delivery,” she explained. “In aerospace, understanding how and at which frequency a liquid will slosh around the wall of a container is a problem associated with aerospace engineering, particularly in designing rocket boosters.”

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Helping Women in Math Hohenegger serves as the faculty advisor for the U’s student chapter of the Association for Women in Mathematics. “I only realized some of the challenges faced by women in mathematics as my career progressed,” she said. “The biggest one I experienced, which is common to women, is the ‘imposter syndrome’—the idea that I wasn’t good enough.” She learned to overcome this by focusing on her work, forging her own path, and not comparing herself to others. “If it takes you an extra year to graduate or find a job, so what? It’s fine,” she said. “I would also encourage anyone to take full advantage of the help and benefits offered by a department—things such as mentoring or the opportunity to chair a committee—as well as basic benefits like maternity leave.” She believes that both her Ph.D. advisors and postdoctoral advisors were critical in shaping her research and helping her achieve career milestones. She chose her Ph.D. advisor Peter Mucha, now professor of mathematics and applied physical sciences at the University of North Carolina at Chapel Hill (UNC), because of his energy and excitement for the material. In turn, he introduced Hohenegger to her postdoctoral advisor, Gregory Forest, a Grant Dahlstrom Distinguished Professor in the Department of Mathematics, also at UNC. She credits Michael Shelley, a Lilian and George Lyttle Professor of Applied Mathematics and professor of mathematics, neural science, and mechanical engineering at New York University, with helping her become her own person in the field.

Christel Hohenegger

“My research is evolving to new and exciting areas where math, physics, engineering, and biology intersect,” she said. “Finding the balance between teaching and research is difficult. My biggest challenge is still managing my time efficiently, but I’m getting there.”

Association for Women in Mathematics The Association for Women in Mathematics (AWM) is a professional society whose mission is to encourage women and girls to study and have active careers in the mathematical sciences. The association promotes equal opportunity and equal treatment of women and girls. Founded in 1971, the AWM has approximately 3,000 members (both women and men) who represent a broad spectrum of the mathematical community in the U.S. and around the world. The organization also has institutional members, such as colleges, universities, institutes, and mathematical societies. It offers numerous programs and workshops to mentor women and girls in the mathematical sciences. For more information about the U’s student chapter, contact uofuAWM@math.utah.edu or visit https://www.math.utah.edu/awmchapter/.

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János Kollár Endows Lecturer in Mathematics János Kollár, a Hungarian mathematician

specializing in algebraic geometry and a former professor of mathematics at the University of Utah, is a co-recipient of the 2017 Shaw Prize in Mathematical Sciences. Established in 2002 in Hong Kong, and first awarded in 2004, the Shaw Prize honors outstanding contributions in astronomy, life science and medicine, and mathematical sciences. Kollár has donated a significant portion of his half of the prize to the U’s Department of Mathematics to establish the János Kollár Endowed Assistant Professor Lecturer at the U. Kollár says he was motivated to make the gift because the U provided such excellent working conditions during the 12 years he was here at the beginning of his career, and because several of the results that the prize committee recognized were developed while he was at the U. Algebraic geometry—what exactly is it? Kollár defines it as the study of geometric objects that can be described by equations, the simplest examples being lines, circles, and ellipses. “I very much liked that one can use geometry and algebra— which are usually thought of as opposites—to solve problems together,” he says. “Then, as the subject advances, it brings in other areas of mathematics, like analysis, differential equations, and topology.”

Kollár’s Legacy at the U Davar Khoshnevisan, chair of the math department, said, “What makes this whole story compelling is that it’s directly related to the fact that algebraic geometry in the math department at Utah has a long and distinguished history, and János Kollár is an important part of that history.

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János Kollár

“In 1970, when the College of Science was formed, the math department was already considered a powerhouse and one of the top research programs in the country. Kollár was recruited in 1987 and, at the time, was recognized as one of the top algebraic geometers in the world. He and his department colleagues were instrumental in attracting and recruiting graduate students and postdoctoral scholars to the U.” “The dedication of the department and the students, the friendliness of the people, and the beautiful mountains and deserts were so memorable,” says Kollár, of his time at the U. The new endowment will help support the research activities of postdoctoral instructors in algebraic geometry or related fields in the department, continuing a legacy of excellence in mathematics research and education at the U. It will provide young faculty members with the financial flexibility to explore and advance scientific research and education at their discretion. This measure of academic freedom is critically important in the formative years of a faculty career and for the long-term success and vitality of the department. “The university has a rich history in mathematics teaching and research,” says Khoshnevisan. “We owe a great debt of gratitude to János Kollár for his contributions to that legacy.” It is anticipated that the first János Kollár Lecturer will be selected by fall semester to coincide with the new academic year.

Frederick Adler Honored with Ecology Award Three University of Utah biology professors have been honored for their contributions to ecology. Frederick Adler, professor of mathematics and biology, and Phyllis Coley, distinguished professor of biology, were elected fellows of the Ecological Society of America (ESA), and William Anderegg, assistant professor of biology, was named an Early Career Fellow. Fellows are members of ESA who have made outstanding contributions to a wide range of fields served by the society. They are elected for life. Early Career Fellows are members within eight years of completing their doctoral training who have advanced ecological knowledge and show promise of continuing to make outstanding contributions. They are elected for five years. Adler is elected for his theoretical contributions to the areas of physiological, disease, evolutionary, population, community, behavioral, and most recently urban ecology. Coley is elected for advancing fundamental knowledge of plant-animal interactions and of tropical ecology and for her lifetime commitment to training generations of students from Central and South America. Anderegg is elected for advancing fundamental knowledge of how trees respond to drought and how the interactions of water stress and climate change may impact our nation’s forests.

Frederick Adler

Phyllis Coley

William Anderegg

Dr. Henryk Hecht Wins 2018 Hatch Prize in Teaching Henryk Hecht, professor of mathematics, has received the Calvin S. and

JeNeal N. Hatch Prize in Teaching. The award is given to an outstanding faculty member who has made significant contributions to teaching at the University of Utah for an extended period of time. Specifically, the committee looks for a faculty member who has distinguished him or herself through the development of new and innovative teaching methods, inventiveness in the curriculum and classroom, as well as commitment to enhancing student learning.

Henryk Hecht

Born in Lodz, Poland, Hecht received a bachelor’s degree from the University of Warsaw and obtained a Ph.D. from Columbia University. He joined the U’s math department in 1977.

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Math Teaches Discipline Alumni Profile: Raymond B. Greer, B.S. ’86, in Mathematics Raising a Utah Man When Ray was 12 years old, his mother, Sandra J. Bromley, moved her young family from Texas to Utah. The year was 1976. Sandra was promptly hired at the University of Utah and enjoyed a successful career as a technical illustrator in the College of Mines and Earth Sciences, under the direction of Frank H. Brown. “My mother was the single greatest influence in my life,” said Greer. “She taught me the value of hard work and perseverance. She also insisted that college was not optional. It was like going from junior high to high school—you just did it!”

Ray Greer

Ray enrolled at the U for fall semester in 1981 and was initially interested in computer science and engineering; however, computer science was highly competitive at the time and available classes were scarce. “Fortunately, Hugo Rossi, a math professor, convinced me that if I majored in mathematics, I could get as much course work in computer science as I wanted. The rest is history,” says Greer. After receiving his math degree at the U, Greer went on to earn a Master’s of Science in Information Systems and Telecommunications from Christian Brothers University, a small private college in Memphis.

Honoring a Legacy In 2000, after retiring from the U, Ray’s mother, Sandra, moved back to Texas for the remaining years of her life. She passed away in 2011. Shortly thereafter, Ray established the Sandra J. Bromley scholarship in the College of Science to honor his mother by providing a way for deserving students to earn a college degree. “She worked hard to provide for her family, but her greatest regret in life was not attending college, hence the vision behind the Bromley scholarship,” said Greer. “She was adamant that she would support me as long as I didn’t quit school,” he said. “That is why the Bromley scholarship requires a commitment to ongoing enrollment.” The Bromley scholarship is designed to provide financial support to undergraduate students who stay enrolled and make steady progress towards a science degree. The award covers full tuition for up to four years.

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Four students currently hold the scholarship: Lauryn Angell, Faye Porter, Cindy Liao, and Michelle White. Greer visited the campus in January and was able to meet and encourage the student recipients.

On the Move Greer has more than 30 years of experience in logistics and transportation industries. He has held senior management positions for Greatwide Logistics Services, Newgistics, Ryder Logistics, and FedEx. He served as president of BNSF Logistics, headquartered near Dallas, Texas, from 2011 to 2018.

In February, he was selected as CEO of Omnitracs, the leading company in onboard technology for the trucking industry. Omnitracs is an international billion-dollar company that provides telematic devices to support drivers and their organizations to be compliant, safe, and efficient. “Math is universal and most importantly teaches you discipline and persistence to work a problem until it is solved. That has served me more throughout my career than anything,” said Greer. Greer has high hopes and expectations for today’s college students. His advice: “Connecting with people, not apps and cell phones, will differentiate you from the competition.”

New Development Coordinator Named for Math Department Michele Swaner joined the University of Utah in October and is responsible for conducting communications, development, and fundraising activities for the Department of Mathematics and the Department of Physics & Astronomy. Swaner is skilled in all areas of communications, including philanthropy and fundraising, public relations, marketing, advertising, media relations and social media, community relations, and public outreach. A native of Salt Lake City, she began her career at Manufacturers Hanover Bank in New York City and spent a number of years working in New York and Greenwich, Conn. She joined R&R Partners in Utah, where her work was awarded a Silver Anvil from the Public Relations Society of America for a voter initiative for the Utah Transit Authority. She worked for a decade for Williams Northwest Pipeline in public outreach and community giving activities. Swaner has a bachelor’s degree in theater from Whitman College and a master’s degree in communications from Westminster College. She is accredited in public relations and was inducted into PRSA’s College of Fellows in 2012 for her career accomplishments.

Michele Swaner

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Scott Neville Receives Churchill Scholarship Scott Neville of Clearfield, Utah, who

graduated from the University of Utah in December with degrees in mathematics and computer science, has received the prestigious Churchill Scholarship to study at the University of Cambridge in the United Kingdom. He becomes one of only 15 students nationally to receive the award this year and is the third Churchill Scholar for the U, all of whom are mathematicians.

Scott Neville

“Having three Churchill scholars in the last four years is truly remarkable,” said Ruth Watkins, U President. “There is no doubt that Scott will continue to successfully represent the University of Utah at Cambridge.”

The Churchill Scholarship,

established in 1963 at the request of Winston Churchill, provides undergraduates with outstanding academic achievement in the science, technology, engineering, and math fields the opportunity to complete a oneyear master’s program at the University of Cambridge. Students go through a rigorous endorsement process in order to apply, but only after their home institution has been vetted with the Churchill Foundation. The U was added to the foundation in spring 2014. Neville was drawn to math when he was introduced to the Collatz Conjecture in high school. “The conjecture is interesting for its simplicity and difficulty, as well as its lack

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of consequence,” said Neville. “I proved via enumeration and equation manipulation that there was only one cycle with exactly one odd number, and none with exactly two odd numbers. This was a known result, but I was ecstatic. There were unsolved problems in math, and I could answer them.” While at the U, Neville has presented his research in Japan, completed advanced courses in modern algebra and number theory, took second place in the ASFM national collegiate mathematics championship in 2017, been awarded many scholarships for his academic achievements, and co-authored three publications with U faculty. He credits many U faculty for supporting him through his undergraduate career. Suresh Venkatasubramanian, Tommaso de Fernex, Duncan Metcalfe, Arjun Krishnan, Aditya Bhaskara, Peter Trapa, and Gordan Savin were each instrumental in helping him with research, presentations, course work, and advising. Neville aspires to become a professor at a research university, so he can continue working on math and sharing it with others. “I want to give back to a community that’s given so much to me. I want to continue learning and pushing the limits of what mathematics (and hence humanity) can do,” said Neville.

Overview of Mathematics Department graduates This year 85 undergraduates will receive a bachelor’s degree in mathematics. At the graduate level, three students will receive a master’s degree; four will receive the Master of Statistics degree; and seven will receive the Master’s in Mathematics – Teaching degree.

Students who obtained a Ph.D. in 2017-2018 are: Andrew Bydlon Samuel Carroll Kyle Gaffney Radhika Gupta Chung Ching Lau Ethan Levien Jie Ma Christopher Miles Anna Miller Anna Romanova Christian Sampson Derrick Wigglesworth Keyvan Yaghmayi Heather Zinn Brooks

College of Science Distinctions Faculty

• Tom Alberts—for Fostering Undergraduate Research Excellence

Undergraduate Student

• Rebecca Hardenbrook—Research Scholar Award

Department of Mathematics Distinctions Faculty

• Christopher Hacon—McMinn Presidential Endowed Chair

University Faculty Award • Henryk Hecht—Hatch Prize

Other Faculty Awards

• Frederick Adler—Elected fellow of the Ecological Society of America • Aaron Bertram—Simons Foundation Fellowship • Tommaso de Fernex—Research Professorship at the Mathematical Sciences Research Institute • Christopher Hacon—Breakthrough Prize • Christopher Hacon—Elected member of the National Academy of Sciences • Sean Lawley—SIAM Activity Group on Life Sciences Early Career Prize

Graduate Student Awards

• Anna Romanova—National Science Foundation postdoctoral research fellowship • Anna Romanova—“Best Graduate Student Research Poster” from Association for Women in Mathematics

Undergraduate Student Award • Scott Neville—Churchill Scholarship

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DEPARTMENT OF MATHEMATICS 155 SOUTH 1400 EAST, JWB 233 SALT LAKE CITY, UT 84112 Social @uofumath @uofumath development@math.utah.edu Online math.utah.edu Phone (801) 581-6851 The University of Utah Department of Mathematics

is committed to educational excellence. Donations and bequests are gratefully received and help the department provide opportunities to students, conduct research, support faculty, and enrich the educational experience. For more information about giving opportunities, please contact Michele Swaner, development coordinator, at 801-580-9590, or email her at swaner@science.utah.edu.