Biannual Newsletter | Fall 2018 | Volume 18, Issue 1
A Love for
Puzzles Page 4
In This Issue Using Stochastics and Machine Learning. . . . . . . . . . . . . . . . . . . . . . 2
A Love for Puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
The Engaging World of Number Theory . . . . . . . . . . . . . . . . . . . . . 6
A Perfect Match: Math and Neuroscience . . . . . . . . . . . . . . . . . . . . 8
U Math Professors Named Fellows of the American Mathematical Society. . . . . . . . . . . . . . . . . . . . . . 10
Awards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
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 with state-of-the-art teaching laboratories and flexible classroom spaces. The building also has integrated advising and tutoring centers.
Message from the Chair As our fall semester comes to a close, we have a wonderful opportunity to reflect on the accomplishments of the Math Department in 2018. We were pleased to welcome a new faculty member to the U and to our department. Harish Bhat, associate professor of mathematics, joined us after teaching for a decade at the University of California, Merced. His specialty is stochastics and machine learning, and you can read more about his work on page 2. Our faculty members continue to win recognition for their work, and two professors have been invited to join a prestigious math society. Tommaso de Fernex and Peter Trapa were named members of the 2019 Class of Fellows of the American Mathematical Society (AMS). The Society recognizes members who have made outstanding contributions to the creation, exposition, advancement, communication, and utilization of mathematics. Professors de Fernex and Trapa join eleven other professors in the department who were previously named fellows by the AMS. The newsletter also provides information about the dedication of our faculty in providing leadership to the departmentâ€™s undergraduate and graduate studies programs. See more about our AMS Fellows, as well as the work being done by our talented faculty, in the newsletter.
We are committed to encouraging faculty research, recruiting the best new talent, and providing a world-class educational experience for our undergraduate and graduate mathematics students. To help advance our work, please consider supporting the Crimson Laureate Society, established by the College of Science. The goal of the Society is to build a community of alumni and friends who are passionate about the advancement of scientific research and education at the U. 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. As always, we are grateful for your support. Sincerely,
Davar Khoshnevisan Professor and Chair Department of Mathematics
Using Stochastics and Machine Learning
Harish Bhat, associate professor of mathematics, likes to
tackle difficult problems and find solutions that help people, especially if he can use novel approaches in math or computer science. “I got into stochastics and machine learning because I enjoy solving real-world problems,” he said, “and finding solutions often involves using models and algorithms from these areas.” He recently joined the U’s Math Department after teaching for a decade at the University of California, Merced. “When I joined UC Merced,” he noted, “it was still the newest campus in the UC system, so it felt a bit like a startup—there was always plenty to do besides the usual teaching and research duties.” In addition to teaching, Bhat served on faculty hiring committees and developed curricula for undergraduate and graduate students.
Algorithms and Forecasting Harish Bhat
Initially he got into stochastics (an area concerned with random probabilities) and machine learning through the subprime loan financial crisis of 2008. He and another graduate student saw this focus as a way to develop a more accurate pricing model, and they began using machine learning that relied on using short-term memory models instead of the usual Black-Scholes-Merton model that uses long-term price variation. “We developed and used a large database of historical option prices to show that our model could outperform competing models, such as Black-Scholes,” said Bhat. Data collection played a huge role in both the development
and testing of their model. Following this, Bhat worked with Silicon Valley Bank to build models to forecast startup earnings; to evaluate and determine the price for common and preferred shares issued by startups with venture capital funding; and to predict the potential bankruptcy rates of startups. Today Bhat teaches and does research in two areas. He works with public health researchers to build machine-learning models that can predict (and help prevent) suicides within a target group. This is of interest because suicide rates have increased over the past decade in Utah as well as in other western states. “We need to figure out the reasons for the increase,” said Bhat, “and find ways to help those at risk. But we also need better tools to help mental health professionals, educators, counselors, and families determine who is at risk. Both machine learning and deep learning show promise in helping us build stateof-the-art prediction algorithms.” Bhat also develops algorithms that can automatically infer motion equations from time series data. For example, if there were enough videos of apples falling from trees, could an algorithm automatically discover the differential equation that governs the position of the apple as a function of time? Bhat sees applying this technique to complex systems, such as cognitive science models; quantum chemistry models for many-body systems in time-dependent potentials; and powergrid models that incorporate renewable energy sources such as wind and solar power. Raised in San Jose, Calif., Bhat attended Harvard University and graduated with a degree in mathematics. While there, he took classes in computer science, philosophy, and literature. He was a weekly deejay on WHRB-FM, the latenight on-campus indie/punk rock radio station.
He regularly attended the Brattle Theatre and the Harvard Film Archive, soaking up the work of classic filmmakers such as Satyajit Ray, Akira Kurosawa, and François Truffaut. At Caltech, he was part of a small, interdisciplinary Ph.D. program called “Control and Dynamical Systems.” He became interested in the mathematics of compressible fluid flow and shock waves, and his thesis explored new Lagrangian and Hamiltonian methods to smooth out Euler equations for a compressible fluid. “I have fond memories of my years at Caltech because I worked with some incredible people,” he said. As a newcomer to Utah, Bhat is interested in learning about Salt Lake City and the state. One thing he’s already discovered is the local coffee scene. “I love that there are so many places to get an espresso on campus, including, but not limited to: Two Creek, Brio, and Coffee Lab,” he said. “I’ve also visited places around the city—there is clearly a burgeoning coffee culture here, and I’m grateful!” Bhat is married and has two young kids. In his leisure hours, he spends time with his family, discovers local musicians, and enjoys hiking and skiing. As he continues his research on suicide prevention, the goal is to improve the machine-learning models and training methods. His work on the equations of motion is progressing, but he admits there is still much to learn. “I’m really excited to be at the U. There’s great potential to collaborate, and I expect to find a number of researchers whose interests overlap with mine,” he said. “Together, I’m hoping we can make great strides.”
A Love for Puzzles Elena Cherkaev, professor and director of graduate studies for the Math Department, has always enjoyed solving logical paradoxes, and she believes mathematics is full of such intellectual challenges. She is also interested in linguistics, philosophy, and art history.
Originally from St. Petersburg, Russia, Cherkaev received a Ph.D. in mathematics from St. Petersburg State University. She studied measure and game theory for her master’s degree but later switched her focus to partial differential equations, optimization, and numerical methods. After graduation, she worked in the Academy of Sciences studying the Earth’s magnetic field and propagation of electromagnetic waves.
Director of Graduate Studies
Last spring Elena became the director of graduate studies for the department while continuing to teach and do research. “I have great faculty members and staff who help me to keep on track,” she said. She works with faculty and staff, including Paula Tooman, Karl Schwede, Kelly MacArthur, Maggie Cummings, Lajos Horvath, and others. “Paula is an indispensable member of the department,” said Cherkaev. “She knows everything about the graduate program—she watches every deadline and keeps track of events, and she truly cares about each student.” Cherkaev also relies on Karl Schwede, who served as the director of the program before her. He created an electronic system to keep all the graduate records together and to track a student’s progress. With help from math professor Nelson Beebe, Schwede created a thesisformatting template, so graduate students who use the template no longer have to send their thesis to the Thesis Office for format approval. Cherkaev noted the excellent graduate teaching workshops organized and run by Kelly MacArthur, the supervising and advising done by Maggie Cummings for the master’s degree in teaching, and the guidance Lajos Horvath provides for the master’s degree in statistics. “We have a strong graduate program,” said Cherkaev, “and I depend on these individuals and others to keep it running smoothly and effectively.” As with any graduate studies program, the goal is to prepare students for their future professional life. “In recent years, there has been a growing interest and demand in industry for statisticians and data scientists, and some graduate students choose
nonacademic careers. We also have students who are great instructors—they enjoy teaching and want to pursue a teaching path,” said Cherkaev. “All of these careers are great professional paths, and I want to create an atmosphere that allows students to develop to the best of their abilities, so they are well prepared for their future.”
Research Projects Cherkaev’s research encompasses a range of topics in applied mathematics that use partial differential equations, variational methods, and optimization. “The driving force behind any project is always an intellectual challenge, an interesting mathematical problem that I am trying to solve,” said Cherkaev. One of the topics she is working on is inverse problems and efficient numerical methods for their solution. An inverse problem arises whenever the measurements of the observed process contain only indirect information about the property of interest. An example can be an electrical tomography imaging or nondestructive testing to find the structure of a human’s body or the Earth’s subsurface from measurements of the responses due to the currents (or electromagnetic waves, or ultrasound sources) applied on the boundary. Using a variational approach and spectral decomposition in an imaging problem, Cherkaev developed a method of finding boundary excitations that bring the most valuable information about the structure and properties inside the body by concentrating the energy of the scattered field to the region of interest. This approach resulted in a model order reduction method that allowed an increase in the resolution and the ability to significantly speed up the computations. Another focus for her research is mathematics related to the structure of heterogeneous materials or composites. Properties of natural and artificial composites depend on their fine-
scale microstructure. For instance, mechanical properties and the ability of bone to withstand fracture depend on the structural organization of bone as a hierarchical composite. In many applications, we need to know the response of the composite to applied forces or electromagnetic fields. Cherkaev works on this homogenization problem and the related inverse homogenization when it is required to characterize parameters of the structure given the response of the medium. To solve the last problem, Cherkaev used a spectral decomposition developing a method for extraction of information about the micro-geometry of heterogeneous material from homogenized measurements of its response to the long-wavelength electromagnetic or acoustic field. “My work showed that microstructural statistics could be extracted from such data,” said Cherkaev. “This is important in many applications, for instance, for evaluation of the structure of bones, metamaterials, soil, sea ice, etc.” In collaboration with her former Ph.D. student Carlos Bonifasi-Lista, Cherkaev developed a method of characterizing bone micro-architecture that has a potential for osteoporosis monitoring. Her methods apply to modeling, optimization, and imaging of geophysical, biological, and artificial materials, as well as to high dimensional data sets. “The results obtained by applied mathematicians have many applications,” said Cherkaev, “because similar mathematical problems often describe different physical phenomena.” Cherkaev finds teaching to be very rewarding and enjoys working with students on research projects. In her free time, she likes to attend the Utah Symphony, read The New Yorker, walk in Red Butte Garden, or hike in a canyon. She has worked on several research projects with her husband, Andrej Cherkaev, also a professor in the Math Department. They like to spend time together and enjoy visits from their grown children.
The Engaging World of Number Theory For Stefan Patrikis, assistant professor of mathematics, an interest in math developed over a long period. He says two experiences particularly helped make him a research mathematician. The summer after ninth grade he attended an intensive math camp—the Ross Mathematics Program—for eight weeks, and for the first time was able to see what math outside the classroom is about. He went on to major in math in college but wasn’t sure about continuing with graduate school until his undergraduate advisor suggested a research problem, and he was hooked! Eventually, he stopped going to classes and only worked on the problem, which he found thrilling.
What is Number Theory?
Ever since attending the Ross Program, studying mathematics has for Patrikis been all about number theory. At first it was simply the subject he had first fallen in love with. He then set out to learn the other things he would need in order to understand more number theory. “Ironically, what might sound like a narrow focus was in practice immensely broadening,” he said. “Number theory draws in deep ways on the widest range of modern mathematics: algebraic geometry, representation theory, topology, analysis, etc. That aspect of the subject—I think it’s the best single witness to the ‘unity of mathematics’—is one of the things I most appreciate.” Number theory has deep historical roots, and the mathematical objects studied today have grown out of more classical questions that have been studied for centuries. Galois representations are an example of this. Named after 19th-century French mathematician Évariste Galois, these are ways of packaging “symmetries” of polynomial equations. “This is probably a surprising phrase,” said Patrikis. “We’re used to thinking of geometric objects as having ‘symmetries,’ but a fundamental discovery of the 19th-century is that equations do as well!” Galois representations encode all of classical algebraic number theory—many questions about prime numbers and ordinary integers—and vastly extend its scope, providing connections with algebraic geometry, representation theory, and more. “Much of the appeal in studying the modern subject is these astonishing connections that bind together what seem to be very different subjects of study,” he said. “We understand relatively little about these conjectural connections, so there is a great deal of freedom of exploration. Ultimately, this is what I enjoy and find most precious about mathematical research.”
Funding from the U and the National Science Foundation Patrikis is grateful for funding provided both by the U’s John E. and Marva M. Warnock Presidential Chair in Mathematics and by a National Science Foundation (NSF) CAREER grant. Funding has given him the means to travel to conferences and invite visitors to Utah. However, just as important, funding has made a big difference in the training of his Ph.D. students, giving them more time to focus on their research and allowing them to travel to conferences and see some of the wider world of number theory. “This is crucial to their education—otherwise they would only be getting my perspective on the subject,” Patrikis said. The NSF CAREER grant, along with support from the U’s Mathematics Department, helps fund the department’s Summer Mathematics Program for High School Students. The program tries to give a group of local high school students an experience comparable to what Patrikis enjoyed and benefited from in the Ross Program.
Applications for Number Theory “Number theory has important applications to cryptography and computing,” said Patrikis. “But I should add that the relationship between today’s basic science and tomorrow’s practical application can be so unexpected. In 1940, G.H. Hardy wrote a now-famous essay called ‘A Mathematician’s Apology.’ Heartbroken to see the world again at war, and disgusted by science’s contributions to modern warfare, he wrote a defense of ‘pure’ and even ‘useless’ mathematics. Hardy expressed relief that neither number theory nor Einstein’s theory of relativity would find any practical, let alone war-like, applications for many years. He was completely wrong! Today, number theory plays a key part in securing our internet communications, and the accuracy of GPS depends on understanding relativity.”
Move to the University of Utah Born and raised near New Haven, Conn., Patrikis obtained a Ph.D. in mathematics from Princeton University in 2012. He spent time as an NSF postdoctoral fellow at Harvard University and as a Moore Instructor at MIT. “There’s so much mathematical energy in Princeton,” he said, “and so many people who are so devoted to mathematics. The resulting intellectual camaraderie makes it a very special place.” He has equally fond memories of strolling along the Charles River and walking through Mount Auburn Cemetery in Cambridge. “I was relatively unconstrained by formal responsibilities in those years, so I could use that time to broaden my mathematical reach and think about new kinds of problems,” he said. “My own research has gained a great deal from this, and it has also made me a much more versatile doctoral advisor. I owe this to having the time to work with few distractions.” He came to the University of Utah in 2015 and was struck by how extraordinarily welcome he was made to feel by the Math Department. When he isn’t teaching, doing research, or mentoring students, he enjoys cooking, reading fiction and poetry, playing the piano, and playing soccer. As he continues with his research, Patrikis believes there are still peaks to climb. “It’s clear that other peaks will have to be discovered even to find a route up to those that we can see.”
A Perfect Match: Math and Neuroscience Alla Borisyuk, associate professor of mathematics and the department’s director
of undergraduate studies, has always been “good at math” and fascinated with the brain. When it came time to choose her major at Moscow State University, she seized the opportunity to study mathematics with a strong department. After completing a five-year master’s degree in pure mathematics, she found that neuroscience still held the greatest interest for her. She also recognized the math she had been learning could be used as a tool to study the brain, so she looked for a graduate school where she could complete a degree in math and do research in computational neuroscience. New York University (NYU) fit the bill, and she was able to do interdisciplinary study between NYU’s Courant Institute of Mathematical Sciences and its Center for Neural Science. She obtained a Ph.D. in mathematics from NYU in 2002 and spent time as a postdoc at the Mathematical Biosciences Institute at Ohio State University. In 2005, she and her husband, Firas Rassoul-Agha, who works in probability and stochastic processes, both joined the U’s Math Department. “My research seeks to understand how different parts of the brain do what they do,” said Borisyuk. For that purpose, she and a team model brain processes by creating an idealized representation of them as a system of differential equations, or a stochastic process on a graph, for example. The choice of the model for a particular project depends on the biology of the system and the questions the team hopes to answer. She works with experimental neuroscientists to keep her models relevant to biology. Once a model is developed, it becomes a mathematical object suitable for analysis. Alla Borisyuk
“For a long time, one of the most powerful tools we used was dynamical systems, which allowed us to characterize a system’s general behavior in different regions of parameter space,” said Borisyuk. “As experimental methods have evolved, it’s crucial now to treat many processes as stochastic, either because of the small number of components or because noise is an inseparable part of brain activity. The nature of the models we build often requires us to venture into different areas of mathematics—areas that I’m not an expert in—so I appreciate insight from my colleagues in math.”
National Institutes of Health Grant Recently, Borisyuk and fellow researcher, Matt Wachowiak, a Utah Science Technology and Research (USTAR) professor of neurobiology and anatomy at the U, received a grant from the National Institutes of Health to investigate how olfactory information (different odors) is represented in the brain. Scientists know a lot about how the visual and auditory parts of the brain are organized, but less is known about olfaction. Borisyuk notes that math plays an important role in the research. “We use linear algebra, graph and network theory, and data analysis, in addition to ordinary differential equation model analysis and simulation,” she said. Understanding how the olfactory system encodes, processes, and decodes odors is likely to reveal new principles underlying brain function in general and will also facilitate future engineering applications.
Director of Undergraduate Studies
Borisyuk also gives her time to other programs at the U, including Mathematical Biology Research, Neuroscience, and the ACCESS Program for Women in Science & Mathematics. “I guess juggling all of this keeps me energized,” said Borisyuk. She credits her graduate students and collaborators in neuroscience with keeping her focused. “They motivate me, and our discussions keep me excited about the unknown we have to explore.” When she isn’t teaching or doing research, she loves spending time with her husband and two sons. They like to travel, hike, and play board games. As Borisyuk continues with her research, her priorities will remain focused on brain research and computational neuroscience. “We have a lot to learn, and, without a doubt, math will continue to play a central role in elucidating the principles of brain function,” she said.
In addition to her teaching and research duties, Borisyuk directs the department’s undergraduate studies, which includes majors in math (including statistics and computing emphases), applied mathematics, and math education. “For me, the most interesting part of the undergraduate studies program is helping students find research projects through our Research Experience for Undergraduates program, or REU,” said Borisyuk. “For many students, the research experience is the highlight of their time at the U. While some take on projects to satisfy an honors degree or other program requirements, most do it for the experience.” Borisyuk works with the Math Department Curriculum Committee to ensure that class offerings and degree requirements remain relevant, interesting, and satisfying to students.
U Math Professors Named Fellows of the American Mathematical Society Two professors in the U’s Department of Mathematics—Tommaso de Fernex and Peter Trapa— have been named members of the 2019 Class of Fellows of the American Mathematical Society (AMS). The Society recognizes members who have made outstanding contributions to the creation, exposition, advancement, communication, and utilization of mathematics. De Fernex and Trapa join eleven other professors in the department who were previously named fellows by the AMS.
Tommaso de Fernex “It’s such an honor to be selected to join the Society,” said de Fernex, professor and associate chair of the department. “It’s also gratifying to have my work recognized by my peers for contributing to the profession.”
Tommaso de Fernex
As a child and throughout his school days, de Fernex always enjoyed math. At the University of Milan, he studied math in the morning and worked as an illustrator at an advertising agency in the afternoon. For a time, he gave up studying math and switched to architecture. “It was while studying architecture that I began to realize my true passion for math,” said de Fernex. “I was on a train to Venice with some friends when it hit me. They were majoring in math and telling me about the things they were learning. In that moment I realized how much I missed it.” He left architecture and advertising and began to see himself as a mathematician. He completed his undergraduate degree and wrote a dissertation in the field of algebraic geometry. “What I like about algebraic geometry is the balance between intuition and mathematical rigor,” said de Fernex. “The algebraic part of it provides a powerful and rigid structure, which, paradoxically, gives geometry its flexibility.” Algebraic
geometry has applications in many fields— for example, certain topics, such as CalabiYau manifolds, are important in string theory because they meet the supersymmetry requirement for the six “unseen” spatial dimensions of string theory. He began working on his Ph.D. at the University of Genoa but later moved to the U.S. to complete his studies at the University of Illinois at Chicago. The importance of his work was recognized early on, and his research has been well-funded throughout his career. He has received various fellowships as well as support from the National Science Foundation (NSF) and the Simons Foundation. “The funding I received from the U’s John E. and Marva M. Warnock Presidential Chair in Mathematics and the NSF CAREER grant was especially helpful,” said de Fernex. “They funded my research and provided support for grad students and postdocs. The years supported by the NSF at the Institute for Advanced Study and later by the Simons Fellowship in my sabbatical year allowed me to fully focus on research and collaboration for extended periods of time.” While de Fernex enjoys doing research, he is equally enthusiastic about teaching. “You never know where or when you’ll find talented students,” he said. “That’s what keeps teaching exciting and fulfilling.”
Peter Trapa “I was delighted to learn the news from the AMS,” said Trapa, professor and former chair of the Mathematics Department and currently chair of the Physics & Astronomy Department. “I’m grateful to be recognized in this way.” Trapa has always been fascinated by mathematics, but his interests drifted as an undergraduate at Northwestern University, first to chemistry, then to physics, before finally returning to mathematics. “I realized that the common thread that I enjoyed most about the basic sciences was the underlying math.” Trapa also credits two math professors—Michael Stein, emeritus professor, and the late Mark Pinsky—who took him under their wing and “really changed the trajectory of my career.” After a brief stint doing statistical analysis for the Ford Motor Company, Trapa headed to MIT for his Ph.D. “My time at Ford was a lot of fun, but not for the reasons that my bosses would have liked,” Trapa said, adding that the company had a decent mathematics library where he spent most of his time. At MIT, Trapa studied representation theory with David Vogan, Norbert Wiener Professor of Mathematics. Vogan later became a close friend and collaborator. “Working with David has
been one of the great honors of my life. I’m constantly learning from him how to be a better mathematician.” Trapa held postdoctoral appointments at the Institute for Advanced Study at Princeton and at Harvard before joining the faculty at the U in 2001. His most important contributions involve classifying the kinds of symmetry that can appear in physical and mathematical problems, socalled unitary representations of reductive Lie groups. “In the past few years, there have been some beautiful and unexpected developments in the subject that lead in many new directions,” Trapa said. His work in this area has been supported by grants from the National Science Foundation, the National Security Agency, and the Simons Foundation. Since 2015, Trapa has served as managing editor for the AMS journal Representation Theory.
Outside of his research, Trapa enjoys working with talented students of mathematics. He helped found the Utah Math Circle for high school students, served as its director for many years, and still lectures regularly in it. “The kind of math that students learn in school is often very different from the experience of actually doing mathematics,” Trapa said. “I think it’s important to give young kids a taste of what mathematics is all about.”
Mathematics Department Awards in 2018 The awards were given in April 2018.
Undergraduate Students Calvin H. Wilcox Memorial Scholarship Brian Udall Junius John Hayes Diversity Scholarship Staci Jewkes Junius John Hayes Endowed Scholarship Mckay Jensen and Camiryn Toeun The Golden Scholarship Emerson Ford D. Keith Reed Memorial Scholarship Gabrielle Legaspi Susan C. Christiansen Memorial Scholarship Carl Fauver Thomas Andrew Hurd Mathematics Scholarship Miriam Galecki Tom and Cathy Saxton Scholarship Veronica Riker and Matteo Sogne C. Bryant and Clara C. Copely Scholarship Katelyn Queen
Undergraduate Problem-Solving Contest Student Representative Michael Allen Pi Mu Epsilon Charlie Barth, Whitney Bitner, Keiko Cawley, Lukas Gust, Dylan Johnson, and Gabrielle Legaspi T. Benny Rushing and Gail T. Rushing Fellowship Joaquin Moraga Outstanding Graduate Student Award Nathan Willis and Laura Strube Don H. Tucker Postdoctoral Fellow Award Donald Robertson Outstanding Postdoctoral Award Ornella Mattei and Dong Wang Faculty Undergraduate Teaching Award Aleksandra Jovanovic-Hacon and Nick Korevaar Outstanding Staff Award Pieter Bowman and Angie Gardiner
Continuing Department Scholarship Charlotte Blake, Miles Hubbard, Shalynne Orth, Erica Park, Taylor Walker, and Thomas White
Participants in the COMAP Mathematics Contest in Modeling Jack Garzella, Dylan Johnson, and Kira Parker, Prathusa Boppana, Chong Wang, and Bo Zhu
Mathematics Department Scholarship Connor Houghton
University Graduate Research Fellowship Stefano Filipazzi and Greg Handy (honorable mention)
J.L. Gibson Senior Award Joshua Peterson and Hannah Waddel
University Teaching Assistantship Anna Nelson (honorable mention)
Putnam Award Kira Parker Undergraduate Problem-Solving Contest (Top Problem Solver) Charlotte Blake
Other Awards 2018 International Congress of Chinese Mathematicians Best Paper Award Yuan-Pin Lee 2018 Emil Artin Junior Prize in Mathematics Davit Harutyunyan (former postdoc in the Math Department)
Students who obtained a Ph.D. during the summer are: Leonard Carapezza Javier Carvajal-Rojas Kyle Steffen Shiang Tang Chuanhao Wei Leif Zinn-Bjรถrkman
DEPARTMENT OF MATHEMATICS 155 SOUTH 1400 EAST, JWB 233 SALT LAKE CITY, UT 84112 Social @uofumath @uofumath email@example.com Online math.utah.edu Phone (801) 581-6851
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