math-news

Royal Fellow

August 9, 2019

Christopher Hacon, McMinn Presidential Endowed Chair and Distinguished Professor of Mathematics, can now add another honor of a lifetime to his already stellar resume: Election to The Royal Society of London.

Hacon, born in England, is one of 50 eminent scientists elected as a Fellow of the Royal Society, along with 10 Foreign Members, in 2019. Founded in 1660, the Royal Society is the oldest national scientific institution in the world. Through its history, the society has named around 1,600 Fellows and Foreign Members, including around 80 Nobel laureates.

“Of course it is a great honor to be elected to the Royal Society and I am very happy and excited for the positive light it sheds on my research and my department,” Hacon said.

“Over the course of the Royal Society’s vast history, it is our fellowship that has remained a constant thread and the substance from which our purpose has been realized: to use science for the benefit of humanity,” said Royal Society president Venkatraman Ramakrishnan in a release. “It is with great honor that I welcome them as Fellows of the Royal Society.”

“Christopher Hacon,” according to the Royal Society’s biography page, “is a mathematician who specializes in the field of algebraic geometry which, loosely speaking, is a branch of mathematics that studies the geometric properties of sets defined by polynomial equations. Together with his co-authors, Hacon has proved many foundational results on the geometry of higher dimensional algebraic varieties including the celebrated result on the finite generation of canonical rings.” Because algebraic geometry is closely connected to other fields within and beyond mathematics, Hacon’s work has had broad impact.

He has been honored with prestigious awards such as 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, a member of the National Academy of Sciences and holds the U’s McMinn Presidential Chair in Mathematics.

Hacon and other newly elected fellows will be formally admitted to the society in July, when they will sign the Charter Book and the Obligation of the Fellows of the Royal Society.

Other U connections in the Royal Society

Venkatraman Ramakrishnan is the current president of the Royal Society of London (elected as a fellow in 2003). He is a 2009 Nobel laureate and taught at the University of Utah from 1995 to 1999.

Simon Tavaré is the director of the Cancer Research UK Cambridge Institute. He taught at the University of Utah from 1978 to 1981 and from 1984 to 1989. He was elected as a Fellow of the Royal Society in 2011.

Philip Maini is the director of the Wolfson Centre for Mathematical Biology at the University of Oxford. He taught at the University of Utah from 1988 to 1990. He was elected as a Fellow of the Royal Society in 2015.

John Knox was a leader in the field of gas chromatography and began working with liquid chromatography after a sabbatical fellowship at the University of Utah in 1964. He was elected as a Fellow of the Royal Society in 1984. He died in 2018.

> UNEWS - 2019 - Paul Gabrielsen

Teaching Excellence

June 1, 2019

Kelly MacArthur, assistant chair and an instructor lecturer in the U’s Mathematics Department, has received two teaching awards from the U—the Career Services Faculty Recognition Award and the Excellence in Education Award. Both awards are given annually with students nominating faculty.

“An Amazing Teacher”

Career Services recognizes outstanding faculty who have made significant contributions to their students’ professional development in helping students find resources, guide their career paths, and realize their potential. Since 2005, the Latter-Day Saint Student Association has given the Excellence in Education Award.

“Kelly is an amazing teacher and role model,” said Shams Al-shawbaki in nominating MacArthur for the Career Services Faculty Recognition Award. “Not only is she great at her job and understands the responsibility behind what she does, but she shows passion and care towards her students. Kelly has affected me in positive ways in math as well as in my self-confidence and career at the University of Utah. We need more teachers like her.”

Aubrey Mercer, who nominated MacArthur for the Excellence in Education Award, was initially nervous about taking calculus as a freshman, but it turned out to be her favorite class. “Kelly creates such a welcoming environment,” said Mercer. “She really cares about our success.” Both students noted that MacArthur makes a point to learn the names of every student in her class—no small feat since MacArthur often teaches between 150-200 students each semester.

 Teaching Students to Fail

MacArthur said her teaching style has evolved over 25 years, especially during the last decade. Every day she writes the same sentence on the whiteboard: “This is a kind, inclusive, brave and failure-tolerant class.” She created the statement to encourage a sense of community and collaboration within the context of math class. “Failure tolerance is so important, and permission to fail often gets lost in math if students are only looking for the “right” answer,” said MacArthur. “It’s important to create an environment where students feel safe and free to make mistakes. My goal is to humanize the classroom and teach human beings. Teaching math is not the primary goal—it’s learning about my students and what speaks to them.”

In addition to teaching, MacArthur co-created and appears in the Math Department’s public lecture videos. She has developed math materials for elementary and secondary teachers; developed an online math course for non-STEM majors, organized the Math Department’s involvement in the Ndahoo’ah American Indian summer outreach project in the Mohave Valley on the Navaho Reservation; and created a math program for men and women at the Utah State Prison. She serves on the Math Education Committee and on the Undergraduate Mathematics Curriculum Committee. She is also chair of the U’s Senate Advisory Committee on Diversity, among other administrative positions.

MacArthur received a bachelor’s degree in mathematics from Arizona State University and a master’s in mathematics from the U. She is currently working on a Ph.D. in undergraduate mathematics education.

Staff: Mary Levine

May 15, 2019

Staff Excellence Award

 

The College of Science is pleased to announce that Mary Levine has received an inaugural College of Science Staff Excellence Award in 2019. The Staff Excellence Awards were created this year to recognize the impactful contributions from staff in the College and will be an ongoing award in the future.

Mary Levine joined the University of Utah 35 years ago, more than 20 years of this service being in the Department of Mathematics.  She is Assistant to the Chair of Mathematics, and provides administrative support to the faculty.

The College of Science has many truly wonderful staff who work tirelessly to assist students and faculty. Our sincerest thanks to this group for taking the initiative each day to make the College excellent in so many different ways!

 

Lynn Miller

April 15, 2019

Throughout the University of Utah’s remarkable 169-year history, there have been many outstanding alumni who have made a significant impact in Utah, the country, and the world.

College of Science alumnus Lynn C. Miller, BS’ 63 in Mathematics, is an excellent example. As the Chief Actuary at E.F. Hutton Life, in 1978, he was instrumental in the development of a revolutionary form of life insurance known as Universal Life.

Lynn grew up in Salt Lake City near the University of Utah campus. His father, Clyde Miller, BA’34 in Business, spent the majority of his career in Utah politics. Clyde ascended the legislative ranks and eventually served as the Secretary of State and Lieutenant Governor for the State of Utah from 1965-1977. Although Lynn did not follow in his father’s footsteps in the political forum, Lynn’s mastery of diplomacy would become a great asset to complement his mathematics skills.

Lynn was a fervent University of Utah basketball fan and he attended many games at the Einar Nielsen Field House. His enthusiasm for basketball would fuel his passion for mathematics and statistics. For example, he used probability modeling to create a dice game that could statistically simulate a basketball game. His interest in mathematical analysis and statistics would eventually lead to a career in mathematics and actuarial science.

However, when Lynn enrolled at the U as a student, it wasn’t always smooth sailing. “I lacked the focus and confidence to initially thrive,” says Miller. “In fact, due to my early academic struggles, I was placed on academic probation!”

During his junior year, Lynn found the confidence and commitment to academics, due to the kindness and encouragement of Mathematics Professor J.D. Smith. Professor Smith took a special interest in Lynn’s success and encouraged him to realize his true potential.

“I credit the University for supporting me. In addition to my degree, I also received valuable life lessons of hard work, dedication, and perseverance,” says Miller.

After graduating from the U, Lynn began his professional career at the Hercules Powder Company in Magna, Utah. His job allowed him to apply his mathematical skills to analyze test firings for quality control.

While at Hercules, one of his colleagues witnessed Lynn’s mathematical brilliance and mentioned that he should look into becoming an actuary, a specialized math discipline based on the measurement and management of risk and uncertainty.

Lynn seized upon an opportunity at Surety Life Insurance in Salt Lake City and began his career as an actuary. For eight years Lynn juggled his advanced actuary classes and exams, worked long hours, and along with his wife, helped to raise his young family. Ultimately, due to the job at Surety Life, Lynn found himself leveraging his mathematics and actuary skills to the pathway of disrupting the life insurance industry.

In 1972, Lynn discovered that E.F. Hutton had an opening for a Senior Vice President and Chief Actuary position. Observing the grand opportunity that presented itself, Lynn interviewed and, eventually, won the position. During his time at E.F. Hutton, Lynn became one of the key individuals to reinvent the life insurance industry. Lynn shared that a big part of his career growth was due to his awareness of opportunities and faith in his abilities to succeed.

In the late 1970s, traditional whole life insurance came under heavy criticism from the investment community. Policy cash values were being credited with very low interest rates in the 2-3% range, while external new money rates exceeded 10%. In addition, the rigid nature of a typical contract made it difficult to adapt to changing needs of the client. This created the ideal environment for the creation of the universal life product that offered the following:

  • An open, fully disclosed architecture that allows flexibility in the amount and timing of premium payments and in the balance between the savings (cash value) and pure insurance elements.
  • An earnings rate on cash values that reflected the high investment yields available at that time. This provided a significant advantage over established companies who were burdened with investment portfolios earning well under new money rates.

It’s not surprising that universal life created significant controversy, turmoil, and resistance from established insurance companies.

In fact, Mass Mutual and other large mutual companies launched expensive ad campaigns that tried to disparage and rebuke the new product. Lynn met with many groups and key individuals including the IRS, U.S. Treasury, federal and state legislators, tax attorneys, and even fellow industry antagonists to convince them of the attributes and legitimacy of universal life.

In 1981, the IRS provided a Private Letter Ruling, which held that universal life was a legitimate insurance product. The ruling was challenged in 1984. This led to an effort to permanently enact into law what constitutes a legitimate life insurance product. Lynn was extensively involved in this effort and was one of the original authors of the federal income tax definition of what constitutes life insurance for policyholder and company tax purposes, enacted in the DEFRA Tax Act of 1984.

Universal life has since become the dominant form of life insurance for the past quarter century. Last year it represented more than 60% of permanent cash value type life insurance sales.

In 1999, Lynn moved to Pacific Life Insurance Company and became the Chief Actuary for the Life Insurance Division. In 2002, he was promoted to Executive Vice President and Head of the Life Insurance Division. He retired in 2012.

His stellar career positively impacted millions of life insurance customers, and their families, who have benefited from universal life insurance.

Lynn and his wife, Sue, reside in San Diego, CA, and are strong supporters of Utah athletics. They have season football tickets and attend many home games in Rice-Eccles stadium.

 

AMS Fellow

November 5, 2018

“It’s such an honor to be selected to join the American Mathematical 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.”

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 Calabi-Yau 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 were 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.”

AMS Fellow

November 5, 2018

“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 a couple of 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, so-called 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.”

Breakthrough Prize

August 9, 2018

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 things—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

Today Hacon has carved out a career as one of the world’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 $3M 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 2018, Hacon was elected to the National Academy of Sciences, and in 2019, he was elected Fellow of the Royal Society of London. He was recently named the first recipient of the McMinn Presidential Endowed Chair in Mathematics at the U.

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.

 

> first published in Aftermath - 2018

2018 Churchill Scholar

June 3, 2018

Scott Neville receives Utah's third straight Churchill Scholarship.

Scott Neville of Clearfield, Utah, who graduated from the University of Utah in December with a degree in mathematics and in computer science, has received a prestigious Churchill Scholarship to study at the University of Cambridge in the United Kingdom.

He is one of only 15 students in the U.S. to receive the award this year and is the third Churchill Scholar from the U, all of whom are mathematicians.

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

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 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. I realized there were unsolved problems in math and I could answer them.”

Neville enrolled at the U because he was already involved in an applied mathematics project with professor Duncan Metcalfe in the Anthropology department. The objective was to investigate infeasible years in radiocarbon dating. The work was funded by the Undergraduate Research Opportunities Program.

“This was a good learning experience in both research and communicating mathematics, since the senior researcher had only passing familiarity with the math involved,” says Neville.

The project resulted in a poster given at the Undergraduate Research Symposium in 2016.

“In addition, I knew the U had a rigorous mathematics and computer science program, but I hadn’t actually met any of those professors,” says Neville.

While attending the U, Neville presented his work in Japan, completed advanced courses in modern algebra and number theory, and took second place in the ASFM national collegiate mathematics championship in 2017. He also has co-authored three publications with university faculty.

Neville credits many U faculty for helping him through his undergraduate career. Suresh Venkatasubramanian, Tommaso de Fernex,Duncan Metcalfe, Arjun Krishnan, Aditya Bhaskara, Peter Trapaand 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.

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 one-year Master’s program at the University of Cambridge. The award is worth about $60,000 in U.S. dollars, depending on the exchange rate.

Candidates go through a rigorous endorsement process in order to apply, but only after their home institution has been vetted with the Winston Churchill Foundation. The U was added to the Foundation in spring 2014.

The Churchill Scholarship has been called “the most academically challenging of the U.K. scholarships.”

Neville will begin his studies at Cambridge in October 2018.

 

2017 Churchill Scholar

February 28, 2017

Michael Zhao, a Salt Lake City native and senior in mathematics pursuing an honors degree at the U, has received the prestigious Churchill Scholarship to study at the University of Cambridge in the United Kingdom. Zhao is one of only 15 students in the U.S. to receive this award and is the second Churchill Scholar from the U.

“It’s a common perception that skill in mathematics is only due to talent, but hard work counts for much more,” said Zhao. “Having mentors is also extremely helpful, and I am indebted to many faculty members, graduate students and engineers for their guidance and encouragement.”

Zhao was drawn to math at an early age. Through an “Art of Problem Solving” online course he was introduced to number theory. He likens this first encounter to how the Hubble Space Telescope revealed thousands of ancient galaxies in what appeared to be a small, blank patch of the night sky.

In high school, he attended the Canada/USA Mathcamp and took math courses at the U. Upon graduating he was awarded a fouryear Eccles Scholarship – supported by the George S. and Dolores Doré Eccles Foundation–to continue his studies at the U.

In his freshman year at the U, Zhao took a yearlong reading course exploring algebraic number theory with Gordan Savin, a professor in mathematics. He continued his studies by taking reading courses with

Dragan Milicic, a professor in mathematics, and graduate courses in algebraic geometry, number theory, and representation theory. “We often have discussions on various topics related to these courses. I was always impressed that talking to Mike feels more like talking with a colleague and not a student,” said Milicic.

Zhao has also done research in computer science. In the summer of 2015, he participated in the Research in Industrial Projects for Students Program held on the campus of the Hong Kong University of Science and Technology. His project used computer vision techniques to create a logo recognition application for Android phones. In spring 2016, he was awarded the prestigious Barry Goldwater scholarship for excellence in STEM research.

This past summer, Zhao was an intern at Google. He developed a software-testing framework that allowed engineers to select exactly the servers they needed to handle login action in their software tests, thereby reducing computer memory usage and server startup times. “He is on a path to becoming a very powerful figure in whatever industry he chooses,” said Tyler Sellmayer, Zhao’s supervisor at Google. “His superpower is the ability to hold an enormous abstract structure in his head, and to speak intelligently about any aspect of it at any time.”

Currently, Zhao is working on his Honor’s thesis in number theory. His thesis advisor, Gordan Savin, says of Zhao: “Mike is one of the strongest undergraduate students we have had since I have been at the University of Utah, more than 20 years. For someone his age, he already has an incredible level of maturity and mathematical knowledge.”

Zhao will use the Churchill Scholarship to pursue a Master of Advanced Study in Pure Mathematics at Cambridge starting in the fall. Upon completion, Zhao plans to come back to the U.S. to complete his doctorate in mathematics focusing on number theory. “It wasn’t easy to choose in what area I wanted to specialize, even within computer science and mathematics, since they were all very exciting. Only by trying many different things – an internship, several research projects – was I able to make a decision,” said Zhao. Zhao aspires to become a professor, and hopes to make contributions to pure mathematics through research and teaching.

“Many times, pure mathematics research found its way to important applications, such as cryptography, relativity and GPS. From a different perspective, I believe research is important since it enriches society just as much as art, literature or philosophy,” said Zhao.

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 one-year master’s program at the University of Cambridge. The Churchill Scholarship has been called “the most academically challenging of the U.K. scholarships.”