math-news

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.”

2016 Churchill Scholar

June 3, 2016

Mackenzie Simper, Salt Lake City native and senior in mathematics at the University of Utah, has received the prestigious Churchill Scholarship to study at the University of Cambridge in the United Kingdom. Simper becomes one of only 15 students nationally to receive this award and is the first Churchill Scholar for the University of Utah.

“Mackenzie’s receipt of the Churchill Scholarship marks a tremendous milestone for the university. As our first Churchill Scholar, we have no doubt that she will be an excellent representative of our university and state. Mackenzie has forged the path for other U Churchill Scholars to follow,” said the U’s Senior Vice President for Academic Affairs Ruth Watkins.

The Churchill Scholarship, established in 1963 at the request of Sir 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. Students 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 University of Utah was recently added to the foundation in spring 2014. The scholarship has been called “the most academically challenging of the U.K. scholarships.”

“The process of applying was intense, but it was very beneficial for me to think about what I want to do in the future. I am also grateful to the people who I met throughout the process and the many opportunities the math department has provided.  I am excited to go to Cambridge and be the U’s first Churchill scholar,” said Simper

Simper initially planned to attend medical school, which prompted her decision to double major in mathematics and biology at Salt Lake Community College. She soon realized, though, that math was a spectacular field with many applications and areas to explore. When she transferred to the University of Utah in fall 2014, she knew that math was the subject she wanted to pursue.

“Math is so much fun. My research has allowed me to work on problems that truly interest me, and has shown me the connections between different areas of math.  Any student who is excited by math should try doing research, because it is a chance to experience math in a completely different way than in the classroom,” said Simper.

Under the direction of Tom Alberts, assistant professor in mathematics at the University of Utah, Simper has worked on two research projects over the past year and half. One focused on the stochastic heat equation on Markov Chains. The second studied the Bak-Sneppen model, a simplified model of evolution that incorporates natural selection and spatial interaction between species. She is currently writing up the results of this second project for publication.

“I’m proud to have called her my student and research collaborator, just as the mathematics department as a whole is proud of her as one of our best students ever,” said Alberts.

Simper continued her research experience this past summer on aNational Science Foundation Research Experience for Undergraduates fellowship, where she did research with Bjorn Sandstede, a professor in applied mathematics at Brown University. Her project focused on dynamical systems with noise, studying them both analytically and numerically. This research was the basis for another publication in progress and was the focus of a presentation she gave to the University of Utah Department of Mathematics.

Sandstede said that Simper’s “intellectual achievements are outstanding; she is passionate about mathematics and is one of the most creative and advanced undergraduate students I have known and worked with during my career.”

Recently, Simper was awarded the Alice T. Schafer Prize for Undergraduate Women in Mathematics, which highlights one outstanding undergraduate woman nationally who demonstrates high quality of performance in advanced mathematics course, a real interest in mathematics and an ability for independent work.

Simper will use the Churchill Scholarship to pursue a Master of Advanced Study in Pure Mathematics at the University of Cambridge starting in the fall.  Don Tucker, professor in math at the University of Utah and mentor to Simper, said, “She will be a credit to our nation both as a scholar and as a person.” Upon completion, Simper plans to come back to the U.S. to complete her doctorate in mathematics.

Simper aspires to become a professor, and hopes through research and teaching to inspire students to realize math is more than just solving equations, it is all around them. Alberts, described Simper as such: “Mackenzie has tremendous faith in the ability of mathematics research to make important contributions to humanity and to improve the lives of others.”