Students Earn NSF Fellowships

We are excited to announce that three students in the Department of Mathematics have earned prestigious National Science Foundation funded Graduate Research Fellowships. We congratulate second year graduate student Samantha Moore, first year graduate student Maddie Brown, and undergraduate Keshav Patel on this remarkable achievement.

The NSF GRFP recognizes and supports outstanding graduate students in NSF-supported STEM disciplines who are pursuing research-based master’s and doctoral degrees at accredited US institutions. The five-year fellowship includes three years of financial support including an annual stipend of $34,000 and a cost of education allowance of $12,000 to the institution.

Strayer and Morgan FPG Honor Society

Department of Mathematics graduate students Katrina Morgan and Michael Strayer have been inducted into the Frank Porter Graham Graduate and Professional Student Honor Society.

This honor recognizes outstanding service to the university and to the community. Katrina and Michael are the first inductees from the Department of Mathematics since 1994. Both have served as officers of the Graduate Student Association for Mathematics, for the local chapter of the Association for Women in Mathematics, AWM, and for the local Graduate Student Chapter for the American Mathematical Society, AMS.

Both have been mentors through the AWM chapter and through the new Directed Reading Program, which pairs interested undergraduate and graduate students for intensive one on one study. Moreover, Katrina’s work as a co-founder and co-director of the Girls Talk Math, summer program and Michael’s work as the founder and first president of the Graduate Student Chapter of the AMS, which first brought the TAGMAC Conference to UNC, have been particularly influential.

We are very proud of Katrina and Michael’s achievements. Congratulations both!

Cardiac Computation

In his youth, Boyce Griffith was writing computer programs before he could drive a car. Now a UNC mathematician, he creates computational models of the human heart to improve the prediction and treatment of cardiac diseases.

If there’s an asteroid coming toward Earth, how early do you have to start pushing on it to deflect it? At one point in time, this question consumed Boyce Griffith. To find the answer, he wrote a computer program to simulate the scenario, conducting a handful of numerical experiments in the process.

“It was a pretty simple thing, two- or three-body particle dynamics,” Griffith says of the physics calculations he performed. Most adults would probably disagree about the simplicity of such calculations – and when Griffith wrote the code, he was just a middle schooler trying to finish his science fair project.

“I kind of grew up doing that sort of thing,” he says. “I don’t know when or why I got interested in simulation, but I’ve been intrinsically interested in it for a really long time.”

Because his passion for computer modeling seems innate, it’s no surprise that Griffith pursued research. He grew up in the science-focused community of Oak Ridge, Tennessee – a town built around a nuclear laboratory developed during the Manhattan Project. Post-World War II, Oak Ridge National Laboratory was converted to a multiprogram research facility and is the largest science and energy laboratory in the U.S. Department of Energy system. Griffith’s father was an engineer at the lab, and many of his friends’ parents were scientists or engineers there.

“My dad was an early adopter of personal computers in the ’80s, so I grew up with these non-user-friendly computers as things that I could play with,” Griffith explains. “Just the act of getting them to play computer games sometimes required reworking the operating system, so there was a lot you had to do to make things work.”

Years later, Boyce Griffith still works with computers. But instead of simulating asteroid deflection or programming games, he’s trying to understand the fluid mechanics of the human heart.

An associate professor in the Department of Mathematics at UNC, Griffith runs the Cardiovascular Modeling and Simulation Lab. He and his team use mathematical computation to research and develop beating heart simulations, modeling the interactions of the heart’s fluid movement, physical structure, and electrical system. Long-term goals are to improve both the prediction and treatment of heart conditions and the design of cardiac medical devices.

The Heart Of The Issue
More than 91 million people in the United States live with some form of cardiovascular disease, which claims more lives than all forms of cancer and chronic lower respiratory disease combined. Congestive heart disease, stroke, and heart valve failure are only a few of the many ailments contributing to the number-one cause of death worldwide.

While imaging techniques such as MRI have laid the groundwork for understanding cardiovascular mechanics, they can be expensive and time-consuming. Moreover, they often don’t provide adequate detail about the heart’s dynamic architecture, electricity, and fluid forces.

Cardiac electrophysiology, or the movement of electricity through the heart, is key to understanding heart function. Heartbeats are triggered by regular electrical impulses that spread through the cardiac walls, causing the contraction of each chamber in succession. Cardiac fluid dynamics, the pressures and movement of blood in the heart, can vary greatly among patients.

“You’ve got complex electrical dynamics, you’ve got structural motions and complicated fluid flow,” Griffith explains. “There’s a lot of components that all talk to each other.”

The interaction between these components needs to be considered when designing prosthetics and pinpointing treatment options for certain heart conditions.

“Understanding these forces is not just an image analysis project,” Griffith says. “It fundamentally requires mathematical modeling for physiological aspects that you can’t directly image, but still need to account for.”

Modeling Mechanics
Creating models to account for fluid structure interactions wasn’t part of Griffith’s original plan. As an undergraduate student at Rice University, he became interested in heart models while working on a cardiac electrophysiology project with his undergraduate advisor, Steve Cox. He was hooked and went to graduate school at New York University, specifically, to work with Charlie Peskin – a pioneer in heart modeling – with the intent of modeling the coupling between the heart’s electrical system and its mechanics.

But there was a catch. At that time, the existing modelling software included fluid and structural dynamics — but not electrophysiology. Griffith ended up rewriting this software in order to make it flexible enough to integrate the electrical models required for his research.

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“At some point, it was clear that it needed to be done, so I did it – and I’m still doing it!” Griffith admits. “It wound up being a bigger project than I anticipated.”

But how does one go about creating software to simulate these complicated processes?

Much of the mathematics behind Griffith’s work involves developing approximate solutions to complex equations. He and his team conduct laboratory experiments to calculate fluid force distributions. With this information, they can construct and tweak computer simulations.

For example, they are currently trying to model artificial heart valve functionality. Within these prosthetics, leaflets open and close to control blood flow, just like valves in a human heart. Using a technique called particle image velocimetry, they can image fluid movement through the leaflets with the help of a tabletop heart model called a pulse duplicator.

During these experiments, particles suspended in fluid are pushed through an artificial valve within a chamber of the pulse duplicator. As this happens, the particles in the chamber are illuminated by a rapidly pulsing laser beam, and their movement is tracked by a camera that takes a photo for each laser flash.

The resulting snapshots allow Griffith’s team to reconstruct the fluid’s motion through the valve and calculate the velocity of that fluid by examining the displacement of the particles between images. This analysis helps validate computer-generated models of the same process.

Getting Back On Beat
Another project Griffith and his team are working on is cardiac modeling for assessing the risk of clot development in the bloodstream, specifically focusing on clot formation due to atrial fibrillation. This heart condition, characterized by desynchronized beating between the left and right atrial chambers, is the most commonly diagnosed form of arrhythmia in the United States.

In atrial fibrillation, the electrical wave triggering a heartbeat is fragmented and chaotic, often reentering the cardiac tissue instead of being extinguished. The heart beats irregularly and often much faster than normal, greatly reducing blood flow. With this reduction comes the risk of blood coagulation and clotting, which can lead to stroke. Many patients with atrial fibrillation are prescribed anticoagulants, but these aren’t safe and effective for all cases. To determine whether patients should receive them, relatively simple metrics are used to assess clotting risk, and most patients are placed at intermediate risk.

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“You might find out blood pressure, age, or whether the patient has diabetes. And those kinds of measurements might be correlated to the risk of a patient developing a blood clot, but from those measurements you’re not really understanding what the mechanism is. You just know that it’s indicative that something could happen,” Griffith says.

To improve these metrics, Griffith works with cardiologists and researchers from UNC, Duke, and the University of Utah to develop computer models that simulate atrial fibrillation and blood clotting.

Co-investigator John Vavalle, an interventional cardiologist at UNC, hopes models from this project will help identify which patients might benefit more from a procedure called left atrial appendage occlusion, rather than from taking anticoagulants. This appendage is a thumb-like tissue pocket that extends from the left atrium.

“We know that in most people who have strokes due to atrial fibrillation, the clot originates from the left atrial appendage,” Vavalle says. “If you can plug it, you can trap the clot in the appendage and prevent it from making its way to the brain.”

For The Love Of Math
Both Griffith and Vavalle believe that mathematical models can greatly improve current healthcare and the lives of those affected by heart disease.

“I think they’ll ultimately make us better at what we do and improve outcomes for our patients,” Vavalle says. “Imagine the benefits of really understanding, at a level that we never have before, the flow states through the heart and what devices might be effective for certain patients.”

Griffith shares these ideals, emphasizing that computer models are needed most in the space where components of physiological systems such as the heart are well understood individually, but difficult to understand when interacting as a whole. Characterizing the interaction of individual components within a model will allow scientists to test hypotheses for how they function in their real biological setting.

But his ambitions to understand the inner workings of the heart are rooted in the same interest that had him simulating asteroid impact as a teenager – he simply loves math.

“I want to make models because the dynamics are cool,” Griffith says. “I like the mathematical parts. There are these fascinating patterns and difficult numerical analysis problems to solve. We need to solve them in order to make the models and have the impact we desire.”

Boyce Griffith is an associate professor in the Department of Mathematics and adjunct faculty in the Department of Applied Physical Sciences within the UNC College of Arts and Sciences. He is also adjunct faculty in UNC and NC State’s Joint Department of Biomedical Engineering.

He is a member of the McAllister Heart Institute and the Carolina Center for Interdisciplinary Applied Mathematics and is affiliated with the Computational Medicine Program at the UNC School of Medicine.

John Vavalle is an interventional cardiologist and professor of medicine in the Division of Cardiology within the UNC School of Medicine. He is the medical director of the UNC Structural Heart Disease Program and leads the UNC Heart Valve Clinic.

Story by Liah McPherson, Endeavor Magazine, April 4th, 2019

Katie Newhall chosen by APS

Katie Newhall, Assistant Professor with the Department of Mathematics, has been chosen among the 143 Outstanding Referees of the Physical Review journals!

The American Physical Society, APS, has selected Outstanding Referees for 2019 that have demonstrated exceptional work in the assessment of manuscripts published in the Physical Review journals. A full list of the Outstanding Referees is available online at here.

Instituted in 2008, the Outstanding Referee program annually recognizes approximately 150 of the currently active referees for their invaluable work. Comparable to Fellowship in the APS and other organizations, this is a lifetime award. The selection this year was made from 30 years of records on over 71,000 referees who have been called upon to review manuscripts, including more then 40,000 that were submitted in 2018.

The basis for the Outstanding Referees selection takes into account the quality, number and timeliness of a referee’s reports, without regard for membership in the APS, country of origin, or field of research. Individuals with current or very recent direct connections to the journals, such as editors and editorial board members, were excluded.

Congratulations, Katie!

Scott Emmons Named Churchill Scholar

Scott Emmons, a fourth-year student at the University of North Carolina at Chapel Hill, has been named a recipient of the prestigious Churchill Scholarship, a research-focused award that provides funding to outstanding American students for a year of master’s degree study in science, mathematics and engineering at Churchill College, based at the University of Cambridge in England.

Emmons is one of only 16 students and recent graduates selected for the award this year, which not only requires exemplary academic achievement but also seeks those with proven talent in research, extensive laboratory experience and personal activities outside of academic pursuits, especially in music, athletics and social service. He is Carolina’s 18th Churchill Scholar.

Emmons, 22, is a senior from Bloomington, Indiana, majoring in computer science and mathematics in the College of Arts & Sciences. He is a Robertson Scholar, a Goldwater Scholar and an Honors Carolina student.

At Carolina, Emmons has focused on unsupervised machine learning in the field of network science, leveraging mathematics to enable users to guide community detection algorithms. Collaborating with researchers at Duke through the Robertson Scholars Leadership Program, he has also developed artificial intelligence algorithms for robotic motion planning.

Emmons has dedicated his summers to volunteer teaching. He has taught mathematics to middle school students in the Mississippi Delta at the Sunflower County Freedom Project and he has mentored students in mathematics, physics and computer science in Tamil Nadu, India, at the Shanti Bhavan Children’s Project.

At Cambridge, Emmons plans to study how to align machine intelligence with human values. His long-term goal is for society to realize the extraordinarily beneficial opportunities of machine intelligence such as safe, efficient transportation and effective, low-cost medical care while overcoming their associated challenges.

“Scott is one of the most admirable and prolific students I’ve encountered at UNC-Chapel Hill. He has already published four papers in peer-reviewed journals and is poised to become a leader at the intersection of mathematics, computer science and the ethics of artificial intelligence in the future. The UNC-Chapel Hill community can be very proud to be represented by Scott as a Churchill Scholar,” said Inger Brodey, director of Carolina’s Office of Distinguished Scholarships.

The Churchill Scholarship started in 1963 with three awards and has since grown to an average of 14 awards. The scholarship was set up at the request of Sir Winston Churchill in order to fulfill his vision of U.S.-U.K. scientific exchange with the goal of advancing science and technology on both sides of the Atlantic, helping to ensure our future prosperity and security. There have now been approximately 500 Churchill Scholars.

Birthday conference for Richard Rimanyi

A conference titled “Characteristic Classes and Singularities” will be held in honor of Richard Rimanyi on the occasion of his 50th birthday. The conference will be hosted at the University of Geneva, Geneva, Switzerland October 4-7 2018. See the conference webpage for more details.

Professor Richard Rimanyi is the Bowman and Gordon Gray Distinguished Term Professor in the Department of Mathematics, and has been on the mathematics faculty since 2003.

Metcalfe Awarded for Excellence

Jason Metcalfe meets with a student during office hours in Phillips Hall

Congratulations to Jason Metcalfe, Professor in the Department of Mathematics, who has been awarded the 2018 Board of Governors Award for Excellence in Teaching. Each year, the award is presented to a tenured faculty member on each campus of the UNC System for excellent and exceptional undergraduate teaching over a sustained period. The Ottoville, Ohio native told us about his teaching experiences.

No other teacher has cared more about my understanding of the material nor put as much effort towards making a course this challenging into manageable, but still intellectually engaging, work.
-Excerpt from award citation

Who was the best teacher you ever had and why?
Professor Aparna Higgins at the University of Dayton stands out. She held her classes to the highest expectations, yet her students were always supported to the fullest. Her office hours were welcoming, her explanations were patient, and her encouragement was unwavering. Her mastery of challenging students and inspiring them to actively engage with the subject while providing the utmost support is something that I aspire to emulate.

Describe an “Aha!” moment you had when learning how to teach students.
A pair of students came to office hours to work on an assignment, and they were off to a very good start. Their remaining obstruction was well within their abilities. Though I wanted to give them a hint, I just encouraged them to keep trying. I believe that they learned more about the material in that 20 minutes of struggling on their own than they would have with hours of “help” from me. Ever since, I remind myself often not to say too much.

Describe a time when you learned something from a student.
My favorite thing to see is when a student correctly implements a strategy that had not occurred to me. Several memory aids for trigonometry were taught to me by students. A guide that I teach for learning integration by parts is something that I found in a student’s scratch work on an exam.

What is something your students would be surprised to learn about you?
I did not take calculus in high school, as it wasn not offered at the time at my small school, and seeing the rigorous definition of limit on my first day of college almost caused a panic attack.

Story by Korie Dean, University Gazette

UNC Graduate Paul Cornwell

Congratulations to one of our very own, Paul Cornwell, for being a recipient of the 2018 Dean’s Distinguished Dissertation Award in the area of Mathematics, Physical Sciences, and Engineering. His dissertation, titled “A Symplectic View of Stability for Traveling Waves in Skew-Gradient Systems, ” was written under the advising of Professor Christopher Jones.

The Department is very proud of you, Paul!

Bernardi and Morgan Awarded

Pictured from left to right: Gloria Thomas, Emily Hagstrom, Katrina Morgan, Francesca Bernardi, Erica Wallace, Marcey Waters and Chancellor Carol L. Folt

Graduate students Katrina Morgan and Francesca Bernardi, from the Department of Mathematics, were honored as the co-founders of Girls Talk Math, a two-week summer day camp to encourage high school girls to consider careers in mathematics. At the camp, the students explore interesting mathematical concepts, learn about the rich history of women in mathematics and create a blog and podcast series. The camp will meet on campus for the third time this summer.

The University Awards for the Advancement of Women honor individuals who have mentored or supported women on campus, elevated the status of women or improved campus policies for them, promoted women’s recruitment and retention, or promoted professional development for women.

“We all have more power than we think we do,” Morgan said. “No matter who you are, you’re capable of making an impact.”

Congratulations to Katrina and Francesca!

Katrina Morgan Graduate Fellow

Katrina Morgan, a Ph.D. candidate in the Department of Mathematics, has been selected in the inaugural cohort of Kenan Graduate Fellows in the College of Arts & Sciences. One of only ten graduate students in the college chosen for this fellowship, Katrina has distinguished herself as an outstanding researcher and teacher, and will serve as an ambassador in sharing her story with prospective students the college hopes to recruit.

A generous gift from alumnus Thomas S. Kenan III, ’59, funds the Thomas S. Kenan III Graduate Fellows Program. Kenan is passionate about funding graduate students at a level that enables them to be fully immersed in their scholarship and realize their potential. This new program will help some of the College’s most talented graduate students work toward completion of their doctorates. The ten students in the first cohort of this program will receive a $5,000 top-up to their regular stipend in 2018-2019 and a $2,500 summer stipend in either 2018 or 2019.

Congratulations, Katrina!