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NSF CAREER Award

June 7, 2021

NSF CAREER Award

Priyam Patel receives National Science Foundation CAREER Award.

Priyam Patel, assistant professor of mathematics at the U, has received a National Science Foundation CAREER Award. The National Science Foundation's CAREER Award is the most prestigious NSF award for faculty members early in their careers as researchers and educators. It recognizes junior faculty members who successfully integrate education and research within their organizations. The award comes with a federal grant for research and education activities for five consecutive years.

Priyam Patel

“I'm thrilled to receive the award, and I'm very excited to have the ability to pursue the research and educational projects the grant will afford,” said Patel. “The award also recognizes the support the Math Department and the University of Utah provide to faculty.”

Patel works in geometry and topology. The two areas differ in that geometry focuses on rigid objects where there is a notion of distance, while topological objects are much more fluid. In her research, Patel’s goals are to study and understand curves on surfaces, symmetries of surfaces, and objects called hyperbolic manifolds and their finite covering spaces. Topology and geometry are used in a variety of fields, including data analysis, neuroscience, and facial recognition technology. Patel’s research doesn’t focus on these applications directly since she works in pure mathematics.

She is currently working on problems concerning groups of symmetries of certain surfaces. Specifically, she has been studying the mapping class groups of infinite-type surfaces, which is a new and quickly growing field of topology. “It’s quite exciting to be at the forefront of it. I would like to tackle some of the biggest open problems in this area in the next few years, such as producing a Nielsen-Thurston type classification for infinite-type surfaces,” she said. She is also interested in the work of Ian Agol, professor of mathematics at Berkeley, who won a Breakthrough Prize in 2012 for solving an open problem in low-dimensional topology. Patel would like to build on Agol’s work in proving a quantitative version of his results. Other areas she’d like to explore are the combinatorics of 3-manifolds and the theory of translation surfaces.

Patel joined the Math Department in 2019.

by Michele Swaner, first published @ math.utah.edu

Patterns in Sound

April 22, 2021

Fernando Guevara Vasquez

U mathematicians create quasiperiodic patterns using sound waves.

Mathematicians and engineers at the University of Utah have teamed up to show how ultrasound waves can organize carbon particles in water into a sort of pattern that never repeats. The results, they say, could result in materials called “quasicrystals” with custom magnetic or electrical properties.

The research is published in Physical Review Letters.

“Quasicrystals are interesting to study because they have properties that crystals do not have,” says Fernando Guevara Vasquez, associate professor of mathematics. “They have been shown to be stiffer than similar periodic or disordered materials. They can also conduct electricity, or scatter waves in ways that are different from crystals.”

Quasiperiodic two-dimensional pattern by Fernando Guevara Vasquez

Non-pattern patterns

Picture a checkerboard. You can take a two-by-two square of two black tiles and two white (or red) tiles and copy and paste to obtain the whole checkerboard. Such “periodic” structures, with patterns that do repeat, naturally occur in crystals. Take, for example, a grain of salt. At the atomic level, it is a grid-like lattice of sodium and chloride atoms. You could copy and paste the lattice from one part of the crystal and find a match in any other part.

But a quasiperiodic structure is deceiving. One example is the pattern called Penrose tiling. At first glance, the geometric diamond-shaped tiles appear to be in a regular pattern. But you can’t copy and paste this pattern. It won’t repeat.

The discovery of quasiperiodic structures in some metal alloys by materials scientist Dan Schechtman earned a 2011 Nobel Prize in Chemistry and opened up the study of quasicrystals.

Since 2012, Guevara and Bart Raeymaekers, associate professor of mechanical engineering, have been collaborating on designing materials with custom-designed structures at the microscale. They weren’t initially looking to create quasiperiodic materials—in fact, their first theoretical experiments, led by mathematics doctoral student China Mauck, were focused on periodic materials and what patterns of particles might be possible to achieve by using ultrasound waves. In each dimensional plane, they found that two pairs of parallel ultrasound transducers suffice to arrange particles in a periodic structure.

But what would happen if they had one more pair of transducers? To find out, Raeymaekers and graduate student Milo Prisbrey (now at Los Alamos National Laboratory) provided the experimental instruments, and mathematics professor Elena Cherkaev provided experience with the mathematical theory of quasicrystals. Guevara and Mauck conducted theoretical calculations to predict the patterns that the ultrasound transducers would create.

Creating the quasiperiodic patterns

Cherkaev says that quasiperiodic patterns can be thought of as using, instead of a cut-and-paste approach, a “cut-and-project” technique.

If you use cut-and-project to design quasiperiodic patterns on a line, you start with a square grid on a plane.  Then you draw or cut a line so that it passes through only one grid node. This can be done by drawing the line at an irrational angle, using an irrational number like pi, an infinite series of numbers that never repeats. Then you can project the nearest grid nodes on the line and can be sure that the patterns of the distances between the points on the line never repeats. They are quasiperiodic.

The approach is similar in a two-dimensional plane. “We start with a grid or a periodic function in higher-dimensional space,” Cherkaev says. “We cut a plane through this space and follow a similar procedure of restricting the periodic function to an irrational 2-D slice.” When using ultrasound transducers, as in this study, the transducers generate periodic signals in that higher-dimensional space.

The researchers set up four pairs of ultrasound transducers in an octagonal stop sign arrangement. “We knew that this would be the simplest setup where we could demonstrate quasiperiodic particle arrangements,” Guevara says. “We also had limited control on what signals to use to drive the ultrasound transducers; we could essentially use only the signal or its negative.”

Into this octagonal setup, the team placed small carbon nanoparticles, suspended in water. Once the transducers turned on, the ultrasound waves guided the carbon particles into place, creating a quasiperiodic pattern similar to a Penrose tiling.

“Once the experiments were performed, we compared the results to the theoretical predictions and we got a very good agreement,” Guevara says.

Custom materials

The next step would be to actually fabricate a material with a quasiperiodic pattern arrangement. This wouldn’t be difficult, Guevara says, if the particles were suspended in a polymer instead of water that could be cured or hardened once the particles were in position.

“Crucially, with this method, we can create quasiperiodic materials that are either 2-D or 3-D and that can have essentially any of the common quasiperiodic symmetries by choosing how we arrange the ultrasound transducers and how we drive them,” Guevara says.

It’s yet to be seen what those materials might be able to do, but one eventual application might be to create materials that can manipulate electromagnetic waves like those that 5G cellular technology uses today. Other already-known applications of quasiperiodic materials include nonstick coatings, due to their low friction coefficient, and coatings insulating against heat transfer, Cherkaev says.

Yet another example is the hardening of stainless steel by embedding small quasicrystalline particles. The press release for the 2011 Nobel Prize in Chemistry mentions that quasicrystals can “reinforce the material like armor.”

So, the researchers say, we can hope for many new exciting applications of these novel quasiperiodic structures created by ultrasound particle assembly.

Find the full study here.

 

by Paul Gabrielsen, first published in @theU

Amanda Cangelosi

April 19, 2021

Amanda Cangelosi receives U's Early Career Teaching Award

Amanda Cangelosi, instructor (lecturer) in the Mathematics Department, has received the 2021 Early Career Teaching Award from the University of Utah. The award is given to outstanding young faculty members who have made significant contributions to teaching at the university. Specifically, the University Teaching Committee looks for a faculty member who has distinguished her or himself through the development of new and innovative teaching methods, effectiveness in the curriculum and classroom, as well as commitment to enhancing student learning.

“I’m honored to receive this award and recognition from the university,” said Cangelosi. “Since my work focuses on the preparation of future Utah K-12 teachers, which intersects with social justice goals in a foundational way, this award means that the U cares about dismantling systemic oppression. There is nothing more systemic than K-12 education, and thus no more impactful space to invest one’s energy.”

In her approach to teaching, Cangelosi believes it's important for children to have math teachers who are skillfully trained to break the unhealthy and dangerous cycle of students who make value judgments about their self-worth based upon their achievement (or lack of) in math. “Issues of mathematical status and power between students in a math classroom need to be recognized and attended to by teachers so children don’t label themselves as “stupid” or, equally-dangerously, as “smart” relative to each other,” she said.

To overcome social divisions and stratifications within the classroom, Cangelosi believes teachers need to focus on creating productive, collaborative, and student-centered learning activities, implementing culturally relevant lessons, using multiple approaches to teaching math, and embracing unconventional approaches. Implementing these strategies require teachers to engage in challenging identity work, understanding the history of education in the U.S., embracing heterogeneous classrooms, and engaging in anti-bias and anti-racist training within mathematical contexts.

In her own teaching, Cangelosi draws heavily from the mainstream math education literature. For example, several of her students were personally affected from watching and reflecting upon Danny Martin's Taking a Knee in Mathematics Education talk from the 2018 annual conference of the National Council of Teachers of Mathematics.

Cangelosi’s teaching contributions include the following:

  • She taught a math lab class at Bryant Middle School for the 2019-2020 academic year to deepen productive collaborations between the U and local schools, thereby creating a seamless practicum space for undergraduate Math Teaching majors, while providing long-term outreach to the local community.
  • Inspired by Utah State University’s teaching practicum, in 2011 she established the current innovative structure of the Math 4095 course—including funding (often out of her own pocket) for mentor teachers, which resulted in onsite, fully-contained classrooms at local schools for University of Utah teaching majors.
  • During the pandemic, she created a sustainable and equitable virtual after-school tutoring program that allowed local high school students to meet with math undergraduates for homework support.
  • She created sanitized manipulatives kits to be distributed to her students for use in online synchronous lectures and labs, to help maintain the integrity of her hands-on collaborative Math 2000/4010/4020 classes during the COVID-19 pandemic.
  • She helped develop course curricula for Math 2000, Math 1010, and Math 4090/4095, introducing and modifying resources from her previous work as a secondary math teacher at The Urban School of San Francisco, bringing what are now mainstream practices to the University of Utah.
  • She has made numerous community, school-district-level, and Utah State Board of Education (USBE) contributions, such as diverse teacher recruitment, committees, and professional development.

“I love approaching old concepts in new, nontraditional ways, because we so often confound our understanding of concepts with the arbitrary conventions that we use to communicate them,” she said. “This often challenges student perceptions of classroom status and power in productive ways, often flipping the previously conditioned dynamic on its head and inviting students to rewrite their mathematical identities in a positive light.”

Cangelosi received her Bachelor of Science degree in Mathematics Education, as well as a Master’s of Statistics degree from Utah State University. She also has a post-baccalaureate degree in mathematics from Smith College. She joined the U’s Math Department in 2011.

 

by Michele Swaner - first published @ math.utah.edu

2021 Churchill Scholar

April 8, 2021

Six in a Row!

Isaac Martin brings home the U's sixth straight Churchill Scholarship.

For the sixth consecutive year a College of Science student has received the prestigious Churchill Scholarship to study at the University of Cambridge in the United Kingdom. Isaac Martin, a senior honors student majoring in mathematics and physics, is one of only 17 students nationally to receive the award this year.

Martin’s designation ties Harvard’s six-year run of consecutive Churchill Scholars (1987-1992) and is second only to Princeton’s seven-year streak (1994-2000).

“Isaac’s recognition as a Churchill Scholar is the result of years of remarkable discipline and dedication to a field of study that he loves,” said Dan Reed, senior vice president for Academic Affairs.

Martin decided to apply for a Churchill Scholarship as a freshman, after meeting for lunch with Michael Zhao, a 2017 Churchill Scholar who unexpectedly passed away in 2018.

“I am positively delighted and quite flabbergasted to receive the scholarship,” Martin says, “but I wish I could phone Michael to thank him for making the opportunity known to me. His legacy lives on in the undergraduate program of the math department here at Utah, where many others like me have greatly benefited from the example he set.”

Martin, a recipient of an Eccles Scholarship and a 2020 Barry Goldwater Scholarship, remembers as a kindergartener trying to write down the biggest number in existence and, as an eighth grader, suddenly understanding trigonometry after hours of reading on Wikipedia.

“That sensation of understanding, the feeling that some tiny secret of the universe was suddenly laid bare before me – that’s something I’ve only felt while studying math and physics, and it’s a high I will continue to chase for the rest of my life,” he says.

Books by Carl Sagan and Jim Baggott also kindled his love of math and physics, and after several years of self-directed study in middle and high school and a year at Salt Lake Community College, Martin enrolled at the U as a mathematics and physics double major.

After early undergraduate experiences in the research labs of physics professors Vikram Deshpande and Yue Zhao, Martin found himself gravitating more toward mathematics. He completed a Research Experience for Undergraduates (REU) at UC Santa Barbara studying almost Abelian Lie groups, which have applications in cosmology and crystallography, under Zhirayr Avetisyan. This experience resulted in Martin’s first research paper. He later completed another REU at the University of Chicago.

“This research was incredibly rewarding because while it applied to physics, the work itself was firmly rooted in the realm of pure math.” Martin says.

Returning to Utah, Martin worked with professors Karl Schwede and Thomas Polstra to study F-singularities, and developed this work into a single-author paper and his currently-in-progress honors thesis with professor Anurag Singh.

“I would not be where I am today without the incredible faculty at Utah and their willingness to devote time to undergraduates,” Martin says.

At Cambridge, Martin hopes to study algebraic geometry, number theory and representation theory (“in that order,” he says) in pursuit of a master’s degree in pure mathematics.

“I’m particularly interested in learning as much as I can about mirror symmetry, which I intend to make my essay topic,” he adds. “I also plan to drink a lot of tea and to buy one of those Sherlock Holmes coats. I will also begrudgingly begin using the term ‘maths’ but I promise to stop the instant I board a plane back to the U.S. in 2022.”

After he returns from Cambridge, Martin plans to earn a doctoral degree in pure mathematics and enter academia, using his experiences in many different educational systems including U.S. and British public schools, homeschooling and online learning, to broaden opportunities for students from a diversity of backgrounds.

“My past has molded me into who I am today,” he says, “and I hope I can use my experiences to create programs in STEM for opportunity-starved students, whether they are held back due to non-traditional schooling or to socio-economic factors.”

 

by Paul Gabrielsen - First Published in @theU

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Cameron Soelberg

March 11, 2021


Cameron Soelberg

Cameron Soelberg, HBS’00

Honors science graduate, Cameron Soelberg, HBS’00, forged an adventurous—and rigorous—path as a student at the U. He continues to travel on a pioneering trail to this day.

Soelberg recently climbed to the summit of the highest point in Utah—Kings Peak at 13,528 feet—and has also lived and worked in Colorado, Illinois, New Hampshire, and New York.

“I think my personal history is a good example that your education and career don't need to necessarily move in a straight line from point A to point B, because your goals might change as you gain experience and that could launch you on a completely new path from what you had in mind originally,” said Soelberg.

When Soelberg first enrolled at the U in 1994, his intention was to pursue a Ph.D. and become a college professor.

After he completed his honors degrees in mathematics and physics, he stayed on campus to complete a Master’s Degree in Mathematics. While in graduate school, he was supported with a teaching assistantship in the Math Department and taught one or two courses each semester.

"After finishing the Master’s Degree, I felt like I needed some time away from school and decided to pursue an opportunity with a startup company in Colorado Springs. There I was involved in prototyping projects for the U.S. Special Forces, which was fascinating work,” said Soelberg.

In 2006, Soelberg took a job as a systems engineer with Lockheed Martin in Salt Lake City, developing biometric tagging and identification algorithms. “I enjoyed engineering and appreciated the quick learning curve and exposure to cutting-edge technology, but I wanted to broaden my horizons in the direction of business management, so after a year at Lockheed, I chose to leave Utah again to pursue an MBA at Dartmouth College,” he said.

While at Dartmouth, Soelberg became interested in investment banking. He completed an internship with Deutsche Bank in New York in the summer of 2008, between his first and second years of business school.

“The timing couldn’t have been worse as that was the start of the global financial crisis but witnessing it firsthand was an invaluable experience, and I was fortunate to receive a full-time offer to join the firm in Chicago after graduation,” said Soelberg. (He earned an MBA at the Tuck School of Business at Dartmouth College in 2009.)

The first few years following the financial crisis were tough for investment banking, as regulatory changes impacted the industry, but Soelberg worked hard and was promoted to vice president and then to director and managing director. He spent a total of nine years at Deutsche Bank. In 2018, he joined the Global Industries Group at UBS Investment Bank and now splits his time between Chicago and Salt Lake City.

“My current position involves a lot of numbers and a keen understanding of the capital markets and valuation,” said Soelberg. “It’s not sophisticated or complex in the way that algebraic topology or particle physics may be, but it does require critical thinking and a high degree of accuracy. The most important contribution my University of Utah education has made is the rigorous way I was taught to analyze and attack problems. The scientific method (and mathematical proof, similarly) is a disciplined framework for progressing from a hypothesis or question to a well-reasoned and logical conclusion. I use this every day in my job, and I’m grateful for how well my learning at the U prepared me to succeed.”

Soelberg recalls many people and experiences from his undergraduate years on campus.

“Lab work in chemistry and physics especially stands out, mostly because I was so impatient that I could never do the experiments quite right, but I had good lab partners who kept me on track,” he said.

“In the Math Department, Jerry Davey really had an impact on me as a student. I took a couple of undergraduate courses from him and helped with an accelerated calculus series one summer as a TA,” said Soelberg. “He was a kind person and a great teacher. He also lived an interesting life that spanned multiple dimensions in mathematics, the military, engineering, and private industry. I’ve always thought of his career path as a role model for my own.”

“Within the Physics Department, I’d be remiss if I didn’t recognize Charlie Jui for all that he taught me in the pre-professional physics program as a freshman. I wasn’t always the most present or attentive student, but his love of physics and wry sense of humor has stuck with me, and I still enjoy seeing him on campus,” said Soelberg.

Soelberg also remembers studying in the Fletcher building (Physics) and the Cowles building (Math) after it was renovated. He was active in many organizations on campus, including a fraternity, and he held offices in student government and the Alumni Association.

“I think there are a couple of lessons I’ve kept in mind that could prove useful for current students. The first is that there will always be challenges, obstacles, and setbacks to overcome, no matter how or when you start out in life. Adversity creates opportunity. Being adaptable is one of the most important keys to success (and happiness),” said Soelberg.

“Second, I would say that no matter how difficult things may become, you are not alone in the struggle. There are many other people, both historically and in different parts of society today, who have faced grave difficulties and found ways to rise above their circumstances. Take comfort and inspiration in that realization and use it as a model for yourself,” he said.

Soelberg is already planning his next adventure—to run the Chicago marathon. “There’s always another mountain to climb,” said Soelberg. “Life’s challenges, and rewards, can be found anew each day.”

A solid educational foundation in mathematics and physics, and the Honors College, is an exceptional “base camp” from which to operate.

Connor, Annabelle, Hayden, Charlotte, Cameron, and partner, Amanda.

Soelberg has four children: Hayden (19), Annabelle (16), Connor (13), and Charlotte (10). Hayden is a freshman at the U, studying computer science. He’s enrolled in the Honors College and lives on campus at Kahlert Village.

 

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Sea Ice Science

February 28, 2021

The Science of Sea Ice

A sheet of floating Arctic or Antarctic ice probably isn’t the setting in which you’d expect to find a mathematician. But that’s exactly where distinguished professor Ken Golden trains students and carries out experiments, as explained in a video introduction to Golden’s Frontiers of Science lecture, hosted by the College of Science and held on Feb. 18.

“It’s one thing to sort of sit in your office and develop theorems and theories and models about as complex a system as sea ice,” Golden says. “It exhibits all kinds of fascinating phenomena and behavior that you wouldn’t necessarily expect or think is important until you actually get down there and see it in action.”

Watch the full video introduction, produced by University Marketing & Communications, below or find the video here. Golden talks about his experiences in the Arctic and Antarctica and about what he and his students have learned from bringing the principles of mathematics into some of Earth’s most remote and most vulnerable environments.

Golden studies how sea ice forms and melts using mathematical models. He’s logged 18 trips to the Arctic and Antarctic, and is a Fellow of the Explorers Club. He is also a Fellow of the Society for Industrial and Applied Mathematics, and an Inaugural Fellow of the American Mathematical Society.

The Frontiers of Science lecture series was established in 1967 by University of Utah alumnus and Physics Professor Peter Gibbs. Today, Frontiers of Science is the longest continuously running lecture series at the University of Utah. The 2020-2021 Frontiers of Science lectures, featuring University of Utah faculty, are online only.

In Golden’s lecture, he discusses his research, his Arctic and Antarctic adventures and how mathematics is currently playing an important role in addressing these fundamental issues and will likely play an even greater role in the future. Watch the full video of the presentation below, or find the video here.

Ken Golden’s Recent Research

 

by Paul Gabrielsen - first published in @THEU

 

Vignesh Iyer

February 17, 2021

Vignesh Iyer

How did you become interested in math?
I’ve always gravitated toward STEM subjects even in elementary school. In college, I was exposed to various subjects but a common language each subject used was math. I’m a curious student and hungry to consume as much knowledge as possible. Math is a universal language that allows me to communicate with those in different fields and tells me how things work. Math has allowed me to explore other subjects and influences the way I interact with problems—from social sciences to applied sciences and engineering.

What kind of internship did you have while at the U? How did you get it?  What did you like about it?
At the beginning of 2020, I started interning for the Pharmacotherapy Outcomes Research Center (PORC) at the University of Utah College of Pharmacy. I applied using the College of Science internship page. I loved interning with the PORC because it allowed me to engage in computational mathematics, work in pharmacology, and interact with different data science and statistical analysis techniques. The team I worked with was performing a correlational study between medication types and bile-duct cancers. I was able to work on the entire computing and mathematics aspect of the study and learn some cool chemistry along the way. My favorite part of the internship was learning how to access databases and interpret the information using data analysis.

You finished your bachelor’s degree and are now in graduate school at the University of California, Irvine. What are you studying?
I entered UC Irvine last fall to begin my graduate studies in mathematics. Graduate school is a whole new challenge but it’s such an enjoyable challenge! My coursework has really taught me to think in new ways, and I’m able to explore new areas of mathematics. At the moment, my favorite class is abstract algebra because it’s a whole new area of math I’ve never been exposed to. I think the online learning part of graduate school has presented learning curves but they’re interesting learning curves.

I’d like to continue my graduate studies in mathematics and get a Ph.D., whether that’s returning to the U. or staying here at home in Southern California.

Is there an area of research that interests you in math? What do you like about it?
I’m interested in applied and computational mathematics. More specifically, I’m interested in applying computational mathematics to data science and machine learning. Applied and computational mathematics explores modeling and/or simulating systems using computers and various mathematical subjects, such as numerical methods, inverse problems, etc. What I like about applied and computational mathematics is that it allows me to be an all-around researcher and engage and contribute to different fields.

Long-term career plans?
After my graduate studies are completed, I’d like to pursue a career in robotics, focusing primarily on research and development in machine learning and artificial intelligence.

 - first published by the Department of Mathematics

Kyle Kazemini

February 10, 2021

Kyle Kazemini

How did you become interested in math?
I had an exceptional math teacher in high school. He had a great sense of humor and genuinely cared about all of his students. He also loved math and it was apparent in his teaching. His lessons were both fun and interesting. My enjoyment prompted me to take calculus and decide to study math further. My interest in math has only continued to grow.

How did you get your internship?
My math advisor, Angie Gardiner, told me about the College of Science Internship Program, and I applied for some positions. I was hired as a sports science intern for University of Utah Athletics. The people I worked with were great, and they all made me feel like part of the team.

My first project was to transform ForceDecks data. ForceDecks is a system for analyzing an athlete’s performance and to make assessments. The data from ForceDecks has a unique format that’s difficult to use in statistical programming languages like R and Python. My job was to develop a tool to fix this issue. I used Excel and VBA (Visual Basic for Applications) to create an automated tool for transforming the data into a user-friendly format.

My second project was to analyze the ForceDecks data. Now that it had a better format, I used R to analyze the data. The purpose of the analysis was to detect athlete asymmetries and possible injury risks. I generated statistics, tables, and plots. These projects made use of both my statistical and programming skills. I enjoyed this internship because I love applying math and computer science in interesting and impactful ways. Because of this internship, I have since become interested in quantitative medicine.

You’re involved in the Directed Reading Program. What is it? 
The Directed Reading Program is a mentoring program between graduate and undergraduate students, who work together on a reading project in mathematics. Any student can sign up for the program, regardless of their level in math. I heard about it through Math Department announcements, and I’m so happy I did. My graduate student mentor is awesome! We’ve read about differential equations and basic mathematical biology. Currently, we’re reading about partial differential equations.

What year are you?  
I’m a junior and plan on graduating in the spring of 2023. I’m taking an extra year since I’m doing a double major with computer science. My interest in computer science started when I took some CS courses as part of my math major. After learning some of the basics of CS, I began to wonder what was out there. Since then, I’ve become excited about theoretical computer science, as well as image processing and computer vision. Studying computer science has made me better at math and vice versa. Although math is the subject I love most, I think studying CS gives me a different perspective on mathematical problems. I also love learning about computing for its own sake.

What about career plans? 
I’m planning on doing a Ph.D. in math, but I’m still narrowing down my research interests. I’m deciding between pure and applied math because I enjoy things like applied mathematical biology, but I also just love math problems on their own. In addition to math bio, I’m interested in partial differential equations. I’m excited to learn about the theory behind PDEs, including real analysis, functional analysis, and Sobolev spaces.

Hobbies or interests outside of math?
I started studying Muay Thai (Thai boxing) when I was 13. Muay Thai is like kickboxing, except with elbows and knees. I was taking classes at a gym for about three years, but now I do it just for fun/exercise at home on a punching bag. I think martial arts are awesome for learning things like discipline and self-confidence.

I also love film—my favorite film is Good Will Hunting, which is pretty typical for a math nerd! I love it because it has a math genius, a great love story, and it’s about triumphing over difficult challenges. I enjoy most film genres—anything from romance to horror to documentaries.

I’m new to snowboarding, and I really like it. My favorite resort (for now) is Brighton. Currently, my favorite video game is CSGO(Counter-Strike: Global Offensive). I don’t play a lot of games because school keeps me busy, but in the past I’ve loved playing Skyrim, Call of Duty, and Halo.

I’ve wanted to build my own computer for years, and I finally did it for the first time a few months ago. I use it for school, work, and for intensive tasks that my laptop just can’t handle. Building it made me really happy!

 - first published by the Department of Mathematics

Priyam Patel

January 6, 2021

Priyam Patel

Visualizing the Topology of Surfaces

Imagine a surface that looks like a hollow doughnut. The “skin” of the doughnut has no thickness and is made of stretchy, flexible material. “Some of my favorite mathematical problems deal with objects like this–surfaces and curves or loops on such surfaces,” said Priyam Patel, assistant professor of mathematics, who joined the Math Department in 2019. “I like how artistic and creative my work feels, and it’s also very tangible since I can draw pictures representing different parts of a problem I’m working on.”

Patel works in geometry and topology. The two areas differ in that geometry focuses on rigid objects where there is a notion of distance, while topological objects are much more fluid. Patel likes studying a geometrical or topological object extensively so that she’s able to get to know the space, how it behaves, and what sort of phenomena it exhibits. In her research, Patel’s goals are to study and understand curves on surfaces, symmetries of surfaces, and objects called hyperbolic manifolds and their finite covering spaces. Topology and geometry are used in a variety of fields, including data analysis, neuroscience, and facial recognition technology. Patel’s research doesn’t focus on these applications directly since she works in pure mathematics.

Challenges as a Minority

Patel became fascinated with mathematics in high school while learning to do proofs. She was fortunate to have excellent high school math teachers, who encouraged her to consider majoring in math in college. “When I was an undergraduate at New York University (NYU), I had a female professor for multivariable calculus who spent a lot of time with me in office hours and gave me challenging problems to work on,” said Patel. “She was very encouraging and had a huge impact on me.”

As a woman of color, Patel often felt out of place in many of her classes at NYU. Later, she was one of a handful of women accepted into a Ph.D. program at Rutgers University. Unfortunately, these experiences led to strong feelings of “impostor syndrome” for her as a graduate student. Eventually, she overcame them and learned to celebrate her successes, focusing on the joy that mathematics brings to her life. She has also worked to find a community of mathematicians to help support her through the tough times. “I’ve received a lot of encouragement from friends and mentors both in and outside of my math community,” she said. “I feel especially fortunate to have connected with strong women mentors in recent years.”

Mentors and Outside Interests

Feng Luo, professor of mathematics at Rutgers, was Patel’s Ph.D. advisor, and he played an active role in the early years of her math career. “Talking about math with Dr. Luo is always a positive experience, and his encouragement has been pivotal to my success as a mathematician,” said Patel. Another mentor is Alan Reid, chair and professor of the Department of Mathematics at Rice University. Patel notes that there are many aspects to being a mathematician outside of math itself, and these mentors have helped her navigate her career and offered support, encouragement, and advice.

Patel loves mathematics but makes time for other things in life. She enjoys rock climbing, yoga, dancing, and painting. Music is also a huge part of her life, and she sings and plays the guitar.

Future Research

Patel is currently working on problems concerning groups of symmetries of certain surfaces. Specifically, she has been studying the mapping class groups of infinite-type surfaces, which is a new and quickly growing field of topology. “It’s quite exciting to be at the forefront of it. I would like to tackle some of the biggest open problems in this area in the next few years, such as producing a Nielsen-Thurston type classification for infinite-type surfaces,” she said. She is also interested in the work of Ian Agol, professor of mathematics at Berkeley, who won a Breakthrough Prize in 2012 for solving an open problem in low-dimensional topology. Patel would like to build on Agol’s work in proving a quantitative version of his results. Other areas she’d like to explore are the combinatorics of 3-manifolds and the theory of translation surfaces.

 

by Michele Swaner