Priyam Patel

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

 

COVID Connections

Creating a Virtual Symposium


Tanya Vickers

Rising to the Challenge

Science is about preparing the next generation of innovators, explorers, and connoisseurs of curiosity. For the last 29 years the College of Science ACCESS program has been the “first step” on this journey of discovery. The ACCESS program runs from June to August and is open only to first-year students freshmen and transfers).

A cornerstone of the ACCESS experience is the opportunity for the student cohort to share their work with faculty and peers during a research poster symposium. The symposium is a powerful learning experience that mirrors professional science conferences and a career in the field, and plays a key role in the program.

When COVID-19 hit the U.S., the longstanding tradition of the Spring Research Symposium was in jeopardy. As the director of ACCESS , I was driven to find a way to continue the capstone symposium, and provide talented first-year student scientists the opportunity to showcase their research, in spite of social distancing.

With just six weeks until the event we decided to design, build, and launch a novel virtual research symposium platform. The sudden shift and short time-frame presented a real challenge, but it was also an opportunity to pursue and explore innovative approaches to current standards that, if not for CO VID-19, would have been stagnant.

It’s been six months since the Virtual Symposium, and we are still surprised by its success. The merits and results of the virtual platform challenged the notion that in-person is best. The in-person symposium normally saw about 200 guests. In contrast, the virtual symposium reeled in nearly 6,000-page views in three days and 260 guests attended the live zoom presentations.

Thinking Differently

COVID-19 upended and reshaped our everyday lives and challenged everyone to find new approaches to routine activities and novel fixes for nascent problems, much like scientists do on a regular basis.

When the on-campus student research experience was cut short in March, it didn’t mark the end of learning for the 2019-2020 ACCESS cohort. Research faculty agreed to continue mentoring remotely, which included helping the students report their research in a scientific poster they would present virtually. Unfortunately, the technology for a virtual research poster presentation did not exist.

That’s when I began the process of envisioning and creating the Virtual Symposium platform, as it’s now known. I started with identifying the critical elements of an in-person research symposium and considering how to transpose them to a virtual model. My experience teaching and using Canvas (used to deliver course content) shaped the content, and with the collaboration and support of Micah Murdock, Associate Director of Teaching and Learning Technologists (TLT ), a novel virtual research symposium was fully realized.

Embracing Technology

The platform was a lofty goal that required three defining features: a webpage for students to introduce their project, a message board for peers, guests, and mentors to pose questions, and a live Zoom presentation with question and answer.

Each student had a personal webpage that included their research poster, a 3-minute video summary of their research project, and a short personal bio. These elements provided guests with an introduction and interactions analogous to an in-person symposium.

In-person symposia can feel rushed, but the virtual platform offered the advantage of providing guests more time to preview projects on their own, before using one, or both, forum tools—the student scientist’s discussion board, or the 30-minute Zoom live session scheduled on the last day—to ask questions or comment.

Building For the Future

Throughout this process, we wanted to build a tool with the future, as well as other disciplines and applications, in mind. We are proud to announce that the platform has already seen use for the School of Biological Sciences Virtual Retreat, ACCESS Alumni Career Panel, and a number of campus-wide projects. Most recently, the Virtual Symposium was chosen to serve as the cornerstone of the new College of Science high school outreach platform SCIENCE NO W—engaging students, presenters, and elite scientists from across the U.S. and around the world.

As a species and as scientists, we always look forward to new ideas and what can be done. In our darkest hours, we find a space for new forms of unity and growth, and can challenge ourselves to create and expand. CO VID has been undeniably difficult, but the development of new platforms and technologies, like the Virtual Research Symposium, show that sometimes, when we are forced to make changes to long held traditions, the outcome goes beyond finding an equivalent, making what we thought was “best” even better.

Special thanks to Dean Peter Trapa, ACCESS Program Manager, Samantha Shaw, and to the ACCESS students and mentors for believing in the vision of a Virtual Research Symposium.

For more information on the Virtual Symposium platform contact: tanya.vickers@utah.edu.

 

by Tanya Vickers