Faculty Fellow

Faculty Fellow Award


Priyam Patel receives Faculty Fellow Award from the University of Utah.

Priyam Patel, assistant professor of mathematics, has received a Faculty Fellow Award from the University of Utah.

Priyam Patel

Faculty Fellow Awards provide a semester of full release time from teaching and administrative tasks at full salary to tenure-line faculty for scholarly and creative projects. The funding can also be used to support pilot studies for external funding proposal submissions.

“Receiving this award is such an honor, and I am thankful for the time it will afford me to build on the momentum in my current research program,” said Patel.

Patel studies curves on surfaces, symmetries of surfaces, and objects called hyperbolic manifolds and their finite covering spaces. Surfaces come in two types: finite or infinite. Traditionally, finite-type surfaces have been studied more extensively; however, infinite-type surfaces are the focus of a quickly growing, new subfield of geometry and topology. One of the biggest unsolved problems in mathematics is to classify the symmetries of infinite-type surfaces. Patel plans to use the award to further her research in this area.

In 2021, she received a National Science Foundation (NSF) CAREER Award, which is considered the most prestigious NSF award for faculty members early in their careers as researchers and educators.

Patel joined the Math Department in 2019.

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

 

NSF CAREER Award

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

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