As a new assistant professor in the Department of Mathematics at the University of Notre Dame, Juanita Pinzón-Caicedo is looking forward to the service component portion that tenure-track professors are asked to complete as much as her research in topology and teaching responsibilities.
Pinzón-Caicedo studies knot theory, gauge theory, trisections, and other areas within low-dimensional topology, which is the study of the properties of “deformed” objects with continuous spaces that have four or fewer dimensions. Notre Dame is highly ranked nationally for its topology program, and Pinzón-Caicedo will be one of two low-dimensional topologists and among 14 topology faculty in the mathematics department.
As a low-dimensional topologist, Pinzón-Caicedo’s objects of study are abstract, and sometimes mathematicians feel that their work can be perceived as “creations of our minds,” she said. But she believes bringing mathematical skills to others and sharing practical applications will help people go further in life. She stressed that people may still go far without math skills, but more paths are open to people who are comfortable with the subject.
Pinzón-Caicedo put together a recital of modern dance and mathematics with her mentor at North Carolina State University, where she was completing her post-doctoral research.
Her mentor danced, and Pinzón-Caicedo was in one of the scenes. After the performance, parents with children came up to speak with her. One girl expressed an interest in mathematics, and another in physics.
“I turned to them and said, ‘keep going. I want you to be my colleague one day. I want you to have the office next to mine,” Pinzón-Caicedo said.
She felt the opportunity to share those opportunities was stronger at Notre Dame than at other universities she considered joining.
“I felt a strange feeling of familiarity when I came to interview at Notre Dame, and it was a gut feeling that I would do well here, and that I would flourish,” she said.
Pinzón-Caicedo earned her bachelor’s degree in mathematics from Universidad de Los Andes, Bogota, Colombia, and her doctoral degree in mathematics from Indiana University. She began teaching math as an undergraduate student, and worked as a postdoctoral teaching and research assistant at the University of Georgia. She has been a postdoctoral research scholar at North Carolina State University from 2017 until 2019, when she visited the Max Planck Institute for Mathematics in Bonn, Germany for the 2019-2020 academic year. She has published several papers, and has several more prepared to submit.
U.S.-based Latinx mathematicians are not common in low-dimensional topology, she said. Though Pinzón-Caicedo plans to explore the social justice opportunities at Notre Dame, she knows that her greatest tool to bring about change runs deeper. In addition to the service work she plans to do, she’s looking forward to beginning her teaching responsibilities and collaborating with other researchers in her department.
“Something I can do that will have a tremendous impact for women and underrepresented minorities in science is to be a really good mathematician,” Pinzón-Caicedo said. “Becoming a professor at the University of Notre Dame has an impact not just for me personally, but also for people who are going to see me in this role.”