When mathematics is like poetry, it must be topology

Author: Naya Tadavarthy

Alexandra Kjuchukova

Before she earned her doctorate degree in math, Alexandra Kjuchukova wrote poetry. The assistant professor in the Department of Mathematics, who joined the Notre Dame faculty in fall 2021, said that she sees similarities between these two passions. 

“There’s a certain patience that you learn when you’re trying to write poetry or do any kind of art, and I think that spending a couple of years working in that field helped me develop the kind of patience and stubbornness that you also need to do math,” Kjuchokova said. 

Kjuchukova was born and raised in Bulgaria before attending Harvard College, where she earned her bachelor’s degree in mathematics in 2008. She then received a Master of Fine Arts in poetry at New York University in 2010 and a doctorate degree in mathematics from the University of Pennsylvania in 2015. She studies topology, with a focus on knots, four-manifolds, singularities, branched covers, trisections, and concordance. Her work relates the geometric and algebraic properties of space. 

“It’s a beautiful subject that kind of defies your intuition, because the three-dimensional space we live in is topologically not very interesting…in reality, sometimes the local structure of a space does not really determine the global structure, and you can get very interesting, surprising phenomena, which our intuition doesn’t prepare us for.”

Kjuchukova is not the only faculty member studying topology at Notre Dame, and she appreciates the collaborative atmosphere that the Department of Mathematics provides. 

“One of my favorite things about this place is it has a very strong topology group with a lot of people working in different areas of topology, and people are very open about approaching each other with questions and finding problems that they can work on together,” she said. 

In addition to being around professors and graduate students with expertise in topology, Kjuchukova appreciates sharing her interests with undergraduate students. She taught an Elements of Calculus class in the fall, and she looks forward to leading a topics course in topology in the spring. Kjuchukova hopes to develop classes for first years, as well, so she can show them how fascinating mathematics can be, outside of the limited subjects students study in high school. She would also like to take advantage of the department’s support for bringing students abroad and attending international conferences in the future. 

“I just think it’s wonderful to be part of such an active community and to have so many resources,” Kjuchukova said.