Joe Breen

Joe Breen, Postdoctoral scholar, mathematics

Untangles shapes beyond three dimensions

Hometown: Findlay, Ohio

Faculty mentor/advisor:
Keiko Kawamuro, PhD, professor, Department of Mathematics, College of Liberal Arts and Sciences

What is your degree program and anticipated graduation date?
I am a postdoctoral research scholar, working at the University of Iowa through 2024-25.

Please describe your research:
I am a theoretical mathematician studying topology, which is a squishy and stretchy kind of geometry. I work on understanding and detecting how higher-dimensional shapes can be tangled up and knotted together. In practice, this involves drawing a lot of pictures and devising diagrams and schematics to help visualize shapes in 4, 5, and 6 dimensions (and beyond).

In simple terms, why does this research matter?
It may be hard to believe, but there are many problems in science and engineering that can be repackaged and transformed into a problem about higher-dimensional shapes. For example, NASA has employed mathematicians working in my field to help find and calculate complicated trajectories of shuttles around Jupiter’s moons. Instead of calculating the trajectories directly, they translate the problem into a different one involving counting how many times certain shapes intersect in higher dimensions. Under this translation, the machinery of topology becomes powerful and insightful.

How soon after starting at the University of Iowa were you able to participate in research?
I have been working on research as soon as I started at the University of Iowa as a postdoc.

How has being involved in research made you more successful at the University of Iowa?
After only one year at the University of Iowa, I have gained a new level of confidence in my ability to do research, make discoveries, and push the boundaries of mathematical knowledge. I have learned so much from students, other postdocs, and professors, and the community of the math department as a whole has been both supportive and also eager to hear my ideas and perspectives. This dynamic has been mutually beneficial.

What are your career goals and/or plans after graduation?
I hope to stay in academia and be a math professor, continuing to do research and also teach. There is no shortage of mysteries about the nature of shapes that are waiting to be solved!

Banner location: Downtown—