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Topologist Explores New Directions at the IMA

Isabel Darcy, an associate professor at the University of Iowa, arrived at the IMA in September 2011 to begin her New Directions Professorship.

"The IMA really is a great place to be. It offers a highly supportive environment, and it's the perfect place to get all of your work done. It's also a great place to meet a lot of other people who are interested in the annual theme," Darcy said.

Darcy, whose current research has been focused on studying the shape of DNA bound by proteins, decided to come to the IMA to spend a year as a New Directions professor because the 2011–2012 annual theme, Mathematics of Information, was a way to expand the research she was doing and explore new applications in her current field of research. She said while there will be some overlap in the mathematics, what she hopes to learn about are the new applications. Moreover, she would like to be able to graphically model a distance table she created that shows the distance between knots based on the minimum number of crossing changes.

"This table tells you the minimum number of times mathematically this protein would need to act to covert one knot type to another knot type," she explained.

This data can be visualized as a graph, and according to Darcy, she's never actually studied the properties of this graph.

"This work relates to my old research, but it would be quite a different view of looking at this graph. While I am here, I would like to study this graph and learn new properties that would give some additional use to the DNA topology community," she said.

For her, the IMA's New Directions program was ideal because it allowed her to spend an entire year exploring a new area.

"You really need to spend the whole year at the IMA to immerse yourself in the research. The supplemental sabbatical support is definitely beneficial so that you can do that," she said.

"Another great benefit is that you can bring your graduate students. That's frequently a concern for those who are mid-career," she added.

In addition, the professorships offer established mathematicians—typically mid-career tenured faculty at U.S. universities—an extraordinary opportunity to branch into new directions and increase the impact of their research by spending an academic year immersed in the IMA’s thematic program. Generally, participants learn new mathematics and applications, connect their research with important problems, and establish new contacts and collaborations. Wenbo Li, University of Delaware, also joined the IMA in 2011 as a New Directions professor.

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