From INQUIRY [News from the University of Chicago/Physical Sciences Division], Spring-Summer 2013, p. 4. See http://psd.uchicago.edu/newsletter/Inquiry%20SpringSummer2013.pdf
A special group

Karin Melnick's scholarship has earned her an AMS Centennial Fellowship.

By Jeanie Chung

Karin Melnick, PhD'06, an assistant professor at the University of Maryland, received the 2012 American Mathematical Society's Centennial Fellowship, presented annually to outstanding early-career mathematicians. The monetary award, given primarily for excellence in research, allowed Melnick to return to Hyde Park this spring to advance her work in differential geometry and dynamical systems.

How have you spent your time on the fellowship?

I divided it into two semesters over two years. I didn't want to take a whole year off, and we're shorthanded for professors in my department. I came here to focus on a project with Tullia Dymarz, PhD'07, at the University of Wisconsin, and David Fisher, PhD'99, at Indiana University.

We're studying delta hyperbolic groups, which are like discrete versions of hyperbolic space. Hyperbolic space is negatively curved; it's a non-Euclidean geometry. There is a nice, contracting dynamical system coming from the geometry of the delta hyperbolic group. From this dynamical system, our goal is to build some additional differential geometric structure so that in the end, we can prove a conjecture about what the original group was. What the conjecture asserts is what we call a rigidity statement; there are some really special examples that are well known in mathematics. We take one of these delta hyperbolic groups and make one seemingly minor assumption about its boundary, and from this we try to prove that it's one of the really special groups.

What if you conclude that it's not?

Then we haven't proven the conjecture.

My expertise is differential geometry, Tullia is a geometric-group theorist, and David knows a lot about dynamical systems. It's fun because we each are learning from the other and hoping to combine our expertise.

How important is collaboration in mathematics?

I think it's a lot more common today than it was 50 years ago, probably because it's been successful. Also, we have more ability to travel and meet potential collaborators. Some people like to work alone, but I think most people enjoy being social and interacting with other people and find it energizing and inspiring. Doing math is problem solving. You need ideas, and the more people you have, the more ideas you're going to come up with.

You are one of only five women to receive the ams Centennial fellowship out of 95 recipients since 1974-75. is it difficult to be a woman in a male-dominated field?

There's a double-edged sword. We get more attention and in some cases more opportunities. For
example, we might be invited to give talks more often because people are making an effort to include women in their conference or their seminar. On the other hand, there are certainly men and women who question whether a woman, or a member of a minority group, has gotten recognition by virtue of being in the minority. Everybody has anxiety when they move up from being a grad student to a postdoc and from a postdoc to starting a tenure- track job. The men I know who are willing to talk about their insecurities have told me they also felt anxious, but I think it's amplified if you're worrying whether other people are looking at you and considering whether you actually deserve to be there.

In march you presented at a UChicago colloquium cosponsored by the association of women in mathematics. Is such a support network something you'd encourage for future women mathematicians?

In my career, I haven't really been mentored by senior women. There were no permanent female faculty in the math department at my college [Reed]. There were no female [mathematics] faculty at the University of Chicago when I was a graduate student. There were no female [mathematics] faculty at Yale when I was a postdoc. Now I'm in a department of 60 people that has five women on the faculty, and before I arrived there were three.

Somehow it hasn't been crucial for me to have these sorts of female role models or mentors, although in the cases where I have met them, I've found it really inspiring and worthwhile. I was joking before my colloquium lecture that as a graduate student here, I complained that they weren't inviting enough senior women to give colloquia or distinguished lectures, but I did not have myself in mind as a potential speaker.
SIDEBAR PHOTO: Photo courtesy Karin Melnick
Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
625 Wham Drive
Mail Code 4610
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Phone:  (618) 453-4241  [O]
            (618) 457-8903  [H]
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E-mail:   jbecker@siu.edu