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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

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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.

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.

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.

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.

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 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.

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--

Jerry P. Becker

Dept. of Curriculum & Instruction

Southern Illinois University

625 Wham Drive

Mail Code 4610

Carbondale, IL 62901-4610

Phone: (618) 453-4241 [O]

(618) 457-8903 [H]

Fax: (618) 453-4244

E-mail: jbecker@siu.edu

Dept. of Curriculum & Instruction

Southern Illinois University

625 Wham Drive

Mail Code 4610

Carbondale, IL 62901-4610

Phone: (618) 453-4241 [O]

(618) 457-8903 [H]

Fax: (618) 453-4244

E-mail: jbecker@siu.edu