David Ambrose
May 2002 Ph.D. Recipient, Mathematics
David Ambrose’s road to graduate school began with his interest in mathematics; he says that “going to graduate school was really the only way I could continue to learn advanced mathematics.” Along the way, he has picked up a few honors; David was elected into Phi Beta Kappa as an undergraduate, went on to hold a James B. Duke Fellowship during his graduate school career, and served as co-president of the Society of Duke Fellows.
David, who graduated this past May, came to Duke in 1997 after graduating from Carnegie-Mellon University in math and economics. He says he chose Duke because “I found the research interests of the math faculty to be compatible with my own. Also, during the visitation weekend after I was accepted, I found that people in the department were generally friendly and easy to talk to. I also liked that Duke was on the east coast.
“I’ve been interested in analysis since I started taking advanced math classes as an undergraduate; the main reason I found it interesting is that I had a variety of great teachers in my analysis courses,” he says of the development of his academic interests. “When I came to Duke, I knew that I was interested in analysis, but I didn’t know what kind of analysis I wanted to do. In the fall of my second year, I had a great course from Professor Andrea Bertozzi on fluid dynamics. Since she knew of my interest in analysis, she had me do a project on the Navier- Stokes equations (the differential equations which describe fluid motion) in which I learned some of the analysis related to fluid dynamics. This convinced me to work in the field.”
As an undergraduate, David was trained “more as a pure analyst,” he says. “When I got to grad school, I took courses in a variety of mathematical subjects, but my fluids course from Andrea Bertozzi made me want to be an applied analyst in fluid dynamics.” David went through four candidates before choosing Tom Beale, a fluid dynamics expert, to be his advisor on his dissertation, “Well-posedness of vortex sheets with surface tension.” When asked to put this in layperson’s terms, he explains that “I examine the equations of motion which describe the interface between two fluids moving past each other. If surface tension is not included in the equations, then it is well known that they do not have a good solution. With surface tension, I prove that the equations have a good solution for at least a little while.” David kept his project on track by meeting with Professor Beale every week to discuss his progress.
David was recently offered a National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship, but declined it in favor of a Courant Instructorship at the Courant Institute of Mathematical Sciences at New York University. Ultimately, David wants to be a professor at a research-oriented university, and says he plans “to continue to work on analysis of problems in fluid dynamics,” and to branch out to other areas, such as materials science.
New York University’s Courant Institute of Mathematical Sciences is a leading center for research and graduate education in mathematics and computer science. Over the past fifty years, the Institute has contributed to American science by promoting an integrated view of the mathematical and computational sciences as a single unified field. Its research activity ranges from the theoretical to the applied. It covers a broad frontier that includes pure mathematics and computer science, as well as applications of mathematics and computation to the biological, physical, and economic sciences.
David spent his last summer in Durham as an instructor in Duke’s Talent Identification Program, but he’s more than ready to head to New York. “It’s been interesting living in the South for a while, but I think I’m happy to be heading back to the Northeast now,” notes the Delaware native. He will, however, miss spending time with his friends, who, he says, “are almost all grad students at Duke, too.”
Tom Beale
Professor, Mathematics
Analysis is the part of mathematics that begins with calculus. It grows from attempts to make systematic models and predictions of the physical world.
Work in the style of David’s thesis requires careful and intense effort over a long period of time, as well as skill and insight. It also takes patience; we have to get used to failing in our attempts, with the experience from each attempt leading to an improved approach the next time. David is very capable, but it was also important that he was genuinely interested in the problem, so that he had the motivation to carry him through.
(This profile originally appeared in the Fall 2002 issue of The GRIND.)