Note: Anybody who is interested in a postdoctoral position in
my research group should go to our web page and follow the
instructions to apply for a position in the UCLA Department of
Mathematics. To see advertised positions that start in the 2024-25
academic year, go to this
page. Do not send applications directly to me, and do not ask me
if the instructions don't apply to you (because they do). In your
application procedures, it makes sense to mention in your cover letter
that you are interested in working with me. I am happy being contacted
informally, but any official application has to be sent through
official channels.
Note 2: Our deadlines for positions that start in Fall (usually
July) of year N tend to be in November of year N - 1. If we will be at
the same conference or otherwise in the same location, I am happy to
chat informally.
Note 3: Similarly, for people who are interested in becoming a
PhD student at UCLA and being in my group as a Ph.D. student, you
should go to our
departmental website and follow the instructions to apply. It then
makes sense to mention me in the Statement of Purpose that you submit
as part of your application materials. Admissions are done centrally,
and I am not authorized (nor should I be!) to admit people on my
own.
Background
I was born and raised in California. I was technically born in
Los Angeles, but I actually lived in Beverly Hills until I went to
college.
In order, the schools I attended are Temple Emanuel preschool
(because, of course, you really needed to know that), Hawthorne
Elementary School, Beverly Hills High School (yes, I really did go
there), California Institute of Technology (BS, Applied Math, 1998;
member of Lloyd House), and Cornell University (PhD, Center for
Applied Mathematics, 2002).
From Fall 2002 through Spring 2005, I did a postdoc in
Mathematics and the Center for Nonlinear Science (housed in the School
of Physics) at Georgia Tech. (In Spring 2003, I was on leave from
that position to be a postdoc in the Semiclassical Analysis program at
the Mathematical Sciences Research Institute in Berkeley,
California.)
From June 2005 until 30 September 2007, I was a postdoc at
Caltech in the Center for the Physics of Information. I was also part
of the condensed matter physics group.
On 1 October 2007, I became a faculty member in the Mathematical
Institute at University of Oxford. (Can you tell that I take
vacations? Quickly check the dates you just read.)
On 30 June 2016, I became a faculty member in the Department of
Mathematics at UCLA. In September 2016, I physically moved back to Los
Angeles. (That's right: I have moved back to the West Side, where I
last lived full-time when I was in high school.)
This is completely irrelevant for my research group page, but I
am a diehard fan of the Los Angeles Dodgers. I'm not going to write a
web page this extensive without putting that information somewhere
prominent.
Got all that?
Research Interests
I am interested in numerous areas of applied mathematics, and I am
always looking for new areas to try. (I basically keep adding new
research interests.) However, here are a few buzzwords describing
areas in which I have already written research papers or have projects
in progress:
How I got interested in my research area in the first place
People run into mathematicians (not usually literally, but I have a
few stories...) and sometimes wonder how they got that way. Both
normal people and junior scientists (I'm thinking in particular of
undergrads and grad students who are still trying to figure out what
they want to do) also wonder how scientists got interested in their
particular research areas. I think it's extremely useful to provide
an answer to this question, so here's my story:
My initial interest in nonlinear dynamical systems arose from a
childhood fascination with patterns. The sketches that I began
drawing when I was very young included many such displays of
contrasting color. (I glanced through these sketches a few years ago,
and several of them look remarkably similar to patterns that occur in
nonlinear science. This is a statement either of how little I've
progressed since then or of how I was born to study nonlinear science.
I'm not really sure which...)
In high school, I noticed that fractals could produce colorful
patterns in the same vein as what I liked to draw, which led to my
interest in them. In college, I discovered that what really intrigued
me was trying to understand the mechanisms that could produce such
interesting pictures and the natural and human-made systems that
exhibited them. Since then, my interests have branched out into
several fields of science that can be studied using dynamical systems
and other methods.
In short, while my research interests have diversified in the last
several years, my academic interests initially arose largely from what
I consider visually appealing.