I'm a second-year graduate student at the
University of Notre Dame, in the Departments of
Mathematics
and
Mechanical Engineering. My goal for this phase of my education is two Ph.Ds -- one in mathematics, and one in mechanical engineering.
On the math side, my principal research interest is rook theory. Rook
theory is a lovely little corner of enumerative combinatorics, with
some great links to graph theory, hypergeometric series, and even
quantum mechanics!
Rook polynomials are (at least, on the surface) tools for
enumerating restricted permutations -- for instance, how many ways
there are to match a set of employees to a set of jobs that need doing,
subject to some sort of restrictions given about who can do what.
My advisor is
Dr. Joachim Rosenthal, who is currently on leave at the
University of Zurich.
In engineering, I study canonical kinematics; my advisor for this is
Dr. Michael Stanišić.
Kinematics is sometimes defined as the geometry of motion --
basically, it's the study of motion without consideration to the causes
of that motion. Another way to say it is that kinematicians study
velocity and acceleration, without studying forces and momenta.
Canonical kinematics is concerned with finding frames of reference
in which the equations describing a motion become minimally
complicated. (This is an important problem in robotics; if you have to
solve these equations repeatedly to move a robot, it makes sense to
have them in as simple a form as possible.)
A copy of my CV, in html format, can be found
here.
