Faculty Website: http://faculty.rwu.edu/rjacobson
Math and Education Blog: http://robertjacobson.herokuapp.com
I am always interested in talking with students wanting to do research projects. My primary scholarly interests are in mathematics and computer science, but interdisciplinary projects are also a possibility. Here are some topics that would make great research projects:
My research interests are in analysis, in particular complex analysis, and even more specifically several complex variables. A first course in complex analysis usually covers the elementary theory of holomorphic functions defined on nonempty connected open sets of the complex plane. Thus a student in such a course would learn that the zero set of every nonconstant holomorphic function is a discrete set, that is, the zeros of holomophic functions are isolated; that holomorphic functions can be reproduced via integration against a single (independent of the domain) holomorphic kernel, namely the Cauchy kernel; and that every bounded simply connected planar domain is biholomorphic to the unit disk. None of these things are true when we translate them into statements about holomorphic functions of more than one complex variable. We have, then, a different theory of holomorphic functions in several variables than when we restrict attention to the single variable case.
My primary object of study is the Bergman kernel function, a reproducing kernel for the Hilbert space of L2-integrable holomorphic functions. My dissertation focuses on computing explicit formulas for a reasonable class of weighted Bergman kernel functions. Also of interest is the question of which domains are associated to Bergman kernels which take the value zero, a question known as the Lu Qi-Keng problem.
I am an advocate for women and girls and an LGBT Ally. I cofounded the Hawk Allies program at RWU.
I am interested in religion, belief, and nonbelief.
I have a deep interest in and commitment to education generally and math education specifically.
Professional Societies: Mathematical Association of America, the American Mathematical Society, and the Association of Adventist Mathematicians.