|The main focus of my research is on developing and applying
techniques from algebra (in particular, algebraic geometry, commutative
algebra, and combinatorics) to theoretical and computational problems
in statistics and biology. Thus, my research falls under the
scope of algebraic statistics and algebraic biology. See my CV for details on my research experience and my publications page for preprints of all the papers I have written.
On the algebraic side, I am interested in problems and techniques that lie on the boundary of two fields. I spend a fair amount of time working on problems in combinatorial commutative algebra, which, stated simply, is concerned with the development of combinatorial techniques for studying polynomial ideals and modules. A range of combinatorial tools are needed including algebraic and geometric combinatorics, polyhedral geometry, and graph theory, to name just a few.
On the applied side, I work on studying the geometry of statistical models, and developing algebraic and combinatorial tools for data analysis. Some application areas I have worked in include: contingency table analysis, conditional tests, disclosure limitation, phylogenetics, and evolutionary biology. The models that I study are typically graphical models and exponential families or hidden variable analogues of such models.
Aside from the specific problems of my research, I am broadly interested in both pure and applied mathematics. I find especially interesting the research that makes unexpected connections between seemingly unrelated areas, which is probably why I enjoy working in algebraic statistics.
|I am looking for students who are interested in working on
these problems at the boundary of algebra, combinatorics, statistics,
and biology. This is an opportunity to get in on the ground floor
of an exciting research area where there are truly more problems to
work on than people to work on them. The problems in this area
have the advantage there is much room for experimentation, there is the
potential for interesting new theorems, and there are many
possibilities for the development of algorithms and software for
I am looking for students with a range of backgrounds and there is much possibility to tailor research problems based on a student's background and interest. Please contact me if any of this sounds interesting or if you would like to hear about some specific research problems.
I expect my students to take the following courses:
A range of other courses are likely to benefit you in working with me. Plan to take at least 2 of the following sequences of courses: