My current research centers on topics at the interface between combinatorics and analysis.  In particular, I am interested in novel and unexpected positivity properties that arise for some combinatorially defined polynomials and power series.  Some of these properties are closely connected with the Stieltjes moment problem and with continued fractions.

I am also interested in the real and complex zeros of combinatorially defined polynomials such as the Tutte polynomial (and its specializations such as the chromatic polynomial and the flow polynomial), and their relation to phase transitions in statistical mechanics. Some of this work leads to the investigation of "classical" problems in complex analysis.