Research interests:
My work is mainly concerned with differential equations, in particular:
integrability, or establishing nonintegrability (Painleve property, the Painleve-Kovalevski test, the poly-Painleve test, local linearization, normal forms)
Painleve equations (asymptotic behavior of solutions)
asymptotic analysis (formation of singularities, series and transseries solutions and their generalized Borel summation)
Schrodinger equation (time-dependent, and other aspects)
Also: difference equations (continuum limit, asymptotic behavior of solutions)
and, more recently, orthogonal polynomials and their matrix-valued generalizations (which have appeared naturally in problems of linearization of differential equations).