The investigator uses numerical simulations and analytic techniques related to amplitude equations to study pattern formation dynamics in swimming bacteria, wave number selection in a Swift-Hohenberg equation modeling traveling wave patterns, and traveling hole solutions of the complex Ginsburg-Landau equation. The broad topics of pattern formation and the behavior of patterns are widely important in mathematics and in application areas. The investigator studies the conditions under which certain equations have solutions that show such patterns, and what these patterns say about the underlying physical or biological problems.
