Dabkowski earned his bachelor's degree in mathematics from the University of Michigan-Dearborn. After spending several years of graduate study at Michigan State University, he followed his advisor to the University of Wisconsin, where he earned his Ph.D. for his work on the supercritical quasi-geostrophic equation. He spent the year after the completion of this doctoral degree as a postdoctoral fellow at the University of Toronto, where he continued his research on active scalar equations. For the next three years, he worked at the University of Michigan as a postdoctoral fellow studying problems in fluid mechanics, Ostwald ripening, and Kahler conformal geometry. At the start of the fall term in 2015, Dr. Dabkowski joined the staff at Lawrence Tech as an assistant professor.
His research falls into three main categories: the study of nonlocal active scalar equations, Carr-Penrose and Lifschitz-Slyozov-Wagner models, and conformal equivalence of scalar curvatures. Active scalar equations are used widely in applications which include Eckman pumping, the vorticity formulations of the Euler equations for inviscid incompressible flow, and problems in magnetohydrodynamics. The Carr-Penrose and Lifschitz-Slyozov-Wagner equations serve as models of coarsening, and their long time behavior is an essential to understanding steady-state stability of various fluid sols. The scalar curvature problems arise from the study of asymptotically locally euclidean spaces in physics.
Professor Dabkowski is a Michigan native and a lover of mathematics in all of its forms. He earned his Ph.D. from the University of Wisconsin-Madison for his work on the supercritical surface quasi-geostrophic equation. He spent a year at the University of Toronto as a postdoctoral fellow and three years at the University of Michigan as a postdoctoral assistant professor before joining the Lawrence Tech faculty. Professor Dabkowski's research is broadly contained in the study of nonlinear nonlocal partial differential equations, with specific concentrations in the theory of active scalar equations, models of coarsening, and problems in conformal geometry. Eager to discuss mathematics and its applications, Professor Dabkowski invites students to discuss how mathematics can be incorporated into their research projects. The common thread of all of his research is study of various differential equations, and Dr. Dabkowski excited to mentor undergraduates on a wide variety of mathematical projects in any of these fields. His door is always open for students who wish to expand their mathematical knowledge.