Dr. Lancellotti's field of interest is Mathematical Physics, with special emphasis on non-equilibrium statistical mechanics. Statistical mechanics strives to understand how the properties of macroscopic physical systems arise from the interactions among huge numbers of microscopic entities, such as atoms and molecules. This type of question leads to fascinating and hard mathematical problems. In particular, Dr. Lancellotti has been working on the so-called kinetic theory of plasmas and gravitating systems. These are assemblies of many electrically charged particles (plasmas) or large populations of stars (galaxies, globular clusters) that interact through inverse-square forces (e.g. gravity). Over the years, physicists have assembled a body of beautiful theoretical models, called kinetic equations, that are supposed to describe mathematically the behavior of these systems. However, the current understanding of the solutions to these complicated differential equations is still very limited. Hence the need to apply advanced mathematical methods in order to investigate such solutions and compare them with the the phenomena that are observed in nature. Also, the mathematical analysis is often supplemented by numerical simulations that shed light on the nature of the solutions being investigated.
Among other things, Dr. Lancellotti has published research papers on wave propagation in plasmas and on the dynamics of clusters of stars. He is currently studying the equations that regulate energy dissipation in plasmas and gravitating system (Landau and Lenard-Balescu equations), and also the so-called Kuramoto model, that describes the dynamics of large assemblies of oscillating systems (for example, crickets, heart cells and other biological systems). His research is currently supported by a three-year grant from the National Science Foundation and also by a smaller PSC-CUNY grant, and is conducted in collaboration with other researchers both at the College of Staten Island and at other research institutions.