The principal investigator will carry out research on a variety of topics related to probability theory, many involving probabilistic inequalities. These topics include optimal stopping as in prophet inequalities and order selection, partitioning of fair-division inequalities, ranges of vector measures, first-digit implications of perception of randomness, and decision processes and gambling theory. These problems have practical applications within areas of mathematical decision- making such as operations research, management science and statistics, as well as theoretical application in classical probability, measure and function theory.
