REU SITE: Mathematical Sciences: Discrete Random Structures

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Project Abstract Discrete Random Structures The five-year project "Discrete Random Structures" will enable the Principal Investigator to further consolidate his deep involvement with undergraduate research. He will lead eight students each year in a series of meaningful mathematical research endeavours, each designed to convince the participants that there are undeniable links between several sub-disciplines, and that these bonds need to be recognized and exploited. The team-members' problems will emanate in areas such as combinatorics, number theory, geometry, algorithms, and molecular biology, but contemporary probabilistic methods and classical analytic techniques will be used as integral tools in their solution. We expect that most participants will study recently developed probabilistic techniques such as Janson's inequality; the method of bounded and unbounded martingale differences; Talagrand's isoperimetric inequalities; and the Stein-Chen method of Poisson approximation in their effort to understand the concentration in measure of a wide range of discrete structures. The participants will be selected after a nationwide search, and will spend two months at Michigan Tech University during the Summers of 1997--2001. Based on the PI's track record over the last seven years, it can be predicted that the student researchers will work on an average of three problems, either individually or in teams of two or more, and be able to make significant progress on about two of these endeavours. The students' findings will be presented at national meetings such as the Annual AMS/MAA Meeting, or at a carefully selected Probability/Combinatorics conference. As in the past, every effort will be made to submit the students' papers to high-level journals for possible publication. We shall select students from a broad range of colleges and universities, and are totally committed to the vigorous recruitment of women, minorities and disabled students.