Project Grant 2452069

This $180,000 Project Grant, awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports fundamental research on two central combinatorial topics by a principal investigator at Rutgers, The State University.

The first topic focuses on balancing problems for partially ordered sets, which have algorithmic applications in areas like sorting. The principal investigator and a student have recently made significant advances in this area, introducing new methods and identifying additional basic questions for further exploration. The second topic involves thresholds in discrete random systems, an area central to probabilistic combinatorics and statistical physics. Breakthroughs by the principal investigator and others have reinvigorated research in this domain, resolving previously formidable problems.

This 2-year grant, commencing on July 1, 2025, will support the principal investigator's work in these two combinatorial areas, with the involvement of graduate students. The project aims to further scientific knowledge and introduce new mathematical techniques, building upon the principal investigator's track record of applying ideas from diverse disciplines to address fundamental combinatorial questions.