2011–2012 SUMMARY ACCOMPLISHMENTS

Summary of Research Accomplishments

Section 1 summarizes my accomplishments and ongoing research program in the field of geometric Ramsey theory, specifically on finding geometric configurations in sets of positive density in R. Section 2 summarizes my work in arithmetic combinatorics, specifically on single recurrence problems such as finding polynomial configurations in sets of positive density and related problems in diophanti...

Summary of Research Accomplishments

1. Wavelets. One of my early accomplishments was the construction of wavelets on hyper-surfaces, extending the two-dimensional work in Coifman, Jones, Semmes (J. of Amer. Math. Soc., 1989), in a desirable fashion. This answered a question raised by G. David (Springer LNM, 1991, p. 75) and was used to provide a new proof of the fundamental result of Coifman, McIntosh, Meyer (Annals of Math., 198...

Iii. Summary of Professional Accomplishments

Summary of Research Accomplishments and Goals

My Ph.D. thesis centered on a class of univariate polynomials over finite fields known as composed products or root-based compositions . Work related to the thesis appears in [5], [6], and [41], while additional results pertaining to multivariate analogues appear in [48] and [49]. My post-thesis research in finite fields includes not only work with polynomials (see [14] and [44]), but also work...

II. Summary of Activities and Accomplishments

II. Summary of Activities and Accomplishments PD/A CRSP research conducted during this reporting period and described in the Interim Work Plan allowed the successful transition from the third grant, with its focus on production research, to the fourth grant, which emphasizes aquaculture research that addresses environmental effects and social and economic aspects in addition to production optim...