Grant: Discovery Grants Program - Accelerator Supplements

The overall area of my research is the design and analysis of algorithms. My recent research has centered around two lines: the study of algorithms when randomness is considered, and the investigation of algorithms in finite fields and their applications. Probabilistic analysis of algorithms comprises the study of algorithms when randomness is used. In particular, average-case analysis of algorithms focus on the understanding of the behaviour of algorithms on random inputs. An essential goal of the area is to advance in the understanding of randomness. Immediate goals are better understanding of particular algorithms, and the development of new efficient algorithms based on this knowledge. The scientific approach is based on mathematical proofs involving generating functions for counting the properties of interest for the analysis of the algorithms, and asymptotic analysis when exact counting is not possible. My goal in this area is two-folded: to develop algorithms for fundamental problems like sorting and searching with better performance than previously known algorithms, and to contribute to the mathematical understanding of random polynomials over finite fields. My second line of research involves computations in finite fields and their applications. Algorithms that work with finite fields play a fundamental role in practical applications in cryptography, coding theory and information theory. My goal in this area is the design of efficient algorithms in finite fields, and the usage of elements from the theory of finite fields in Engineering and Computer Science applications. Examples are efficient implementation of arithmetic using normal elements and irreducible polynomials; constructions of certain types of polynomials over finite fields (irreducible, primitive, and so on) and their applications to fast LFSR (Linear Feedback Shift Registers) and codes constructions.