My Research and Service to Profession: Highlights

Working in various areas of Mathematics, Computational Mathematics, and Computer Science for more than five decades, I introduced new insights and novel methods, solved a number of challenging research problems, revealed unexpected links among some seemingly distant subjects, and proposed new research directions and new areas of study. I was thrilled when in my research I was lucky to discover new keys that opened wellknown scientific locks, particularly when a single key opened a number of locks, as this was the case with my techniques of active operation/linear substitution, trilinear aggregation, and transformation of matrix structures. My work has led to creation of new fields and disciplines, in particular Complexity of Algebraic Computations, Symbolic-Numerical Computations, and Algebraic Multigrid (see my specific remarks in part 11 of Section 2). My high-impact contributions to the two former fields have been continuing from 1962 and 1992, respectively. Both fields are highly popular with application areas ranging from geometric modeling and robotics to cryptography and computational biology. In 1985-2000 my work on the design of fast and processor-efficient parallel algorithms (by myself and with Reif, Bini, Galil, and other leading researchers) was also seminal. I presented my findings in four books (1623+LXXIV pages overall), over 20 surveys in journals and book chapters, over 170 research articles in journals and over 90 in refereed conference proceedings. Almost all my publications are in Computer Science and Computational and Applied Mathematics. I also disseminated the results of my work through research reports, lectures at the universities, research centers and professional conferences worldwide, the Internet, and personal communication with colleagues and students. My techniques, insights, concepts and definitions are commonly used, sometimes as folklore. I am grateful for recognition and support of my research by leading experts, foundations (over $2,000,000 from NSF in 1980-2020, including Special Creativity Extension Award in 1993 from the Numeric, Symbolic, and Geometric Computation Program of the CCR Division in the Directorate CISE), journals, professional societies, universities (over $130,000 from CUNY in 1989-2016), and research centers. Enthusiastic reviews and citations of my work appeared in books, journals, and magazines. I worked as a journal editor, a managing guest editor of special issues, and a member of the program and scientific committees of international conferences and workshops, where I also organized sessions and mini-symposiums. This work as well as my research and publications helped establish synergistic links among various areas of computing, in particular, theoretical computer science, symbolic computations, numerical computations, and applied linear algebra. My designation of Fellowship in American Mathematical Society in 2013 was for “Contributions to the Mathematical Theory of Computation”.