Roy Adler and the lasting impact of his work

Roy Adler (1931–2016) earned his Ph.D. in 1961 from Yale University under the supervision of Shizuo Kakutani with a dissertation titled “On Some Algebraic Aspects of Measure Preserving Transformations.” His entire career was spent at the IBM Thomas J. Watson Research Center, with many short-term and longterm visits to universities. He was a fellow of the American Academy of Arts and Sciences, the American Mathematical Society, and the New York Academy of Arts and Sciences. He also served on the Board of Trustees of the American Mathematical Society. Among his seminal scientific achievements are the invention of topological entropy, the first applications of Markov partitions for dynamical systems and the application of symbolic dynamics to coding problems in hyperbolic geometry and information theory. These will be discussed in more detail later on. Roy’s interest in ergodic theory and symbolic dynamics led him to develop an algorithm to design codes to meet the constraints for data storage and transmission channels. A paper, including co-authors, Don Coppersmith and Martin Hassner, documenting these developments won the IEEE Information Theory Group 1985 Best Paper prize. IBM awarded Roy a Fourth Plateau Invention Achievement award, two IBM Research Outstanding Innovation awards, an Outstanding Technical Achievement award and the 2000 Research Patent Portfolio award. Roy was a contributor to more than 50 publications, in ergodic theory and symbolic dynamics, and 10 patents on coding, printing, spine modeling, x-ray data acquisition and cryptography. He was also a caring and inspiring mentor to several young mathematicians. An intellectual with a sharp and dry wit, his passions included great food, opera, fishing, good friends, and most of all his family. Roy was married to Audrey Wanner who passed away in 1990 and then to Judith Hershaft. He was a dedicated and adoring father to his two children, Caroline Kosaka and Michael Adler, his stepchildren and grandchildren. Probably Roy’s most important contribution to ergodic theory and topological dynamics was his introduction of topological entropy as the topological analogue of the measure-theoretic dynamical entropy that had been by defined by A. N. Kolmogorov [33] just a few years earlier. A version of topological entropy can be found in earlier work of W. Parry [36] and C. Shannon [42], but only for shifts of finite type. The definition given in Roy’s foundational paper