Throughout a long and distinguished career in the field of Mathematics, Michael Lacey has frequently shown himself to be a person who can solve mathematical problems that have stumped other educated people, sometimes for many years. This trend was evident from the beginning, when he was still a student.
As a student at the University of Illinois at Urbana-Champaign, he did his thesis on the subject of Banach Spaces. A Banach space is a term used in functional analysis for a complete normed vector space.
Mr. Lacey was able to solve a fundamental problem with the law of the iterated logarithm (a mathematical law that describes the fluctuations of a random walk) in relation to empirical characteristic functions. Lacey received his Phd from this university in 1987, under the direction of Walter Philipp. Read more:Michael Lacey | Wikipedia and Michael Lacey |Math Alliance
After receiving his doctorate, he took a position at the University of North Carolina at Chapel Hill, where, once again working with Walter Philipp, he was instrumental in proving the existence of an almost certain central limit theorem in January of 1989. For those who don’t know, this is a concept most often used when calculating probabilities.
What Lacey and Philipp proved is that, when you start with random variables, their normalized sum tends to fall within a certain distribution range (sometimes called a “bell curve”). It is referred to as an “almost sure” central limit theorem because there are some situations in which it does not apply, but it does apply to most situations.
After this, Mr. Lacey took a position at Indiana University, where he was involved in an extensive study of the bilinear Hilbert transform. This is an important concept in the area of signal processing, but prior to Mr. Lacey’s work, it was merely a conjectural concept that had been introduced by Alberto Calderon years prior.
Working with a colleague named Christophe Thiele, he was able to solve the problem, and confirm Calderon’s theory. For this, he and Thiele were awarded the prestigious Salem Prize. The Salem Prize is a prize of 5000 Francs which is awarded once a year, to young mathematicians who have done exemplary work in the field of harmonic analysis.
Over the course of his career, Lacey has distinguished himself in the areas of probability, ergodic theory, and harmonic analysis in particular.
His groundbreaking work in these fields are responsible for the respected position that he enjoys today.