Michael Lacey
Encyclopedia
Michael Thoreau Lacey is an American mathematician
. Lacey received his Ph.D.
from the University of Illinois at Urbana-Champaign
in 1987, under the direction of Walter Philipp. His thesis was in the area of probability in Banach space
s, and solved a problem related to the law of the iterated logarithm
for empirical characteristic functions
. In the intervening years, his work has touched on the areas of probability
, ergodic theory
, and most importantly, harmonic analysis
.
His first postdoctoral positions were at the Louisiana State University
, and the University of North Carolina at Chapel Hill
. While at UNC, Lacey and Walter Philipp gave their proof of the central limit theorem
.
He held a position at Indiana University
from 1989 to 1996. While there, he received a National Science Foundation
Postdoctoral Fellowship, and during the tenure of this fellowship he began a study of the bilinear Hilbert transform
. This transform was at the time the subject of a conjecture by Alberto Calderón
that Lacey and Christoph Thiele solved in 1996, for which they were awarded the Salem Prize
.
Since 1996, he has been a Professor of Mathematics at the Georgia Institute of Technology
. In 2004, he received a Guggenheim Fellowship
, for joint work with Xiaochun Li.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. Lacey received his Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
from the University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign
The University of Illinois at Urbana–Champaign is a large public research-intensive university in the state of Illinois, United States. It is the flagship campus of the University of Illinois system...
in 1987, under the direction of Walter Philipp. His thesis was in the area of probability in Banach space
Banach space
In mathematics, Banach spaces is the name for complete normed vector spaces, one of the central objects of study in functional analysis. A complete normed vector space is a vector space V with a norm ||·|| such that every Cauchy sequence in V has a limit in V In mathematics, Banach spaces is the...
s, and solved a problem related to the law of the iterated logarithm
Law of the iterated logarithm
In probability theory, the law of the iterated logarithm describes the magnitude of the fluctuations of a random walk. The original statement of the law of the iterated logarithm is due to A. Y. Khinchin . Another statement was given by A.N...
for empirical characteristic functions
Characteristic function (probability theory)
In probability theory and statistics, the characteristic function of any random variable completely defines its probability distribution. Thus it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative...
. In the intervening years, his work has touched on the areas of probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
, ergodic theory
Ergodic theory
Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics....
, and most importantly, harmonic analysis
Harmonic analysis
Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves. It investigates and generalizes the notions of Fourier series and Fourier transforms...
.
His first postdoctoral positions were at the Louisiana State University
Louisiana State University
Louisiana State University and Agricultural and Mechanical College, most often referred to as Louisiana State University, or LSU, is a public coeducational university located in Baton Rouge, Louisiana. The University was founded in 1853 in what is now known as Pineville, Louisiana, under the name...
, and the University of North Carolina at Chapel Hill
University of North Carolina at Chapel Hill
The University of North Carolina at Chapel Hill is a public research university located in Chapel Hill, North Carolina, United States...
. While at UNC, Lacey and Walter Philipp gave their proof of the central limit theorem
Central limit theorem
In probability theory, the central limit theorem states conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed. The central limit theorem has a number of variants. In its common...
.
He held a position at Indiana University
Indiana University
Indiana University is a multi-campus public university system in the state of Indiana, United States. Indiana University has a combined student body of more than 100,000 students, including approximately 42,000 students enrolled at the Indiana University Bloomington campus and approximately 37,000...
from 1989 to 1996. While there, he received a National Science Foundation
National Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
Postdoctoral Fellowship, and during the tenure of this fellowship he began a study of the bilinear Hilbert transform
Hilbert transform
In mathematics and in signal processing, the Hilbert transform is a linear operator which takes a function, u, and produces a function, H, with the same domain. The Hilbert transform is named after David Hilbert, who first introduced the operator in order to solve a special case of the...
. This transform was at the time the subject of a conjecture by Alberto Calderón
Alberto Calderón
Alberto Pedro Calderón was an Argentine mathematician best known for his work on the theory of partial differential equations and singular integral operators, and widely considered as one of the 20th century's most important mathematicians...
that Lacey and Christoph Thiele solved in 1996, for which they were awarded the Salem Prize
Salem Prize
The Salem Prize, founded by the widow of Raphael Salem, is awarded every year to a young mathematician judged to have done outstanding work in Salem's field of interest, primarily the theory of Fourier series.-Past winners:...
.
Since 1996, he has been a Professor of Mathematics at the Georgia Institute of Technology
Georgia Institute of Technology
The Georgia Institute of Technology is a public research university in Atlanta, Georgia, in the United States...
. In 2004, he received a Guggenheim Fellowship
Guggenheim Fellowship
Guggenheim Fellowships are American grants that have been awarded annually since 1925 by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the arts." Each year, the foundation makes...
, for joint work with Xiaochun Li.
External links
- List of mathematical publications on MathSciNet
- Home page at Georgia Tech.