Our Sages tell us that we are rewarded for doing theoretical research, for studying subjects that have no practical application.
Rabbi Yom Tov Lipmann Heller (1579-1654)
A Chronicle of Hardship and Hope, p.49
Table of contents
Curriculum Vitae (including links to papers)
Expository papers
Book projects
NSF Focused Research Group at Missouri
My advisor
Collaborators: past and present
Interdisciplinary collaborators
Photographs of my collaborators
Curriculum
Vitae: Includes
links to published papers, accepted papers, submitted papers, and
papers in preparation (mostly
.pdf files).
The published papers are organized by year of publication. Accepted papers are listed in order in which they were accepted. Finally, preprints and papers in preparation are listed in chronological order. At the end of the CV, the papers are also organized by research category.
This page currently contains a set of lecture on the Kakeya problem and related issues, an elementary proof of Fuglede's conjecture relating tiling and exponential bases in the context of lattices, a description of some basic techniques of combinatorial geometry and applications to analysis, an exposition of Roth's theorem on arithmetic progressions of length three, and a proof of Falconer original distance set estimate using the Stein-Tomas restriction theorem.
My book, entitled "A view from the top: analysis, combinatorics and number theory" has appeared in the AMS Student Library Series, volume 39.
Eli Liflyand and I are writing a book on the asymptotics of the Fourier transforms and applications to geometric problems. This project is a few months away from completion.
Julia Garibaldi and I are writing a book on the Erdos distance problem. The book is meant to be accessible to undergradautes and even to advanced high school students. The book will be partly based on the notes we are writing for the high school program on the Erdos distance problem described below. The book is finished and only requires some illustrations to finally get done!
I am writing a research monograph with Derrick Hart on harmonic analysis in vector spaces over finite fields and applications to combinatorics and additive number theory. This book is about three months from completion.
My Ph.D. advisor was Christopher Sogge (sogge@jhu.edu). He is a professor of mathematics at Johns Hopkins University. Chris has been very helpful and supportive over the years, for which I am grateful.My advisor
This
is the list of people I have engaged or am engaged in research projects
with. Some of the projects are still on-going and the list will
hopefully expand! I have recently given up on the idea of keeping the
names in alphabetical order.
Medical physics: J. S. Aldridge
E. E. Fitchard
T. R. Mackie
G. H. Olivera
P. J. Reckwerdt