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
links to papers)
NSF Focused Research Group at Missouri
Collaborators: past and present
Photographs of my collaborators
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 (firstname.lastname@example.org). He is a professor of
mathematics at Johns Hopkins University. Chris has been very
helpful and supportive over the years, for which I am
- Collaborators: past
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!
Medical physics: J. S. Aldridge