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.

Expository papers

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.

Book projects

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 advisor
My Ph.D. advisor was Christopher Sogge ( 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.

Collaborators: past and present
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!

Georgiy Arutuynyants
Mike Bennett
Luca Brandolini
Laura DeCarli
Jeremy Chapman
Leonardo Colzani
Burak Erdogan
Suresh Eswarathasan
Michael Gage
Dan Geba
Giaccomo Gigante
Loukas Grafakos
Allan Greenleaf
Derrick Hart
Steve Hofmann
Philippe Jaming
Hadi Jorati
Kimberly Kinateder
Doowon Koh
Mihalis Kolountzakis
Izabella Laba
Guozhen Lu
Mate Matolci
Judy Miller
Mihalis Mourgoglou
Nets Katz
Jonathan Pakianathan
Eyvindur Palsson
Steen Pedersen
Oliver Roche-Newton
Misha Rudnev
Eric Sawyer
Andreas Seeger
Steven Senger
Igor Shparlinski
Josef Solymosi
Terrance Tao
Krystal Taylor
Vladimir Ten
Giancarlo Travaglini
Ignacio Uriarte-Tuero
M. Xiong
Daniel Weidinger

Interdisciplinary collaborators

Medical physics:
J. S. Aldridge
E. E. Fitchard
T. R. Mackie
G. H. Olivera
P. J. Reckwerdt