Research

Our Sages tell us that we are rewarded for doing theoretical research, for studying subjects that have no practical application.

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.

Medical physics: J. S. Aldridge

E. E. Fitchard

T. R. Mackie

G. H. Olivera

P. J. Reckwerdt

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

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!

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

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

Medical physics:

E. E. Fitchard

T. R. Mackie

G. H. Olivera

P. J. Reckwerdt