Book projects

I am currently in the process of writing four books, listed in the order of likely completion:

Number theoretic consequences of analytic inequalities

This book is intended to describe the often subtle connections between classical inequalities in harmonic analysis and number theoretic problems.

Projected completion date: Spring 2007

A capstone course in undergraduate mathematics

This book is intended to bring together several different areas of undergraduate mathematics and give a student a glimpse of techniques and ideas of research mathematics. This project was originally sparked by and continued to be inspired by a series of conversations I had over the years with a former student, Shannon Reed.

Projected completion date: End of October/beginning of November 2006.

Erdos distance problem, with Julia Garibaldi

In this book we give a simple and thorough exposition of the known results pertaining to the Erdos distance problem in geometric combinatorics. The book is suitable for undergraduates and even advanced high school students.

Projected completion date: End of October 2006.

Geometric methods in harmonic analysis, with Eli Liflyand

In this book we study harmonic analysis problems that have a non-trivial higher dimensional geometric flavor. Particular emphasis is placed on the method of stationary phase and related problems.

Projected completion date: End of 2006.

Orthogonal bases, tiling and the Fuglede conjecture
, with Mihalis Kolountzakis

In this book we describe the past and current developments pertaining to the Fuglede conjecture which links the existence orthogonal bases and tiling properties of sets.

Projected completion date: unclear