A Few of My Publications:

• My ph.d. thesis.

• On Some Questions of Erdos and Graham about Egyptian Fractions

• Binary Egyptian Fractions

  (with D. Dobbs, J. Friedlander, A. Hetzel, and F. Pappalardi)

• On Unit Fractions with Denominators in Short Intervals

• On a Coloring Conjecture about Unit Fractions

• On non-Intersecting Arithmetic Progressions

• Unit Fractions and the Class Number of a Cyclotomic Field

  (with A. Granville)

• On the Oscillations of Multiplicative Functions Taking Values +/- 1

• Complexity of Inverting the Euler Function

  (with S. Contini and I. Shparlinski)

• Reciprocal Power Sums Modulo a Prime

• Long Arithmetic Progressions in Critical Sets

• Long Arithmetic Progressions in Sparse Sumsets

  (with I. Ruzsa and T. Schoen) .

• The minimal number of three-term progressions modulo a prime converges to a limit

• On a combinatorial method for counting smooth numbers in sets of integers

• Smooth Numbers in Short Intervals

• On A Combinatorial Method for Developing Lucas Sequence Identities

• On the Decay of the Fourier Transform and Three-Term Arithmetic Progressions

• Running time predictions for factoring algorithms

  (with P. Tetali, A. Granville, and R. Pemantle)

• A New Proof of Roth's Theorem on Arithmetic Progressions (with O. Sisask)

• Open Problems in Additive Combinatorics

  (with Seva Lev)

• Spectral Gaps and Sumsets (with T. Schoen)

• On rich lines in grids (with Evan Borenstein)

• On sums and products in C[x]

  (with D. Hart).

• h-fold sums from a set with few products

  (with D. Hart)

• A probabilistic technique in additive combinatorics

  (with O. Sisask).

• Sum-product inequalities with perturbation.

  (with S. Backman, D. Hart, and M. Hamel).

• On the Structure of Sets with Few Three-Term Arithmetic Progressions

• On a certain generalization of the Balog-Szemeredi-Gowers Theorem (with Evan Borenstein)

• Sharp transitions in making squares

  (with P. Tetali, A. Granville, and R. Pemantle)

• Deterministic methods to find primes (with T. Tao and H. Helfgott -- Polymath4 project).

Work that I am in the process of editing, improving, and generalizing, or is not even yet finished (i.e. the theorems aren't even fully written up) and has not yet appeared or is not scheduled to appear:

• On the Inventory Cycle Offsetting Problem

  (with K. Huang [my student])

• The structure of critical sets for F_p arithmetic progressions

• Arithmetic progressions in sumsets and Lp-almost-periodicity (with I. Laba and O. Sisask).

• Some properties of lower level-sets of convolutions .