Over the last five years, my research has been funded, in decreasing order of financial commitment, by Columbia University; the National Science Foundation; the Sloan Foundation; and the Mathematical Sciences Research Institute. I am grateful for their financial and in-kind support. Any views expressed in my research or on these web pages are mine, and may or may not reflect the views of these sponsors.

I have received no money from consulting or other business dealings. Beyond serving as a referee for papers submitted to peer-reviewed mathematics journals I have not served as a consultant for any outside organization on a pro bono basis.

Robert Lipshitz

Last updated: January 1, 2011.