Dr. Ahmed earned a PhD in Mathematics at Ohio University. His research is primarily in combinatorial set theory, generally focused on pcf theory and singular cardinal combinatorics. Cardinals are objects which are used to measure the sizes of infinite sets, in the same way that the natural numbers measure the sizes of finite sets. pcf (“possible cofinalities”) theory, originally developed by the Israeli mathematician Shelah in the 1990s, tends to be more effective for comparatively small singular cardinals, since a small singular cardinal can be described as a limit of smaller regular cardinals which are “tightly spaced”, and this is not possible for larger singular cardinals. Mathematicians have tried to overcome this obstacle, and Dr. Ahmed is pushing this program further. Colleagues speak of his seemingly inexhaustible supply of energy and enthusiasm for mathematics.
In the Department of Mathematics at Bar-Ilan, Dr. Ahmed will be working with experts in pcf and the combinatorics of singular cardinals and their successors; he will also benefit from the thriving set theory community in other Israeli universities.
During his time at Ohio University, Dr. Ahmed co-founded a mathematics tutoring lab, helped to found the Association for Women in Mathematics student chapter at Ohio University, and won the Outstanding Graduate teaching associate award.