Chicken McNuggets used to come in 9 and 20 packs. It turns out that for any N greater than 151, you can find a way to buy exactly N McNuggets using 9 and 20 packs, but one can't buy exactly 151 McNuggets in this way. What if we generalized 9 and 20 to a set of integers n_1,n_2, ... ,n_k instead, and asked for the numbers that can be achieved as positive integer combinations of them? Questions like this have rich answers that surprisingly lie at the confluence of fourier analysis, algebraic combinatorics, and numerical semigroups.

Biography: Mohamed Omar is an associate professor of mathematics at Harvey Mudd College and Joseph B. Platt Chair. His research focuses on discrete math with a particular interest in applications of linear and nonlinear algebra in the field. He came to Harvey Mudd after a postdoctoral fellowship at Caltech, a PhD at the University of California at Davis, and undergrad and Master's degrees at the University of Waterloo.