Paul Gallagher graduated in May 2014 from the University of Pennsylvania with a Bachelors and Masters in Mathematics. His mathematical interests lie in both differential geometry and analysis. Research for this paper was done at SMALL 2013 under the guidance of Frank Morgan. Outside of math, he is an avid singer and pianist. In Fall 2014 he enrolled at MIT in a Ph.D. program in pure mathematics.

Faculty Sponsor: Dr. Frank Morgan, Department of Mathematics and Statistics, Williams College