Hans Parshall

Hans Parshall

I am a Zassenhaus Assistant Professor in the Department of Mathematics at The Ohio State University. Recently, I defended my PhD under the supervision of Neil Lyall and Ákos Magyar at the University of Georgia. Years ago, I earned my BA in my hometown of Arcata, CA at Humboldt State University.

My research background is in the field of additive combinatorics, which brings together combinatorial number theory, harmonic analysis, and ergodic theory. I have several results in the area of density Ramsey theory, where the typical problem concerns what "structure" must appear in all "large" sets. Much of my work has involved applications of Fourier analysis (and its generalizations) to problems in number theory and combinatorics.

Some of my current projects apply combinatorial and computational techniques to study optimal packings of points. These have correlated with a growing interest in frame theory and mathematical data science.