Prof. Lawrence Guth

Professor Guh's research interests are in metric geometry, combinatorial geometry, and harmonic analysis. Metric geometry refers to estimates about lengths, areas, volumes, distances, etc. It includes the study of isoperimetric inequalities and systolic inequalities. He is particularly interested in quantitative geometric estimates that are related to topology. In combinatorial geometry, he is interested in estimates about the intersection patterns of simple shapes like lines and circles. This area includes the Szemeredi-Trotter theorem, and the unit distance problem. In harmonic analysis, Guth is interested in Kakeya-type inequalities about how simple shapes like cylinders can overlap in Euclidean space, and in related estimates in Fourier analysis or PDE.