I work on number theory and novel connections and applications from number theory to algebraic geometry, Euclidean lattices, coding theory, and other areas of mathematics. One major area of interest is K3 surfaces of large Picard number and their applications to various questions mostly in Diophantine and algebraic geometry. Applications include explicit formulas for Shimura … Continued
My recent research deals with billiards in rational polygons. The elementary questions posed in this area are connected to many branches of modern mathematics. More broadly, we can motivate the problem as follows: Some natural phenomena are “chaotic” (i.e. unpredictable). These are often studied by statistical methods. Others are “integrable” (i.e. predictable and regular). Other … Continued
Number theory is the study of whole numbers, and ratios of whole numbers (called rational numbers). In particular, number theorists since antiquity have been interested in finding whole number and rational number solutions to equations, such as y2 = x3 + 22 – i.e., can a square be exactly 22 more than a cube? The … Continued