Statement Julian

My mathematical research interests are in number theory and algebraic geometry. My thesis work concerns the arithmetic of a family of rational numbers known as multiple harmonic sums, which are truncated approximations of multiple zeta values. I explore new structures underlying relations involving multiple harmonic sums, p-adic L-values, Bernoulli numbers, and binomial coefficients. This is used to derive a new family of congruences for binomial coefficients, and another family of congruences for padic L-values at positive integers (both involving multiple harmonic sums, and holding modulo arbitrarily large powers of p). I also work on problems with a geometric flavor.