We present a new package Theta. jl for computing the Riemann theta function. It is
implemented in Julia and offers accurate numerical evaluation of theta functions with …

We approach the Torelli problem of reconstructing a curve from its Jacobian from a
computational point of view. Following Dubrovin, we design machinery to solve this problem …

The solutions to the Kadomtsev–Petviashvili equation that arise from a fixed complex
algebraic curve are parametrized by a threefold in a weighted projective space, which we …

We give an algebraic method to compute the fourth power of the quotient of any even theta
constants associated with a given non-hyperelliptic curve in terms of geometry of the curve …

We study various naturally defined subvarieties of the moduli space ${\mathcal A} _g $ of
complex principally polarized abelian varieties (ppav) in a neighborhood of the locus of …

This dissertation consists of two parts. The first part pertains to the Schottky problem, which
asks to characterize Jacobians of curves amongst abelian varieties. This has a complete …