Quadratic Chabauty in higher genus

Determining rational points on modular curves is an important problem in arithmetic geometry. While quadratic Chabauty can be an effective p-adic tool for computing rational points on certain modular curves where the rank of the Jacobian equals the genus, many of the underlying computations, such as computing a basis of de Rham cohomology, as well as the local height computations, become computationally prohibitive for higher genus non-split Cartan modular curves. We will discuss joint work in progress with Steffen Mueller and Jan Vonk to study rational points on the genus 8 non-split Cartan modular curve $X_{ns}^+(19)$ with Jacobian rank 8 using quadratic Chabauty.