We study a class of flat bundles, of finite rank $N$, which arise naturally from the Donaldson–Thomas theory of a Calabi–Yau threefold $X$ via the notion of a variation of BPS structure. We prove that in a large $N$ limit their flat sections converge to the solutions to certain infinite-dimensional Riemann–Hilbert problems recently found by Bridgeland. In particular this implies an expression for the positive degree, genus 0 Gopakumar–Vafa contribution to the Gromov–Witten partition function of $X$ in terms of solutions to confluent hypergeometric differential equations.

In this paper we establish a close connection between three notions attached to a modular subgroup, namely, the set of weight two meromorphic modular forms, the set of equivariant functions on the upper half-plane commuting with the action of the modular subgroup, and the set of elliptic zeta functions generalizing the Weierstrass zeta functions. In particular, we show that the equivariant functions can be parameterized by modular objects as well as by elliptic objects.

This paper presents a model of a 1D–1D dynamic multi-structure, supporting propagation of a transition wave. It is used to explain the recent phenomenon of the collapse of the San Saba bridge. An analytical model is supplied with illustrative numerical simulations.

We consider the focusing nonlinear Schrödinger equation on the quarter plane. Initial data vanish at infinity while boundary data are time-periodic. The main goal of this paper is to introduce a Riemann–Hilbert problem whose solution gives the solution of our initial–boundary-value problem. This is a preliminary step to obtain uniform long-time asymptotics for the solution of this equation using both the stationary phase and the Deift–Zhou methods.