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In this paper we analyse convergence of projected fixed-point iteration on a Riemannian manifold of matrices with fixed rank. As a retraction method we use `projector splitting scheme'. We prove that the projector splitting scheme converges…

We study the problem of super-resolving a superposition of point sources from noisy low-pass data with a cut-off frequency f. Solving a tractable convex program is shown to locate the elements of the support with high precision as long as…

This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…

In this paper, using the Bregman distance, we introduce a new projection-type algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points. Then the strong convergence of the sequence…

We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…

We construct a monotone quantity for the classical obstacle problem with non-smooth obstacle, and show that the blow-ups are homogeneous functions of degree $\alpha<2$.

The scattering of waves by obstacles in a 2D setting is considered, in particular the computation of the scattered field via the collocation or the least-squares methods. In the case of multiple scattering by smooth obstacles, we prove that…

For the contact of two finite portions of interacting rigid crystalline surfaces, we compute the dependence of the pinning energy barrier on the misfit angle and contact area. The resulting data are used to investigate the distribution of…

We present an extended version of an invited talk given on the International Conference "Turbulent Mixing and Beyond". The dynamical and statistical description of stably stratified turbulent boundary layers with the important example of…

We consider an oscillatory obstacle problem where the coincidence set and free boundary are also highly oscillatory. We establish a rate of convergence for a regularized notion of free boundary to the free boundary of a corresponding…

Given a smooth curve on a smooth surface, the Hilbert scheme of the surface is stratified according to the length of the intersection with the curve. The strata are highly singular. We show that this stratification admits a natural…

This paper is concerned with the uniqueness in inverse acoustic scattering problems with the modulus of the far-field patterns co-produced by the obstacle (resp. medium) and the point sources. Based on the superposition of point sources as…

In the 1980's Serre asked how many points of bounded height can lie in a thin set. This has motivated significant research ever since, culminating in a series of recent breakthroughs. It is a good time to take stock of the central questions…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

We consider quantum light-matter interfaces comprised of multiple layers of two-dimensional atomic arrays, whose lattice spacings exceed the wavelength of light. While the coupling of light to a single layer of such a ``superwavelength"…

A balanced sampling design should always be the adopted strategies if auxiliary information is available. Besides, integrating a stratified structure of the population in the sampling process can considerably reduce the variance of the…

Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…

The problem of covering random points in a plane with sets of a given shape has several practical applications in communications and operations research. One especially prominent application is the coverage of randomly-located points of…

In this paper, we study the complexity of the chip-firing reachability problem. We show that for Eulerian digraphs, the reachability problem can be decided in strongly polynomial time, even if the digraph has multiple edges. We also show a…

We construct invariants for any closed semipositive symplectic manifold which count rational curves satisfying tangency constraints to a local divisor. More generally, we introduce invariants involving multibranched local tangency…