Related papers: Residue Balancing on Singular Curves

A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full…

We study the relationship between singularities of finite-dimensional integrable systems and singularities of the corresponding spectral curves. For the large class of integrable systems on matrix polynomials, which is a general framework…

We investigate the bounded derived category of coherent sheaves on irreducible singular projective curves of arithmetic genus one. A description of the group of exact auto-equivalences and the set of all t-structures of this category is…

We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…

In this article we discuss the numerical analysis for the finite difference scheme of the one-dimensional nonlinear wave equations with dynamic boundary conditions. From the viewpoint of the discrete variational derivative method we propose…

We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…

We study localization occurring during high speed shear deformations of metals leading to the formation of shear bands. The localization instability results from the competition among Hadamard instability (caused by softening response) and…

This paper provides a direct method of establishing the existence and uniqueness of saddle-node bifurcations for nonlinear equations in general domains. The method employs the scaled extended quotient whose saddle points correspond to the…

We describe experimental investigations of the structure of two-dimensional spherical crystals. The crystals, formed by beads self-assembled on water droplets in oil, serve as model systems for exploring very general theories about the…

This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…

This paper introduces improved numerical techniques for addressing numerical boundary and interface coupling conditions in the context of diffusion equations in cellular biophysics or heat conduction problems in fluid-structure…

Let $E$ be an Anderson $A$-module over $\mathbb{C}_{\infty}$. The period lattice of $E$ is related to its module of special functions by means of a non-canonical isomorphism introduced by the authors in [GM21]. In this paper, we explain how…

The problem of global-in-time regularity for the 3D Navier-Stokes equations, i.e., the question of whether a smooth flow can exhibit spontaneous formation of singularities, is a fundamental open problem in mathematical physics. Due to the…

We describe stability conditions for pairs consisting of a coherent sheaf and a homomorphism to a fixed coherent sheaf on a projective variety. The corresponding moduli spaces are constructed for pairs on curves and surfaces. We consider…

In this paper, we present a control problem related to a semilinear differential equation with a moving singularity, i.e., the singular point depends on a parameter. The particularity of the controllability condition resides in the fact…

This paper addresses the problem of uniqueness in learning physical laws for systems of partial differential equations (PDEs). Contrary to most existing approaches, it considers a framework of structured model learning, where existing,…

This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…

We propose a new numerical approach to compute nonclassical solutions to hyperbolic conservation laws. The class of finite difference schemes presented here is fully conservative and keep nonclassical shock waves as sharp interfaces,…

Robust and semiparametric statistics are of the same historical origin and largely employ the same locally asymptotically normal framework. In our talk, we consider he following more intrinsic connections of both fields: 1) Robust influence…

We develop a valuation-theoretic framework for studying tangent cones of torsion-free sheaves on algebraic varieties. To analyze these objects, we introduce a slope stability theory, including the Harder-Narasimhan filtrations, for finitely…