Related papers: Pad\'e\ approximants on Riemann surfaces and KP ta…

We prove a characterization for the Peetre type $K$-functional on $\mathbb{M}$, a compact two-point homogeneous space, in terms the rate of approximation of a family of multipliers operator defined to this purpose. This extends the well…

We study spectral properties of second order elliptic operators with periodic coefficients in dimension two. These operators act in periodic simply-connected waveguides, with either Dirichlet, or Neumann, or the third boundary condition.…

We study minimal surfaces in generic sub-Riemannian manifolds with sub-Riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called {\it horizontal} area functional associated to the canonical…

We describe boundedness and compactness properties for the operators obtained by the Weyl-Pedersen calculus in the case of the irreducible unitary representations of nilpotent Lie groups that are associated with flat coadjoint orbits. We…

We prove a "quantified" version of the Weyl-von Neumann theorem, more precisely, we estimate the ranks of approximants to compact operators appearing in the Voiculescu's theorem applied to commutative algebras. This allows considerable…

In the gauge theory approach to the geometric Langlands program, ramification can be described in terms of ``surface operators,'' which are supported on two-dimensional surfaces somewhat as Wilson or 't Hooft operators are supported on…

We study finite dimensional vector spaces over fields of elliptic functions equipped with two commuting aotomorphisms \sigma and \tau induced by isogenies of relatively prime orders. We give a structure theorem for such objects, that…

We extend the idea of approximating piecewise smooth univariate functions using rational approximation introduced in \cite{aka_bas-19a} to two-dimensional space. This article aims to implement the novel piecewise Maehly based…

This text presents some basic notions in symplectic geometry, Poisson geometry, Hamiltonian systems, Lie algebras and Lie groups actions on symplectic or Poisson manifolds, momentum maps and their use for the reduction of Hamiltonian…

Based on the mathematically well defined Pad\'e Theory, a theoretically safe new procedure for the extraction of the pole mass and width of a resonance is proposed. In particular, thanks to the Montessus de Ballore theorem we are able to…

We identify the Kontsevich-Penner matrix integral, for finite size $n$, with the isomonodromic tau function of a $3\times 3$ rational connection on the Riemann sphere with $n$ Fuchsian singularities placed in correspondence with the…

We present a new approach for matching regular surfaces in a Riemannian setting. We use a Sobolev type metric on deformation vector fields which form the tangent bundle to the space of surfaces. In this article we compare our approach with…

Finding appropriate notions of discrete holomorphic maps and, more generally, conformal immersions of discrete Riemann surfaces into 3-space is an important problem of discrete differential geometry and computer visualization. We propose an…

This is a survey of our recent results on the geometry of moduli spaces and Teichmuller spaces of Riemann surfaces appeared in math.DG/0403068 and math.DG/0409220. We introduce new metrics on the moduli and the Teichmuller spaces of Riemann…

We study theta functions of a Riemann surface of genus g from the view point of tau function of a hierarchy of soliton equations. We study two kinds of series expansions. One is the Taylor expansion at any point of the theta divisor. We…

We introduce suitable coordinate systems for pipes and their variants that allow us to transform partial differential equations (PDEs) on the pipe surfaces or in the solid pipes into computational domains with fixed limits/ranges. Such a…

We study discrete period matrices associated with graphs cellularly embedded on closed surfaces, resembling classical period matrices of Riemann surfaces. Defined via integrals of discrete harmonic 1-forms, these period matrices are known…

It is well-known that the algebra of vector fields on the circle acts on the space of Riemann surfaces with a marked point and a local parameter at this point. We show that this action has a natural realization in the soliton theory, indeed…

We show that the Kontsevich integral on $n\times n$ matrices ($n< \infty$) is the isomonodromic tau function associated to a $2\times 2$ Riemann--Hilbert problem. The approach allows us to gain control of the analysis of the convergence as…

This paper develops a discrete theory of real Riemann surfaces based on quadrilateral cellular decompositions (quad-graphs) and a linear discretization of the Cauchy-Riemann equations. We construct a discrete analogue of an antiholomorphic…