Related papers: Lectures on the linearized Kapustin-Witten equatio…
We give explicit realizations of irreducible representations of the Yangian of the general linear Lie algebra and of its twisted analogues, corresponding to symplectic and orthogonal Lie algebras. In particular, we develop the fusion…
The subject of this paper is the consecutive procedure of discretization and quantization of two similar classical integrable systems in three-dimensional space-time: the standard three-wave equations and less known modified three-wave…
This course is intended as an introduction to the analysis of elliptic partial differential equations. The objective is to provide a large overview of the different aspects of elliptic partial differential equations and their modern…
An algebraic Riccati equation for linear operators is studied, which arises in systems theory. For the case that all involved operators are unbounded, the existence of infinitely many selfadjoint solutions is shown. To this end, invariant…
We prove new results regarding the existence, uniqueness, (eventual) boundedness, (total) stability and attractivity of the solutions of a class of initial-boundary-value problems characterized by a quasi-linear third order equation which…
This is an exposition of some recent developments related to the object in the title, particularly the combinatorial computation of the (genus 0) Gromov-Witten invariants of the flag manifold and the quadratic algebra approach. The notes…
We investigate existence and uniqueness of solutions to a class of fractional parabolic equations satisfying prescribed pointwise conditions at infinity (in space), which can be time- dependent. Moreover, we study the asymptotic behaviour…
We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in C^n. Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries…
For a large class of time-dependent non-Hermitain Hamiltonians expressed in terms linear and bilinear combinations of the generators for an Euclidean Lie-algebra respecting different types of PT-symmetries, we find explicit solutions to the…
This work is devoted to the study of the nonlinear second-order neutral difference equations with quasi-differences of the form $$ \Delta \left( r_{n} \Delta \left( x_{n}+q_{n}x_{n-\tau}\right)\right)= a_{n}f(x_{n-\sigma})+b_n%, \ n\geq n_0…
We study solutions to the Kapustin--Witten equations on ALE and ALF gravitational instantons. On any such space and for any compact structure group, we prove asymptotic estimates for the Higgs field. We then use it to prove a vanishing…
In this paper we study quasilinear elliptic Kirchhoff equations driven by a non-homogeneous operator with unbalanced growth and right-hand sides that consist of sub-linear, possibly singular, and super-linear reaction terms. Under very…
Some elementary considerations are presented concerning Catenoids and their stability, separable minimal hypersurfaces, minimal surfaces obtainable by rotating shapes, determinantal varieties, minimal tori in S3, the minimality in Rnk of…
The Einstein-Maxwell equations on a smooth compact 4-manifold are reformulated as a purely Riemannian variational problem analogous to Calabi's variational problem for extremal Kahler metrics. Next, Seiberg-Witten theory is used to show…
The classical analysis of Kazakov and Kostov of the Makeenko-Migdal loop equation in two-dimensional gauge theory leads to usual partial differential equations with respect to the areas of windows formed by the loop. We extend this…
We discuss different cases of dissipative Hamiltonian differential-algebraic equations and the linear algebraic systems that arise in their linearization or discretization. For each case we give examples from practical applications. An…
The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately…
There are studied in details 5-dimensional pseudo-Riemannian manifolds equipped with the structure analogous to the almost cosymplectic (almost coKaehler) structure. The curvature by assumption commutes with the structure affinor and all…
This paper will discuss a class of semilinear partial differential equations induced by studying the limiting behaviour of Hermitian Yang-Mills metrics. We will study the radial symmetry of the $C^{2}$ global solution of this equation in…
This thesis investigates two problems that are discrete analogues of two harmonic analytic problems which lie in the heart of research in the field. More specifically, we consider discrete analogues of the maximal Kakeya operator conjecture…