相关论文: On W-algebras and ODE/IM correspondence

We study eigenvalue problems for the de Rham complex on varying three dimensional domains. Our analysis includes the Helmholtz equation as well as the Maxwell system with mixed boundary conditions and non-constant coefficients. We provide…

As we have shown in the previous work, using the formalism of matrix and eigenvalue models, to a given classical algebraic curve one can associate an infinite family of quantum curves, which are in one-to-one correspondence with singular…

Geometric integration theory can be employed when numerically solving ODEs or PDEs with constraints. In this paper, we present several one-step algorithms of various orders for ODEs on a collection of spheres. To demonstrate the versatility…

We extend the method for constructing symmetry operators of higher order for two-dimensional quantum Hamiltonians by Kalnins, Kress and Miller (2010). This expansion method expresses the integral in a finite power series in terms of lower…

We systematically study inhomogeneous Hamiltonians in two-dimensional conformal field theories within the framework of the AdS/CFT correspondence by relating them to two-dimensional curved backgrounds. We propose a classification of…

We consider Laplacian Growth of self-similar domains in different geometries. Self-similarity determines the analytic structure of the Schwarz function of the moving boundary. The knowledge of this analytic structure allows us to derive the…

For an embedded conformal hypersurface with boundary, we construct critical order local invariants and their canonically associated differential operators. These are obtained holographically in a construction that uses a singular Yamabe…

We consider the 2+1 and 3+1 scalar wave equations reduced via a helical Killing field, respectively referred to as the 2-dimensional and 3-dimensional helically reduced wave equation (HRWE). The HRWE serves as the fundamental model for the…

We present an approach to calculate the optical absorption spectra that combines the quasiparticle self-consistent GW method [Phys. Rev. B, 76 165106 (2007)] for the electronic structure with the solution of the ladder approximation to the…

It has been recently conjectured that the exact eigenfunctions of quantum mirror curves can be obtained by combining their WKB expansion with the open topological string wavefunction. In this paper we give further evidence for this…

We survey recent results in hermitian integral geometry, i.e. integral geometry on complex vector spaces and complex space forms. We study valuations and curvature measures on complex space forms and describe how the global and local…

The ground state of atoms from H to Ar was calculated using a self-interaction correction to local and gradient dependent density functionals. The correction can significantly improve the total energy and makes the orbital energies…

This paper introduces the notion of locally algebraic representations and corresponding sheaves in the context of the cohomology of arithmetic groups. These representations are of relevance for the study of integral structures and special…

We derive a system of TBA equations governing the exact WKB periods in one-dimensional Quantum Mechanics with arbitrary polynomial potentials. These equations provide a generalization of the ODE/IM correspondence, and they can be regarded…

We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted $D^{(2)}_3$ algebra (or the $D^{(2)}_3$ model) with either periodic or integrable open boundary conditions. We obtain the…

We formulate two-dimensional $N=(2,2)$ supersymmetric conformal field theories in terms of unitary full vertex operator superalgebras and develop their cohomology theory. Cohomology rings, Hodge numbers, and the Witten index of a unitary…

We study the massive ODE/IM correspondence for modified $B_2^{(1)}$ affine Toda field equation. Based on the $\psi$-system for the solutions of the associated linear problem, we obtain the Bethe ansatz equations. We also discuss the T-Q…

We develop a numerical method for computing with orthogonal polynomials that are orthogonal on multiple, disjoint intervals for which analytical formulae are currently unknown. Our approach exploits the Fokas--Its--Kitaev Riemann--Hilbert…

We study the umbilic points of Willmore surfaces in codimension 1 from the viewpoint of the conformal Gauss map. We first study the local behaviour of the conformal Gauss map near umbilic curves and prove that they are geodesics up to a…

The eigenvalue problem for second-order ordinary differential equation (SOODE) in a finite interval with the boundary conditions of the first, second and third kind is formulated. A computational scheme of the finite element method (FEM) is…