Irregular conformal block, spectral curve and flow equations

Irregular Conformal States and Spectral Curve: Irregular Matrix Model Approach

We present recent developments of irregular conformal conformal states. Irregular vertex operators and their adjoint in a new formalism are used to define the irregular conformal states and their inner product instead of using the colliding limit procedure. Free field formalism can be augmented by screening operators which provide more degrees of freedom. The inner product is conveniently given...

Spectral Factorization of 2-block Toeplitz Matrices and Refinement Equations

Pairs of 2-block Toeplitz (N×N)-matrices (Ts)ij = p2i−j+s−1, s = 0, 1, i, j ∈ {1, . . . , N}, are considered for arbitrary sequences of complex coefficients p0, . . . , pN . A complete spectral resolution of the matrices T0, T1 in the system of their common invariant subspaces is obtained. A criterion of nondegeneracy and of irreducibility of these matrices is derived, and their kernels, root s...

Spectral Methods for Partial Differential Equations in Irregular Domains: The Spectral Smoothed Boundary Method

In this paper, we propose a numerical method to approximate the solution of partial differential equations in irregular domains with no-flux boundary conditions by means of spectral methods. The main features of this method are its capability to deal with domains of arbitrary shape and its easy implementation via Fast Fourier Transform routines. We discuss several examples of practical interest...

Irregular Spectral Asymptotics

Spectral Conformal Parameterization

We present a spectral approach to automatically and efficiently obtain discrete free-boundary conformal parameterizations of triangle mesh patches, without the common artifacts due to positional constraints on vertices and without undue bias introduced by sampling irregularity. High-quality parameterizations are computed through a constrained minimization of a discrete weighted conformal energy...