Conformal geometry has deep roots in pure mathematics. It is the intersection of complex analysis, Riemann surface theory, algebraic geometry, differential geometry and algebraic topology. Computational conformal geometry plays an important role in digital geometry processing. Recently, theory of discrete conformal geometry and algorithms of computational conformal geometry have been developed....

In a short review of recent work, we discuss the general problem of constructing the actions of new conformal field theories from old conformal field theories. Such a construction follows when the old conformal field theory admits new conformal stress tensors in its chiral algebra, and it turns out that the new conformal field theory is generically a new spin-two gauge theory. As an example we ...

Vector fields whose flow preserves a symplectic form up to a constant, such as simple mechanical systems with friction, are called “conformal”. We develop a reduction theory for symmetric conformal Hamiltonian systems, analogous to symplectic reduction theory. This entire theory extends naturally to Poisson systems: given a symmetric conformal Poisson vector field, we show that it induces two r...

This work concerns in part the construction of conformal Jordan cells of infinite rank and their reductions to conformal Jordan cells of finite rank. It is also discussed how a procedure similar to Lie algebra contractions may reduce a conformal Jordan cell of finite rank to one of lower rank. A conformal Jordan cell of rank one corresponds to a primary field. This offers a picture in which any...

We present a comprehensive discussion of tree-level holographic $4$-point functions scalar operators in momentum space. show that each individual Witten diagram satisfies the conformal Ward identities on its own and is thus valid correlator. When $\beta = \Delta - d/2$ are half-integral, with $\Delta$ dimensions $d$ spacetime dimension, diagrams can be evaluated closed form we explicit formulae...

The notion of conformal algebra appears as an algebraical language describing singular part of operator product expansion (OPE) in conformal field theory [BPZ]. Explicit algebraical exposition of this theory leads to the notion of vertex (chiral) algebra (see, e.g., [B], [DL], [FLM]). Roughly speaking, conformal algebras correspond to vertex algebras by the same way as Lie algebras correspond t...

In this paper, we shall classify “quadratic” conformal superalgebras by certain compatible pairs of a Lie superalgebra and a Novikov superalgebra. Four general constructions of such pairs are given. Moreover, we shall classify such pairs related to simple Novikov algebras.

this research discusses the process of designing a conceptual model for a new information system, i.e. electronic document management system. the new system is designed for an educational institute (itvhe) whose managers are the research population. the research methodology is based on structured analysis and design methodology (ssadm). in the end, the new system proposed using a data flow diag...

We explore the conformal geometric structures of a pair of second-order partial-differential equations. In particular, we investigate the conditions under which this geometry is conformal to the vacuum Einstein equations of general relativity. Furthermore, we introduce a new version of the conformal Einstein equations, which are used in the analysis of the conformal geometry of the PDE’s.