We study scaling limits and conformal invariance of critical site percolation on triangular lattice. We show that some percolation-related quantities are harmonic conformal invariants, and calculate their values in the scaling limit. As a particular case we obtain conformal invariance of the crossing probabilities and Cardy’s formula. Then we prove existence, uniqueness, and conformal invarianc...

This paper studies conformal biharmonic immersions. We first study the transformations of Jacobi operator and the bitension field under conformal change of metrics. We then obtain an invariant equation for a conformal biharmonic immersion of a surface into Euclidean 3-space. As applications, we construct a 2-parameter family of non-minimal conformal biharmonic immersions of cylinder into R and ...

We study the dissipative dynamics of a periodically driven inhomogeneous critical lattice model in one dimension. The closed system starting from pure initial states is well-described by Conformal Field Theory (CFT), which predicts existence both heating and non-heating phases such systems. Heating manifested via emergence black-hole like horizons system. robustness this CFT phenomenology when ...

The standard conformal compactification of Euclidean space is the round sphere. We use conformal geodesics to give an elementary proof that this is the only possible conformal compactification.

The string theory is a fast moving subject, both physics wise and in the respect of mathematics. In order to keep up with the discipline it is important to move with new ideas which are being stressed. Here I wish to give extracts from new papers of ideas which I have recently found interesting. There are six papers which are involved: I ."Strings formulated directly in 4 dimensions " A. N...

A conformal transformation is a diffeomorphism which preserves angles; the differential at each point is the composition of a rotation and a dilation. In its original sense, conformal geometry is the study of those geometric properties preserved under transformations of this type. This subject is deeply intertwined with complex analysis for the simple reason that any holomorphic function f(z) o...

We discuss a numerical implementation of conformal welding for finitely connected regions using the geodesic zipper algorithm and Koebe’s iterative method for computing conformal maps to regions bounded by circles. We also show that a conformal map from a finitely connected region to a region bounded by circles can be written as a composition of finitely many conformal maps of simply connected ...

A bstract The $$ \mathfrak{psu}\left(2,\left.2\right|4\right) psu 2 4 integrable super spin chain underlying the AdS/CFT correspondence has boundary states which describe set-ups where k D3-branes get dissolved in a probe D5...

We study scaling limits and conformal invariance of critical site percolation on triangular lattice. We show that some percolation-related quantities are harmonic conformal invariants, and calculate their values in the scaling limit. As a particular case we obtain conformal invariance of the crossing probabilities and Cardy’s formula. Then we prove existence, uniqueness, and conformal invarianc...