Related papers: On conformally invariant CLE explorations

We study unparametrized conformal circles, or called conformal geodesics, study diffeomorphisms mapping conformal circles to conformal circles in pseudo-Riemannian conformal manifolds. We show that such local diffeomorphisms are conformal…

We present a perturbative method for constructing approximate invariants of motion directly from the equations of discrete-time symplectic systems. This framework offers a natural nonlinear extension of the classic Courant-Snyder (CS)…

This paper describes joint work with Oded Schramm and Wendelin Werner establishing the values of the planar Brownian intersection exponents from which one derives the Hausdorff dimension of certain exceptional sets of planar Brownian…

We consider translation invariant measures on families of nearest-neighbor semi-infinite walks on the integer lattice. We assume that once walks meet, they coalesce. In $2d$, we classify the collective behavior of these walks under mild…

Here we shall consider the topology and dynamics associated to a wide class of matchbox manifolds, including a large selection of tiling spaces and all minimal matchbox manifolds of dimension one. For such spaces we introduce topological…

A new method for the construction of conformally invariant equations in an arbitrary four dimensional (pseudo-) Riemannian space is presented. This method uses the Weyl geometry as a tool and exploits the natural conformal invariance we can…

Conformally invariant functionals on the space of knots are introduced via extrinsic conformal geometry of the knot and integral geometry on the space of spheres. Our functionals are expressed in terms of a complex-valued 2-form which can…

Loop invariants are properties of a program loop that hold before and after each iteration of the loop. They are often employed to verify programs and ensure that algorithms consistently produce correct results during execution.…

We investigate some recursive procedures based on an exact or ``approximate'' Euler scheme with decreasing step in vue to computation of invariant measures of solutions to S.D.E. driven by a L\'evy process. Our results are valid for a large…

Conformal electrodynamics is a particularly interesting example of power Maxwell non-linear electrodynamics, designed to possess conformal symmetry in all dimensions. In this paper, we propose a regularized version of Conformal…

We compute structure constants in N=4 SYM at one loop using Integrability. This requires having full control over the two loop eigenvectors of the dilatation operator for operators of arbitrary size. To achieve this, we develop an algebraic…

We construct new families of conformally invariant differential operators acting on densities. We introduce a simple, direct approach which shows that all such operators arise via this construction when the degree is bounded by the…

Simple semitoric systems were classified about ten years ago in terms of a collection of invariants, essentially given by a convex polygon with some marked points corresponding to focus-focus singularities. Each marked point is endowed with…

Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our…

The problem of quantifying the difference between evolutions of an open quantum system (in particular, between the actual evolution of an open system and the ideal target operation on the corresponding closed system) is important in quantum…

We study Hamiltonian flows in a real separable Hilbert space endowed with a symplectic structure. Measures on the Hilbert space that are invariant with respect to the flows of completely integrable Hamiltonian systems are investigated.…

It is a recent observation that entanglement classification for qubits is closely related to local $SL(2,\CC)$-invariants including the invariance under qubit permutations, which has been termed $SL^*$ invariance. In order to single out the…

We consider the Schramm-Loewner evolution (SLE$_\kappa$) with $\kappa=4$, the critical value of $\kappa > 0$ at or below which SLE$_\kappa$ is a simple curve and above which it is self-intersecting. We show that the range of an SLE$_4$…

We prove that crossing probabilities for the critical planar Ising model with free boundary conditions are conformally invariant in the scaling limit, a phenomenon first investigated numerically by Langlands, Lewis and Saint-Aubin. We do so…

We present a novel framework for deriving integral constraints for correlators on conformal line defects. These constraints emerge from the non-linearly realized ambient-space conformal symmetry. To validate our approach, we examine several…