Related papers: Renormalization of circle diffeomorphisms with a b…
We analyze isomonodromic deformations of rational connections on the Riemann sphere with Fuchsian and irregular singularities. The Fuchsian singularities are allowed to be of arbitrary resonant index; the irregular singularities are also…
In this paper, we address a classical case of the Calder\'on (or conductivity) inverse problem in dimension two. We aim to recover the location and the shape of a single cavity $\omega$ (with boundary $\gamma$) contained in a domain…
We analyze a real one-parameter family of quasiconformal deformations of a hyperbolic rational map known as {\em spinning}. We show that under fairly general hypotheses, the limit of spinning either exists and is unique, or else converges…
We compute instanton corrections to correlators in the genus-zero topological subsector of a (0,2) supersymmetric gauged linear sigma model with target space P1xP1, whose left-moving fermions couple to a deformation of the tangent bundle.…
A systematic treatment of O(a)-improvement in lattice theories with static quarks is presented. The Schr\"odinger functional is discussed and a renormalization condition for the static axial current in the SF-scheme is introduced. Its…
In this paper we study R-reversible area-preserving maps f on a two-dimensional Riemannian closed manifold M, i.e. diffeomorphisms f such that Ro f=f^{-1}o R where R is an isometric involution on M. We obtain a C1-residual subset where any…
Four-fermi models in dimensionality $2<d<4$ exhibit an ultra-violet stable renormalization group fixed point at a strong value of the coupling constant where chiral symmetry is spontaneously broken. The resulting field theory describes…
In this paper, we prove that any group of diffeomorphisms acting on the 2-sphere and properly extending the conformal group of M\"obius transformations must be at least 4-transitive or, more precisely, arc 4-transitive. In addition, we show…
The scaling properties of quantum gravity are discussed by employing a class of proper-time regulators in the functional flow equation for the conformal factor within the formalism of the background field method. Renormalization group…
We prove a variant of the Chance-McDuff conjecture for pseudo-rotations: under certain additional conditions, a closed symplectic manifold which admits a Hamiltonian pseudo-rotation must have deformed quantum product and, in particular,…
Using a multivariable Faa di Bruno formula we give conditions on transformations $\tau:[0,1]^m\to\mathcal{X}$ where $\mathcal{X}$ is a closed and bounded subset of $\mathbb{R}^d$ such that $f\circ\tau$ is of bounded variation in the sense…
The quadratically divergent scalar mass is subtractively renormalized unlike other divergences which are multiplicatively renormalized. We re-examine some technical aspects of the subtractive renormalization, in particular, the mass…
A modified generally covariant Yang-Mills action, which depends on the complex structure of spacetime and not its metric, is proved to be renormalizable. This proof makes this Lagrangian model the unique known generally covariant four…
The renormalized trajectory (RT) is determined from two different Monte Carlo renormalization group techniques with $\delta$-function block spin transformation in the multi-dimensional coupling parameter space of the two-dimensional…
We establish the optimal regularity of solutions to the Neumann problem for the fractional Laplacian, $(-\Delta)^s u=h$ in $\Omega$, with the external condition $\mathcal N^s u=0$ in $\Omega^c$. For this, a key point is to establish a 1D…
We consider the problem to reconstruct a wave speed $c \in C^\infty(M)$ in a domain $M \subset \R^n$ from acoustic boundary measurements modelled by the hyperbolic Dirichlet-to-Neumann map $\Lambda$. We introduce a reconstruction formula…
We study a germ of real analytic $n$-dimensional submanifold of ${\mathbf C}^n$ that has a complex tangent space of maximal dimension at a CR singularity. Under the condition that its complexification admits the maximum number of deck…
We provide a rigorous construction of generalized spin--boson models with commuting transition matrices and form factors exhibiting critical ultraviolet (UV) divergences. That is, we cover all divergences where a self-energy…
We use geometric arguments to prove explicit bounds on the mean oscillation for two important rearrangements on $\mathbb{R}^n$. For the decreasing rearrangement $f^*$ of a rearrangeable function $f$ of bounded mean oscillation (BMO) on…
We give conditions that characterize the existence of an absolutely continuous invariant probability measure for a degree one $C^2$ endomorphism of the circle which is bimodal, such that all its periodic orbits are repelling, and such that…