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In this thesis we study two-dimensional conformal field theories with Virasoro algebra symmetry, following the conformal bootstrap approach. Under the assumption that degenerate fields exist, we provide an extension of the analytic…
We investigate the conformal and superconformal properties of a non-relativistic spinning particle propagating in a curved background coupled to a magnetic field and with a scalar potential. We derive the conditions on the couplings for a…
In this article we study the long-time behaviour of a system of nonlinear Partial Differential Equations (PDEs) modelling the motion of incompressible, isothermal and conducting modified bipolar fluids in presence of magnetic field. We…
We consider the asymptotic solutions of an interface problem corresponding to an elliptic partial differential equation with Dirich- let boundary condition and transmission condition, subject to the small geometric perturbation and the high…
Period doubling H\'enon renormalization of strongly dissipative maps is generalized in arbitrary finite dimension. In particular, a small perturbation of toy model maps with dominated splitting has invariant $C^r$ surfaces embedded in…
A nontrivial conformally invariant model is obtained via generalization the method of obtaining conformally invariant models in $2D$ Euclidean space to the Euclidean space with dimension $D>2$. This method was previously developed by E.S.…
The cusp anomalous dimension is a ubiquitous quantity in four-dimensional gauge theories, ranging from QCD to maximally supersymmetric N=4 Yang-Mills theory, and it is one of the best investigated observables in the AdS/CFT correspondence.…
We study the geometric and topological properties of strange non-chaotic attractors created in non-smooth saddle-node bifurcations of quasiperiodically forced interval maps. By interpreting the attractors as limit objects of the iterates of…
We construct polynomial conformal invariants, the vanishing of which is necessary and sufficient for an $n$-dimensional suitably generic (pseudo-)Riemannian manifold to be conformal to an Einstein manifold. We also construct invariants…
The paper is part of an attempt of understanding non-K\"ahler threefolds. We start by looking at compact complex non-K\"ahler threefolds with algebraic dimension two and admitting locally conformally K\"ahler metrics. Under certain…
Using examples we test formulae previously conjectured to give the fractal information dimension of chaotic repellors and their stable and unstable manifolds in ``typical'' dynamical systems in terms of the Lyapunov exponents and the…
We study Nevai's condition from the theory of orthogonal polynomials on the real line. We prove that a large class of measures with unbounded Jacobi parameters satisfies Nevai's condition locally uniformly on the support of the measure away…
We study quadratic skew-products with parameters driven over piecewise expanding and Markov interval maps with countable many inverse branches, a generalization of the class of maps introduced by Viana. In particular we construct a class of…
We study orientifold projections of families of four-dimensional $\mathcal{N}=1$ toric quiver gauge theories. We restrict to quivers that have the unusual property of being associated with multiple periodic planar diagrams which give rise,…
This article is a short review of the recent results on properties of nonlinear fractional maps which are maps with power- or asymptotically power-law memory. These maps demonstrate the new type of attractors - cascade of bifurcations type…
We offer a measure-theoretic extension of the concept and theory of $k$-contraction, including their generalization on fractional dimensions $d$. The respective contraction property is defined through the exponential decay of the…
We analyze the dynamics of the flow generated by a nonlinear parabolic problem when some reaction and potential terms are concentrated in a neighborhood of the boundary. We assume that this neighborhood shrinks to the boundary as a…
In analogy with the lower Assouad dimensions of a set, we study the lower Assouad dimensions of a measure. As with the upper Assouad dimensions, the lower Assouad dimensions of a measure provide information about the extreme local behaviour…
In this paper, we first prove an abstract theorem on the existence of polynomial attractors and the concrete estimate of their attractive velocity for infinite-dimensional dynamical systems, then apply this theorem to a class of wave…
We refine the multifractal formalism for the local dimension of a Gibbs measure $\mu$ supported on the attractor $\Lambda$ of a conformal iterated functions system on the real line. Namely, for given $\alpha\in \mathbb{R}$, we establish the…