Related papers: Rigid currents in birational geometry
A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…
We study a three-dimensional fluid model describing rapidly rotating convection that takes place in tall columnar structures. The purpose of this model is to investigate the cyclonic and anticyclonic coherent structures. Global existence,…
A flow defined by a nonsingular smooth vector field $X$ on a closed manifold $M$ is said to be parameter rigid if given any real valued smooth function $f$ on $M$, there are a smooth funcion $g$ and a constant $c$ such that $f=X(g)+c$…
Densities of persistent orbital and spin magnetic moment currents of an electron in a cylindrical nanolayer in the presence of external axial magnetic field are considered. For the mentioned current densities analytical expressions are…
Multiparticle collision dynamics (MPCD) is a relatively new algorithm of fluid flow simulations that has been applied mostly to flows around simple objects. One might ask how it behaves in more complex flows. Therefore, we extend MPCD to…
A tight-binding model of electron dynamics in mesoscopic normal rings is studied using boundary conformal field theory. The partition function is calculated in the low energy limit and the persistent current generated as a function of an…
Let $X$ be a compact K\"ahler manifold. We study plurisupported currents on $X$, i.e. closed, positive $(1,1)$-currents which are supported on a pluripolar set. In particular, we are able present a technical generalization of…
Interpreting RG flows as dynamical systems in the space of couplings we produce a variety of constraints, global (topological) as well as local. These constraints, in turn, rule out some of the proposed RG flows and also predict new phases…
We report on recent developments in the dynamics and rigidity of infinite-volume homogeneous spaces, viewed through the lens of circles. By addressing four natural questions about circle packings, we highlight the interplay between…
We study the persistent currents flowing in a mesoscopic ring threaded by a magnetic flux and connected to a stub of finite length. Multistability processes and Coulomb blockade are demonstrated to be present in this system. These…
We propose a minimal model for the emergence of a directed flow in autonomous Hamiltonian systems. It is shown that internal breaking of the spatio-temporal symmetries, via localised initial conditions, that are unbiased with respect to the…
We classify smooth Schubert varieties S_0 in a rational homogeneous manifold S associated to a short root, and show that they are rigid in the sense that any subvariety of S having the same homology class as S_0 is induced by the action of…
Tight triangulated manifolds are generalisations of neighborly triangulations of closed surfaces and are interesting objects in Combinatorial Topology. Tight triangulated manifolds are conjectured to be minimal. Except few, all the known…
We report on some recent progress achieved in [arXiv:2111.14811] on the ergodicity of the frame flow of negatively-curved Riemannian manifolds. We explain the new ideas leading to ergodicity for nearly $0.25$-pinched manifolds and give…
Steady linear gravity waves of small amplitude travelling on a current of constant vorticity are found. For negative vorticity we show the appearance of internal waves and vortices, wherein the particle trajectories are not any more closed…
We prove a new rigidity criterion for families of polarized Calabi-Yau manifolds. Motivated by known non-rigid examples, we conjecture that a family over a quasi-projective curve is rigid if it admits a smooth compactification whose…
We establish global existence and uniqueness of the dynamics of classical electromagnetism with extended, rigid charges and fields which need not to be square integrable. We consider also a modified theory of electromagnetism where no…
We develop a rigidity theory for frameworks in $\mathbb{R}^3$ which have two coincident points but are otherwise generic and only infinitesimal motions which are tangential to a family of cylinders induced by the realisation are considered.…
We present some properties of positive closed currents of type $(1,1)$ on compact non-k\"ahlerian surfaces related to our previous study of these objects started in \cite{ChiTo2}.
Aims: Our aim is to investigate the resistive relaxation of a magnetic loop that contains braided magnetic flux but no net current or helicity. The loop is subject to line-tied boundary conditions. We investigate the dynamical processes…