Related papers: Defects and boundary RG flows in $\mathbb{C}/\math…
We survey the recent progress in defining open enumerative theories for Landau-Ginzburg models. We illustrate the ideas required to develop these new foundations. In particular, we describe how to define the open enumerative invariants as…
We study the two-dimensional rotating shallow-water model describing Earth's oceanic layers. It is formally analogue to a Schr\"odinger equation where the tools from topological insulators are relevant. Once regularized at small scale by an…
In this paper we survey the recent developments of the Ricci flows on complete noncompact K\"{a}hler manifolds and their applications in geometry.
We propose a family of differential models for B-type open-closed topological Landau-Ginzburg theories defined by a pair $(X,W)$, where $X$ is any non-compact Calabi-Yau manifold and $W$ is any holomorphic complex-valued function defined on…
In the context of topological insulators, the shallow-water model was recently shown to exhibit an anomalous bulk-edge correspondence. For the model with a boundary, the parameter space involves both longitudinal momentum and boundary…
Conformal defects describe the universal behaviors of a conformal field theory (CFT) in the presence of a boundary or more general impurities. The coupled critical system is characterized by new conformal anomalies which are analogous to,…
The problem of pattern selection in absolutely unstable open flow systems is investigated by considering the example of Rayleigh-B\'{e}nard convection. The spatiotemporal structure of convection rolls propagating downstream in an externally…
The bulk-edge correspondence (BEC) refers to a one-to-one relation between the bulk and edge properties ubiquitous in topologically nontrivial systems. Depending on the setup, BEC manifests in different forms and govern the spectral and…
In this paper we prove local existence of a Ricci de Turck flow starting at a space with incomplete edge singularities and flowing for a short time within a class of incomplete edge manifolds. We derive regularity properties for the…
In this work, using the method by He, we prove a short time existence for Ricci flow on a complete noncompact Riemannian manifold with the following properties: (i) there is $r_0>0$ such that the volume of any geodesic balls of radius $r\le…
We establish the background for the study of geodesics on noncompact polygonal surfaces. For illustration, we study the recurrence of geodesics on $Z$-periodic polygonal surfaces. We prove, in particular, that almost all geodesics on a…
We present a new generalized topological current in terms of the order parameter field $\vec \phi$ to describe the topological defect system in O(n) symmetric time-dependent Ginzburg-Landau model. With the aid of the $% \phi$-mapping…
Guided by the many-particle quantum theory of interacting systems, we develop a uniform classification scheme for topological phases of disordered gapped free fermions, encompassing all symmetry classes of the Tenfold Way. We apply this…
We consider natural conformal invariants arising from the Gauss-Bonnet formulas on manifolds with boundary, and study conformal deformation problems associated to them. The key technique we used is to derive boundary C^2 estimates directly…
We construct defects describing the transition between different phases of gauged linear sigma models with higher rank abelian gauge groups, as well as defects embedding these phases into the GLSMs. Our construction refers entirely to the…
We study certain relevant boundary perturbations of Liouville theory and discuss implications of our results for the brane dynamics in noncritical string theories. Our results include (i) There exist monodromies in the parameter $\mu_{\rm…
We consider the gauge transformations of a metric $G$-bundle over a compact Riemannian surface with boundary. By employing the heat flow method, the local existence and the long time existence of generalized solution are proved.
We study anomalies of discrete internal global symmetry $G$ in two-dimensional rational conformal field theories based on twisted torus partition functions. The anomaly of $G$ can be seen from the noncommutativity of two symmetry lines…
We consider an elliptic-parabolic free boundary problem that models the fluid flow through a partially saturated porous medium. The free boundary arises as the interface separating the saturated and unsaturated regions. Our main goal is to…
We describe the dynamical behavior found in numerical solutions of the Vector Complex Ginzburg-Landau equation in parameter values where plane waves are stable. Topological defects in the system are responsible for a rich behavior. At low…