Related papers: Balancing conditions in global tropical geometry
We prove that every connected component of an intersection of tropical hypersurfaces contains a point of their stable intersection unless their stable intersection is empty. This is done by studying algebraic hypersurfaces that tropicalize…
Motivated by the power of subregion/subregion duality for constraining the bulk geometry in gauge/gravity duality, we pursue a comprehensive and systematic approach to the behavior of extremal surfaces under perturbations. Specifically, we…
We prove that solutions to linear wave equations in a subextremal Kerr-de Sitter spacetime have asymptotic expansions in quasinormal modes up to a decay order given by the normally hyperbolic trapping, extending the existing results. The…
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
We give a survey of joint work with Mircea Musta\c{t}\u{a} and Chenyang Xu on the connections between the geometry of Berkovich spaces over the field of Laurent series and the birational geometry of one-parameter degenerations of smooth…
Birkhoff normal forms are commonly used in order to ensure the so called "effective stability" in the neighborhood of elliptic equilibrium points for Hamiltonian systems. From a theoretical point of view, this means that the eventual…
For classical discrete systems with constant composition (typically referred to substitutional alloys) under thermodynamically equilibrium state, macroscopic structure should in principle depend on temperature and many-body interaction…
We express the reduction types of Picard curves in terms of tropical invariants associated to binary quintics. We also give a general framework for tropical invariants associated to group actions on arbitrary varieties. The problem of…
An unconstrained optimization problem is formulated in terms of tropical mathematics to minimize a functional that is defined on a vector set by a matrix and calculated through multiplicative conjugate transposition. For some particular…
We discuss the geometric formulation of continuum defects consisting of dislocations and disclinations. After reviewing the metric affine geometry and the present geometric formulation of dislocation and disclination written in terms of…
We explore the idea that non-equilibrium steady states breaking detailed balance are obtained by deforming trajectories (lines in space-time) that have been sampled in a reference system with stochastic dynamics obeying detailed balance,…
Numerical simulations of the evolution of a global topological defect field have two characteristic length scales --- one macrophysical, of order the field correlation length, and the other microphysical, of order the field width. The…
The goal of this paper is to make a connection between tropical geometry, representations of quantum affine algebras, and scattering amplitudes in physics. The connection allows us to study important and difficult questions in these areas:…
In the Batalin-Vilkovisky formalism, gauge conditions are expressed as Lagrangian submanifolds in the space of fields and antifields. We discuss a way of patching together gauge conditions over different parts of the space of fields, and…
We develop the mechanics of combined bending and twisting deformation of a one-dimensional filamentous structure with protruding stiff fish-scale-like plates embedded at an angle on the surface. We develop Cosserat kinematic formulation…
The atmospheric circulation models are deduced from the very complex atmospheric circulation models based on the actual background and meteorological data. The models are able to show features of atmospheric circulation and are easy to be…
I provide a brief summary of the status of supersymmetric models with parameters defined at either the unification or weak scale, based on global fits using the GAMBIT framework.
We analyze geometrical structures necessary to represent bulk and surface interactions of standard and substructural nature in complex bodies. Our attention is mainly focused on the influence of diffuse interfaces on sharp discontinuity…
We consider a finite system of hard spheres that collide inelastically according to a particular model, losing a fixed amount of kinetic energy at each collision. We develop the theory of the Transport-Collision-Transport (TCT) dynamics,…
A minimal, analytically manageable Galerkin type model for convection in binary mixtures subject to realistic boundary conditions is presented. The model elucidates and reproduces the typical bifurcation topology of extended stationary and…