Related papers: Superstability and Symmetry
We study the relation (and differences) between stability and Property (S) in the simple and stably finite framework. This leads us to characterize stable elements in terms of its support, and study these concepts from different sides :…
The s-confining theories are a class of supersymmetric gauge theories with infrared dynamics which are well-understood. Perturbing such theories can give rise to dynamical supersymmetry breaking. We realize simple models of dynamical…
Obtaining realistic supersymmetry preserving vacua in the minimal renormalizable supersymmetric $Spin(10)$ GUT model introduces considerations of the non-trivial topology of the vacuum manifold. The $D$-parity of low energy unification…
We present a new, scalable alternative to the structured singular value, which we call $\nu$, provide a convex upper bound, study their properties and compare them to $\ell_1$ robust control. The analysis relies on a novel result on the…
Using an infinitary version of the Hypergraph Removal Lemma due to Towsner, we prove a model-theoretic higher amalgamation result. In particular, we obtain an independent amalgamation property which holds in structures which are measurable…
We review the origin of soft supersymmetry-breaking terms in N=1 supergravity models of particle physics. We first consider general formulae for those terms in general models with a hidden sector breaking supersymmetry at an intermediate…
It has been suggested by Groot Nibbelink and Pospelov that Lorentz invariance can be an emergent symmetry of low-energy physics provided the theory enjoys a non-relativistic version of supersymmetry. We construct a model that realizes the…
This work proposes a mathematical approach that (re)defines a property of Machine Learning models named stability and determines sufficient conditions to validate it. Machine Learning models are represented as functions, and the…
Dynamical supersymmetry breaking is considered in models which admit descriptions in terms of electric, confined, or magnetic degrees of freedom in various limits. In this way, a variety of seemingly different theories which break…
We introduce some notions of invariant elementary definability which extend the notions of first-order order-invariant definability, and, more generally, definability invariant with respect to arbitrary numerical relations. In particular,…
In this set of four lectures I will discuss some aspects of the Standard Model (SM) as a quantum field theory and related phenomenological observations which have played a crucial role in establishing the $SU(2)_{L} \times U(1)_{Y}$ gauge…
In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is…
Two dynamical models that have been proposed to describe transitions between low and high confinement states (L-H transitions) in confined plasmas are analysed using singularity theory and stability theory. It is shown that the…
We discuss supersymmetry breaking mechanism at the level of low energy N=1 effective superstring actions that exhibit $SL(2,Z)_T$ target space modular duality or $SL(2,Z)_S$ strong-weak coupling duality. The allowed superpotential forms use…
The physics of supersymmetry is reviewed from the perspective of physics at ever increasing energies. Starting from the minimal supersymmetric extension of the Standard Model at the electroweak scale, we proceed to higher energies seeking…
We consider a five-dimensional supergravity model with SU(5) gauge symmetry and the minimal field content. Studying the arising scalar potential we find that the gauging of the $U(1)_R$ symmetry of the five-dimensional supergravity causes…
We classify the constraints on a stationary point of the potential invariant under a finite group into intrinsic and extrinsic based on whether they are independent of the coefficients in the potential or not. We find that the symmetry…
We prove a new kind of stabilisation result, "secondary homological stability", for the homology of mapping class groups of orientable surfaces with one boundary component. These results are obtained by constructing CW approximations to the…
We use algorithmic methods from online learning to explore some important objects at the intersection of model theory and combinatorics, and find natural ways that algorithmic methods can detect and explain (and improve our understanding…
Standard Model may be defined with the additional discrete symmetry, i.e. with the gauge group $SU(3)\times SU(2) \times U(1)/{\cal Z}$ (${\cal Z} = Z_6$, $Z_3$ or $Z_2$) instead of the usual $SU(3)\times SU(2) \times U(1)$. It has the same…