Related papers: Remarks on Alain Connes' approach to the standard …
The subject of this PhD thesis is noncommutative geometry - more specifically spectral triples - and how it can be generalized to semi-Riemannian manifolds generally, and Lorentzian manifolds in particular. The first half of this thesis…
We review the noncommutative approach to the standard model. We start with the introduction if the mathematical concepts necessary for the definition of noncommutative spaces, and manifold in particular. This defines the framework of…
We generalize the Generic Model Theorem for equivariant presheaves of structures; extending the results of Macintyre and Caicedo. We also introduce a new class of generic cohomologies and show how, for some examples, they simplify to non…
We revisit the theory of normal forms for non-uniformly contracting dynamics. We collect a number of lemmas and reformulations of the standard theory that will be used in other projects.
Concept explanation is a popular approach for examining how human-interpretable concepts impact the predictions of a model. However, most existing methods for concept explanations are tailored to specific models. To address this issue, this…
The present paper is the first in a series devoted to the study of asymptotic geometry of Riemann surfaces and their moduli spaces. We introduce the moduli space of hybrid curves as a new compactification of the moduli space of curves,…
This talk summarizes our recent work establishing an algebraic, model-independent basis for the existence of \B bounds and \B equations for topologically non-trivial solitons and instantons. Our arguments use supersymmetry in an essential…
We investigate the Non-Commutative Abelian Higgs model. We argue that it is possible to introduce a consistent renormalization method by imposing the Non-commutative BRST invariance of the theory and by introducing the Non-Commutative…
A renormalization group transformation suitable for spin glass models and, more generally, for disordered models, is presented. The procedure is non-standard in both the nature of the additional interactions and the coarse graining…
We present a concise review of the status of the Standard Model and of the search for new physics.
The first time that the connection between isometric immersion of surfaces and solutions of the Dirac equation appeared in the literature was in the seminal paper of Thomas Friedrich in 1998. In consequence of that, several authors…
: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the…
We present a concise review of the status of the Standard Model and of the models of new physics.
Very high energy physics needs a coherent description of the four fundamental forces. Non-commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the…
For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…
Various aspects of physics beyond the Standard Model are discussed from the perspective of the fantastic phenomenological success of the Standard Model, its simplicity and predictive power
Remarks on the Obstructedness of Cones Over Curves of Low Genus. Reason for replacement: proof of the main lemma was significantly improved.
We discuss the renormalization properties of noncommutative non-gauge supersymmetric field theories.
We present a new supersymmetric integrable model: the $N=2$ superconformal affine Liouville theory. It interpolates between the $N=2$ super Liouville and $N=2$ super sine-Gordon theories and possesses a Lax representation on the complex…
We investigate the representation of diffeomorphisms in Connes' Spectral Triples formalism. By encoding the metric and spin structure in a moving frame, it is shown on the paradigmatic example of spin semi-Riemannian manifolds that the…