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The non-linear evolution of one-dimensional perturbations in a three-dimensional expanding Universe is considered. A general Lagrangian scheme is derived, and compared to two previously introduced approximate models. These models are…
The discovery of cosmic acceleration has raised the intriguing possibility that we are witnessing the first breakdown of General Relativity on cosmological scales. In this article I will briefly review current attempts to construct a…
As the full off-shell theories of supergravity in the important dimensions of eleven and ten dimensions are currently unknown, we introduce a superfield formalism as a foundation and experimental laboratory to explore the possibility that…
These are notes to accompany my lectures at the $2024$ "Current Developments in Mathematics" conference hosted by Harvard/MIT. The lectures were about some recent progress in our understanding of two and three dimensional dynamical systems,…
We give a brief overview on the successes and theoretical problems of the Standard Model and discuss the basics of low-scale supersymmetry. We also address some of recent proposals for physics beyond the Standard Model and the connection to…
We give an overview of the possibility of GLAST to explore theories beyond the Standard Model of particle physics. Among the wide taxonomy we will focus in particular on low scale supersymmetry and theories with extra space-time dimensions.…
I discuss the recent work done in collaboration with Chris Hill, Jing Wang and Hsin-Chia Cheng. We construct four-dimensional renormalizable gauge theories which, in their infrared limit, generate the dynamics of gauge interactions in flat…
The presence of compact extra dimensions in cosmological scenarios in the context of f(T)-like gravities is discussed. For the case of toroidal compactifications, the analysis is performed in an arbitrary number of extra dimensions.…
Extra spatial dimensions are proposed by recent theories that postulate the scale of gravity to be of the same order as the electroweak scale. A sizeable interaction between gravitons and Standard Model particles is then predicted. Effects…
Efforts have been made recently to reformulate traditional Kaluza-Klein theory by using a generalized definition of a higher-dimensional extended space-time. Both electromagnetism and gravity have been studied in this context. We review…
This paper is extended and broadly generalized version of earlier published rapid communication, Phys.Rev.E, Vol.58, R 5213 (1998). It also elaborates on some problems which were left unsolved or just mentioned in Physics Reports Vol.298,…
As Physics did in previous centuries, there is currently a common dream of extracting generic laws of nature in economics, sociology, neuroscience, by focalising the description of phenomena to a minimal set of variables and parameters,…
We introduce two abstract constructions for building new measurable dynamical systems from existing ones and study their ergodic properties. The first of these constructions, a "reciprocal transformation," produces a type of non-singular…
This dissertation investigates three main topics, all of which dealing with alternative, higher-order gravity theories in four dimensions. Firstly, we study the variational and conformal structure of those theories. Next, we analyse their…
Existing discourse formalisms use different taxonomies of discourse relations, which require expert knowledge to understand, posing a challenge for annotation and automatic classification. We show that discourse relations can be effectively…
The introduction of extra space dimensions in the theory could be an elegant way tovsolve the hierarchy problem. There could even be one energy scale at which all interactions could unify. The limits coming from our knowledge of the…
We give a pedagogical introduction to the dynamics of N=2 supersymmetric systems in four dimensions. The topic ranges from the Lagrangian and the Seiberg-Witten solutions of SU(2) gauge theories to Argyres-Douglas CFTs and Gaiotto…
These are the (somewhat extended) lecture notes for four lectures delivered at the spring school during the thematic programme "Mathematical Perspectives of Gravitation beyond the Vacuum Regime" at ESI Vienna in February 2022.
Beginning from a discussion of the known most fundamental dynamical structures of the Standard Model of physics, extended into the realms of mathematics and theory by the concept of "supersymmetry" or "SUSY," an introduction to efforts to…
In these notes, based on a talk given at the Rencontres de Moriond, I give a simple introduction to the tremendous progress that has been made during the last few years towards the understanding of strong-coupling phenomena in quantum gauge…