Related papers: Notes on motivic infinite loop space theory
Lecture notes on selected topics in the theory of gravitation.
Motivated by the analysis and geometry of metric-measure structures in infinite dimensions, we study the category of extended metric-topological spaces, along with many of its distinguished subcategories (such as the one of compact spaces).…
These notes are based on lectures held at the Lanzhou university (China) during a CIMPA summer school in july 2004 but benefit from recent devellopements. Our aim is to explain some perturbations technics that allow to study the long time…
In this paper we introduce the concept of an infinite loop mod $n$ and discuss the properties that these objects have. In particular, we show that a real number $\alpha$ is a counterexample to the $p$-adic Littlewood Conjecture if and only…
We show that the cellular objects in the module category over a motivic E infinity ring spectrum E can be described as the module category over a graded topological spectrum if E is strongly periodizable in our language. A similar statement…
These lecture notes attempt to explain the main ideas of the theory of the quantum Hall effect. The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum Hall effect. The…
These notes accompany a series of three lectures on automorphic loops to be delivered by the author at Workshops Loops '15 (Ohrid, Macedonia, 2015). Automorphic loops are loops in which all inner mappings are automorphisms. The first paper…
Interval Temporal Logic (ITL) is an established temporal formalism for reasoning about time periods. For over 25 years, it has been applied in a number of ways and several ITL variants, axiom systems and tools have been investigated. We…
Formulating a quantum theory of gravity lies at the heart of fundamental theoretical physics. This collection of lecture notes encompasses a selection of topics that were covered in six mini-courses at the Nordita PhD school "Towards…
In this paper we introduce and study motives for rational homotopy types.
In this work we develop a theory of motives for logarithmic schemes over fields in the sense of Fontaine, Illusie, and Kato. Our construction is based on the notion of finite log correspondences, the dividing Nisnevich topology on log…
Motivation and perspective for an exciting new research direction interconnecting logic, spacetime theory, relativity--including such revolutionary areas as black hole physics, relativistic computers, new cosmology--are presented in this…
By directly probing the initial conditions of our universe, cosmological surveys offer us a unique observational handle on quantum field theory in curved spacetime with dynamical gravity and might even allow us to glean information about a…
We abstract and generalize homotopical monadicity statements, placing in a single conceptual framework a range of old and recent recognition and characterization principles in iterated loop space theory in classical, equivariant, and…
This article presents a survey of computability logic: its philosophy and motivations, main concepts and most significant results obtained so far. A continuously updated online version of this article is maintained at…
The modern theory of class field towers has its origins in the study of the p-class field tower over a quadratic imaginary number field, so it is fitting that this problem be the first in the discipline to be nearing a solution. We survey…
We investigate the asymptotically large loop-momentum behavior of multi-loop amplitudes in maximally supersymmetric quantum field theories in four dimensions. We check residue-theorem identities among color-dressed leading singularities in…
We review the main theoretical motivations and observational constraints on Planck scale suppressed violations of Lorentz invariance. After introducing the problems related to the phenomenological study of quantum gravitational effects, we…
The purpose of this paper is twofold. First, we define the new spaces and investigate some topological and structural properties. Also, we compute dual spaces of new spaces which are help us in the characterization of matrix mappings.…
The first part is expository: it explains how finite fields may be used to prove theorems on infinite fields by a reduction mod p process. The second part gives a variant of P.Smith's fixed point theorem which applies in any characteristic.