Translation Invariant States on Twisted Algebras on a Lattice

We construct an algebra with twisted commutation relations and equip it with the shift. For appropriate irregularity of the non-local commutation relations we prove that the tracial state is the only translation-invariant state

Nonlinear PDEs with modulated dispersion II: Korteweg--de Vries equation

We continue the study of various nonlinear PDEs under the effect of a time--inhomogeneous and irregular modulation of the dispersive term. In this paper we consider the modulated versions of the 1d periodic or non-periodic Korteweg--de Vries (KdV) equation and of the modified KdV equation. For that we use a deterministic notion of "irregularity" for the modulation and obtain local and global results similar to those valid without modulation. In some cases the irregularity of the modulation improves the well-posedness theory of the equations. Our approach is based on estimates for the regularising effect of the modulated dispersion on the non-linear term using the theory of controlled paths and estimates stemming from Young's theory of integration.Comment: 37 page

On the notion of conductor in the local geometric Langlands correspondence

Under the local Langlands correspondence, the conductor of an irreducible representation of \Gl_n(F) is greater than the Swan conductor of the corresponding Galois representation. In this paper, we establish the geometric analogue of this statement by showing that the conductor of a categorical representation of the loop group is greater than the irregularity of the corresponding meromorphic connection.Comment: Minor report following referees report. To appear in Canadian Journal of Mat

A weak local irregularity property in S^\nu spaces

Although it has been shown that, from the prevalence point of view, the elements of the S^ \nu spaces are almost surely multifractal, we show here that they also almost surely satisfy a weak uniform irregularity property

Nonlinear PDEs with modulated dispersion I: Nonlinear Schr\"odinger equations

We start a study of various nonlinear PDEs under the effect of a modulation in time of the dispersive term. In particular in this paper we consider the modulated non-linear Schr\"odinger equation (NLS) in dimension 1 and 2 and the derivative NLS in dimension 1. We introduce a deterministic notion of "irregularity" for the modulation and obtain local and global results similar to those valid without modulation. In some situations, we show how the irregularity of the modulation improves the well--posedness theory of the equations. We develop two different approaches to the analysis of the effects of the modulation. A first approach is based on novel estimates for the regularising effect of the modulated dispersion on the non-linear term using the theory of controlled paths. A second approach is an extension of a Strichartz estimated first obtained by Debussche and Tsutsumi in the case of the Brownian modulation for the quintic NLS.Comment: 27 pages. Extensive reorganisation of the material and typos correcte

Localisation and linguistic anomalies

Interactive systems may seek to accommodate users whose first language is not English. Usually, this entails a focus on translation and related features of localisation. While such motivation is worthy, the results are often less than ideal. In raising awareness of the shortcomings of localisation, we hope to improve the prospects for successful second-language support. To this end, the present paper describes three varieties of linguistic irregularity that we have encountered in localised systems and suggests that these anomalies are direct results of localisation. This underlines the need for better end-user guidance in managing local language resources and supports our view that complementary local resources may hold the key to second language user support

Internal kinematics of spiral galaxies in distant clusters IV. Gas kinematics of spiral galaxies in intermediate redshift clusters and in the field

(Abridged) We trace the interaction processes of galaxies at intermediate redshift by measuring the irregularity of their ionized gas kinematics, and investigate these irregularities as a function of the environment (cluster versus field) and of morphological type (spiral versus irregular). Our sample consists of 92 distant galaxies. 16 cluster (z~0.3 and z~0.5) and 29 field galaxies (mean z=0.44) of these have velocity fields with sufficient signal to be analyzed. We find that the fraction of galaxies that have irregular gas kinematics is remarkably similar in galaxy clusters and in the field at intermediate redshifts. The distribution of the field and cluster galaxies in (ir)regularity parameters space is also similar. On the other hand galaxies with small central concentration of light, that we see in the field sample, are absent in the cluster sample. We find that field galaxies at intermediate redshifts have more irregular velocity fields as well as more clumpy and less centrally concentrated light distributions than their local counterparts. Comparison with a SINS sample of 11 z ~ 2 galaxies shows that these distant galaxies have more irregular gas kinematics than our intermediate redshift cluster and field sample. We do not find a dependence of the irregularities in gas kinematics on morphological type. We find that two different indicators of star formation correlate with irregularity in the gas kinematics. More irregular gas kinematics, also more clumpy and less centrally concentrated light distributions of spiral field galaxies at intermediate redshifts in comparison to their local counterparts indicate that these galaxies are probably still in the process of building their disks via mechanisms such as accretion and mergers. On the other hand, they have less irregular gas kinematics compared to galaxies at z ~ 2.Comment: Accepted for publication in A&A, high resolution version available at http://www.astro.rug.nl/~kutdemir/13262/13262_hr.p

Firewall or smooth horizon?

Recently, Almheiri, Marolf, Polchinski, and Sully found that for a sufficiently old black hole (BH), the set of assumptions known as the \emph{complementarity postulates} appears to be inconsistent with the assumption of local regularity at the horizon. They concluded that the horizon of an old BH is likely to be the locus of local irregularity, a "firewall". Here I point out that if one adopts a different assumption, namely that semiclassical physics holds throughout its anticipated domain of validity, then no inconsistency seems to arise, and the horizon retains its regularity. In this alternative view-point, the vast portion of the original BH information remains trapped inside the BH throughout the semiclassical domain of evaporation, and possibly leaks out later on. This appears to be an inevitable outcome of semiclassical gravity.Comment: A slightly different version (with small modifications, mostly semantic, and some updated references) was published in Gen. Relativ. Gravi