Polynomial dynamic and lattice orbits in S-arithmetic homogeneous spaces

Consider an homogeneous space under a locally compact group G and a lattice in G. Then the lattice naturally acts on the homogeneous space. Looking at a dense orbit, one may wonder how to describe its repartition. One then adopt a dynamical point of view and compare the asymptotic distribution of points in the orbits with the natural measure on the space. In the setting of Lie groups and their homogeneous spaces, several results showed an equidistribution of points in the orbits using Ratner's rigidity of polynomial dynamics in homogeneous spaces. We address here this problem in the setting of p-adic and S-arithmetic groups

On SL(3,C\mathbb C)-representations of the Whitehead link group

We describe a family of representations in SL(3,$\mathbb C$) of the fundamental group $\pi$ of the Whitehead link complement. These representations are obtained by considering pairs of regular order three elements in SL(3,$\mathbb C$) and can be seen as factorising through a quotient of $\pi$ defined by a certain exceptional Dehn surgery on the Whitehead link. Our main result is that these representations form an algebraic component of the SL(3,$\mathbb C$)-character variety of $\pi$.Comment: 20 pages, 3 figures, 4 tables, and a companion Sage notebook (see the references) v2: A few corrections and improvement

Dimension of character varieties for 33-manifolds

Let $M$ be a $3$-manifold, compact with boundary and $\Gamma$ its fundamental group. Consider a complex reductive algebraic group G. The character variety $X(\Gamma,G)$ is the GIT quotient $\mathrm{Hom}(\Gamma,G)//G$ of the space of morphisms $\Gamma\to G$ by the natural action by conjugation of $G$. In the case $G=\mathrm{SL}(2,\mathbb C)$ this space has been thoroughly studied. Following work of Thurston, as presented by Culler-Shalen, we give a lower bound for the dimension of irreducible components of $X(\Gamma,G)$ in terms of the Euler characteristic $\chi(M)$ of $M$, the number $t$ of torus boundary components of $M$, the dimension $d$ and the rank $r$ of $G$. Indeed, under mild assumptions on an irreducible component $X_0$ of $X(\Gamma,G)$, we prove the inequality $$\mathrm{dim}(X_0)\geq t \cdot r - d\chi(M).$$Comment: 12 pages, 1 figur

Some Preliminary Evidence on the Globalization-Inflation Nexus.

This paper aims at evaluating the impact of globalization, if any, on inflation and the inflation process. We estimate standard Phillips curve equations on a panel of OECD countries over the last 25 years. We first show that the impact of commodity import price inflation on CPI inflation depends on the volume of commodity imports while the impact of non-commodity import price inflation is independent of the volume of non-commodity imports. Second, focusing on the role of intra-industry trade, we provide preliminary evidence that this variable can account (i) for the low pass-through of import price to consumer price and (ii) for the flattening of the Phillips curve, i.e. the lower sensitivity of inflation to the output gap.Inflation ; Globalization ; Phillips curve ; Intra-industry trade ; Contestability ; Import prices.

Some preliminary evidence on the globalization-inflation nexus

The aim of this paper is to evaluate the impact of globalization, if any, on inflation and the inflation process. We estimate standard Phillips curve equations on a panel of OECD countries over the last 25 years. While recent papers have concluded that globalization has had no significant impact, this paper highlights that trying to capture globalization effects through simple measures of import prices and/or imports to GDP ratios can be misleading. To do so, we try to extend the analysis following two different avenues. We first separate between commodity and non-commodity imports and show that the impact on inflation of commodity import price inflation is qualitatively different from the impact of noncommodity import price inflation, the former depending on the volume of commodity imports while the latter being independent of the volume of non-commodity imports.> ; This first piece of evidence highlights the role of contestability and the insufficiency of trade volume statistics to properly describe the impact of globalization. This leads us to adopt a more systematic approach to capture the contents and not only the volume of trade. Focusing on the role of intra-industry trade, we provide preliminary evidence that this variable can account (i) for the low pass-through of import price to consumer price and (ii) for the flattening of the Phillips curve, i.e. the lower sensitivity of inflation to changes in output gap. We hence conclude that different facets of globalization, especially changes in the nature of goods traded, can be an important channel through which globalization affects the inflation process.Globalization ; Inflation (Finance) ; Time-series analysis ; International trade