Pseudo-Automorphisms of positive entropy on the blowups of products of projective spaces

We use a concise method to construct pseudo-automorphisms f_n of the first dynamical degree d_1(f_n) > 1 on the blowups of the projective n-space for all n > 1 and more generally on the blowups of products of projective spaces. These f_n, for n = 3 have positive entropy, and for n > 3 seem to be the first examples of pseudo-automorphisms with d_1(f_n) > 1 (and of non-product type) on rational varieties of higher dimensions.Comment: Mathematische Annalen (to appear

Geometry and observables in (2+1)-gravity

We review the geometrical properties of vacuum spacetimes in (2+1)-gravity with vanishing cosmological constant. We explain how these spacetimes are characterised as quotients of their universal cover by holonomies. We explain how this description can be used to clarify the geometrical interpretation of the fundamental physical variables of the theory, holonomies and Wilson loops. In particular, we discuss the role of Wilson loop observables as the generators of the two fundamental transformations that change the geometry of (2+1)-spacetimes, grafting and earthquake. We explain how these variables can be determined from realistic measurements by an observer in the spacetime.Comment: Talk given at 2nd School and Workshop on Quantum Gravity and Quantum Geometry (Corfu, September 13-20 2009); 10 pages, 13 eps figure

Non-uniqueness of ergodic measures with full Hausdorff dimension on a Gatzouras-Lalley carpet

In this note, we show that on certain Gatzouras-Lalley carpet, there exist more than one ergodic measures with full Hausdorff dimension. This gives a negative answer to a conjecture of Gatzouras and Peres

Accidental parabolics and relatively hyperbolic groups

By constructing, in the relative case, objects analoguous to Rips and Sela's canonical representatives, we prove that the set of images by morphisms without accidental parabolic, of a finitely presented group in a relatively hyperbolic group, is finite, up to conjugacy.Comment: Revision, 24 pages, 4 figure

Opposing actions of extracellular signal-regulated kinase (ERK) and signal transducer and activator of transcription 3 (STAT3) in regulating microtubule stabilization during cardiac hypertrophy

Excessive proliferation and stabilization of the microtubule (MT) array in cardiac myocytes can accompany pathological cardiac hypertrophy, but the molecular control of these changes remains poorly characterized. In this study, we examined MT stabilization in two independent murine models of heart failure and revealed increases in the levels of post-translationally modified stable MTs, which were closely associated with STAT3 activation. To explore the molecular signaling events contributing to control of the cardiac MT network, we stimulated cardiac myocytes with an a-adrenergic agonist phenylephrine (PE), and observed increased tubulin content without changes in detyrosinated (glutubulin) stable MT’s. In contrast, the hypertrophic interleukin-6 (IL6) family cytokines increased both the glu-tubulin content and glu-MT density. When we examined a role for ERK in regulating cardiac MTs, we showed that the MEK/ERK-inhibitor U0126 increased glu-MT density in either control cardiac myocytes or following exposure to hypertrophic agents. Conversely, expression of an activated MEK1 mutant reduced glu-tubulin levels. Thus, ERK signaling antagonizes stabilization of the cardiac MT array. In contrast, inhibiting either JAK2 with AG490, or STAT3 signaling with Stattic or siRNA knockdown, blocked cytokine-stimulated increases in glu-MT density. Furthermore, the expression of a constitutively active STAT3 mutant triggered increased glu-MT density in the absence of hypertrophic stimulation. Thus, STAT3 activation contributes substantially to cytokine-stimulated glu-MT changes. Taken together, our results highlight the opposing actions of STAT3 and ERK pathways in the regulation of MT changes associated with cardiac myocyte hypertrophy

Algebraic entropy for semi-discrete equations

We extend the definition of algebraic entropy to semi-discrete (difference-differential) equations. Calculating the entropy for a number of integrable and non integrable systems, we show that its vanishing is a characteristic feature of integrability for this type of equations

Geometric Aspects of the Moduli Space of Riemann Surfaces

This is a survey of our recent results on the geometry of moduli spaces and Teichmuller spaces of Riemann surfaces appeared in math.DG/0403068 and math.DG/0409220. We introduce new metrics on the moduli and the Teichmuller spaces of Riemann surfaces with very good properties, study their curvatures and boundary behaviors in great detail. Based on the careful analysis of these new metrics, we have a good understanding of the Kahler-Einstein metric from which we prove that the logarithmic cotangent bundle of the moduli space is stable. Another corolary is a proof of the equivalences of all of the known classical complete metrics to the new metrics, in particular Yau's conjectures in the early 80s on the equivalences of the Kahler-Einstein metric to the Teichmuller and the Bergman metric.Comment: Survey article of our recent results on the subject. Typoes corrrecte

The boundary of chaos for interval mappings

A goal in the study of dynamics on the interval is to understand the transition to positive topological entropy. There is a conjecture from the 1980s that the only route to positive topological entropy is through a cascade of period doubling bifurcations. We prove this conjecture in natural families of smooth interval maps, and use it to study the structure of the boundary of mappings with positive entropy. In particular, we show that in families of mappings with a fixed number of critical points the boundary is locally connected, and for analytic mappings that it is a cellular set

Edge pixel response studies of edgeless silicon sensor technology for pixellated imaging detectors

Silicon sensor technologies with reduced dead area at the sensor's perimeter are under development at a number of institutes. Several fabrication methods for sensors which are sensitive close to the physical edge of the device are under investigation utilising techniques such as active-edges, passivated edges and current-terminating rings. Such technologies offer the goal of a seamlessly tiled detection surface with minimum dead space between the individual modules. In order to quantify the performance of different geometries and different bulk and implant types, characterisation of several sensors fabricated using active-edge technology were performed at the B16 beam line of the Diamond Light Source. The sensors were fabricated by VTT and bump-bonded to Timepix ROICs. They were 100 and 200 μ m thick sensors, with the last pixel-to-edge distance of either 50 or 100 μ m. The sensors were fabricated as either n-on-n or n-on-p type devices. Using 15 keV monochromatic X-rays with a beam spot of 2.5 μ m, the performance at the outer edge and corners pixels of the sensors was evaluated at three bias voltages. The results indicate a significant change in the charge collection properties between the edge and 5th (up to 275 μ m) from edge pixel for the 200 μ m thick n-on-n sensor. The edge pixel performance of the 100 μ m thick n-on-p sensors is affected only for the last two pixels (up to 110 μ m) subject to biasing conditions. Imaging characteristics of all sensor types investigated are stable over time and the non-uniformities can be minimised by flat-field corrections. The results from the synchrotron tests combined with lab measurements are presented along with an explanation of the observed effects