On the finite blocking property

A planar polygonal billiard $\P$ is said to have the finite blocking property if for every pair $(O,A)$ of points in $\P$ there exists a finite number of ``blocking'' points $B_1, ..., B_n$ such that every billiard trajectory from $O$ to $A$ meets one of the $B_i$'s. Generalizing our construction of a counter-example to a theorem of Hiemer and Snurnikov (see \cite{Mo}), we show that the only regular polygons that have the finite blocking property are the square, the equilateral triangle and the hexagon. Then we extend this result to translation surfaces. We prove that the only Veech surfaces with the finite blocking property are the torus branched coverings. We also provide a local sufficient condition for a translation surface to fail the finite blocking property. This enables us to give a complete classification for the L-shaped surfaces as well as to obtain a density result in the space of translation surfaces in every genus $g\geq 2$.Comment: 24 page

A counter-example to the theorem of Hiemer and Snurnikov

A planar polygonal billiard $\P$ is said to have the finite blocking property if for every pair $(O,A)$ of points in $\P$ there exists a finite number of ``blocking'' points $B_1, ..., B_n$ such that every billiard trajectory from $O$ to $A$ meets one of the $B_i$'s. As a counter-example to a theorem of Hiemer and Snurnikov, we construct a family of rational billiards that lack the finite blocking property.Comment: 5 pages, 3 figure

A necessary condition for lower semicontinuity of line energies

We are interested in some energy functionals concentrated on the discontinuity lines of divergence-free 2D vector fields valued in the circle $\mathbb{S}^1$. This kind of energy has been introduced first by P. Aviles and Y. Giga. They show in particular that, with the cubic cost function $f(t)=t^3$, this energy is lower semicontinuous. In this paper, we construct a counter-example which excludes the lower semicontinuity of line energies for cost functions of the form $t^p$ with $0<p<1$. We also show that, in this case, the viscosity solution corresponding to a certain convex domain is not a minimizer.Comment: 13 page

Spreading huge free software without internet connection, via self-replicating USB keys

We describe and discuss an affordable way to spread huge software without relying on internet connection, via the use of self-replicating live USB keys.Comment: 5 pages, accepted to Extremecom 201

Electroweak Precision Tests

International audienceThis lecture deals with the consistency check of the Standard Model (SM) hypothesis driven by the electroweak precision measurements performed at the Z boson pole (LEP and SLC experiments) and at high energy hadronic machines (Tevatron experiments). Together with the Cabibbo-Kobayashi-Maskawa (CKM) matrix parameters t, the Z-pole observables consistency check is a pillar of the SM. Following A. Korshin's lecture on SM, we will rst describe the free parameters of the SM and introduce the necessity to go beyond the Born approximation. We will hence review the relevant radiative corrections which must be considered as far as the processes at the Z pole are concerned and de ne which observables can be used to constrain the yet unknown parameters of the SM in the gauge sector. Eventually, we will interpret the global quantum consistency check in terms of the top quark and Higgs masses constraint. The comparison of the predicted and measured top quark mass is a tremendous success of the SM. The prediction of the Higgs mass is driving to a large extent the physics case of the LHC machine