Energy cost of an electronic hole determined ---------------------------------------------------------------------------------------------------------------------------------------- How much energy does it take to make a hole in an electron gas, or in other words, to withdraw a few quantum particles from a huge collection? An international collaboration has found the answer. There is nothing trivial about the question, which underpins a host of calculations frequently used by specialists in condensed matter physics and astrophysics. And although it seems straightforward, solving this problem required sophisticated mathematical tools. In fact, until recently, only approximate calculations could provide a very partial solution. Now, theorists will be able to make use of a more accurate estimation of the energy cost required. Moreover, the result involves a quantity that appears in certain approximations used in many areas of physics. This should rekindle scientists’ interest in these approximations. Physical Review Letters April 2011 Geometrical intuition is universal An international research team compared the elementary geometry skills (intuitive understanding of parallelism and the infinite nature of a straight line; ability to complete a triangle) of Mundurucu Indians, an Amazon tribe whose language contains very little geometry Images of straight lines obtained by birational transformations (elements of the Cremona group). vocabulary, with those of populations who learned geometry at school. It turns out that all humans above 6 or 7 years of age are Hundred-year-old conjecture innate or acquired when young children become aware of space.endowed with geometrical intuition. This is an ability that is either invalidated Proceedings of the National Academy of Sciences May 2011 Mathematics is a long-term discipline. Two researchers have just invalidated a conjecture put forward in 1894 concerning the Cremona group. This is an abstract object that describes the symmetries associated with a certain family of curve. It turns out that in the case of plane curves, the Cremona group is far more organized and hierarchical than predicted. This opens promising new avenues for further exploration of the mathematical jungle. Eliminating chaos by adding randomness Annals of Mathematics July 2011 Two mathematicians have shown that by tossing a coin to choose the mathematical transformation applied to a particular system (known as Arnold’s cat map), the result obtained no longer exhibits any signs of chaos, which is not the case when the transformation applied is always the same. As if—in a conterintuitive way—adding a dose of randomness to the question simplified the answer. Annals of Mathematics September 2011 Two French mathematicians win 2011 Clay Research Award Yves Benoist (left), CNRS senior researcher at the Paris-based Orsay Mathematics Laboratory, and Jean-François Quint, CNRS researcher at the Laboratory of Analysis, Geometry and Applications in Villetaneuse (Paris) were awarded the prestigious 2011 Clay Research Award for their joint work on ‘stationary measures and orbit closures for actions of non-abelian groups on homogeneous spaces’, at the interface of geometry, dynamic systems and probabilities. They add their names to the list of six French researchers who have already received this prestigious internationalaccolade, which rewards ‘major breakthroughs in mathematical research’. 25 2011 A year at CNRS
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