Unexpectedly, it turned out that this year, I gave twice an introductive mini-course on logarithmic Sobolev inequalities, for distinct audiences, at Institut Henri Poincaré, in April, and at École normale supérieure, in December. Here are the short lecture notes : PDF.
There is something fun about it. I like very much to connect logarithmic Sobolev inequalities to the work of Boltzmann. This is not what I have learned, since my teachers Dominique Bakry, Michel Ledoux, and Laurent Saloff-Coste were not particularly versed in or attracted by Physics. Meanwhile, Cédric Villani, who knows very well Boltzmann, is a limited probabilist. Personally, I like very much the Physics of Boltzmann, however, I am not excited and seduced by the technical mathematics that have been constructed around his evolution equation. I have discovered that many of the mathematicians specialists of this equation are not even aware of what is really a Boltzmann-Gibbs measure. All these facts are striking effects of hyperspecialization in science. A somewhat similar phenomenon can be observed for the Schrödinger equation, which has a deep probabilistic and physical content, but which is studied by several high profile mathematicians from the mathematical analysis perspective, with often a very limited culture in probability and even in Physics. All this should be seen as a motivation to give more introductory talks, across fields, to reduce the effects of hyperspecialization! At least this is what I try to do.
In a way culture is the result of curiosity and memorization. A limited culture comes from a limited curiosity and/or memorization. Curiosity is pulsional, it takes time, requires efforts, and implies a sort of intellectual appetite for danger, since it could force to revisit some foundational certainties. Also it is often replaced by a sort of contempt, hiding an intellectual laziness. These mechanisms can operate at various scales and with various intensities, and vary over time.
Even if it can help, culture is neither necessary nor sufficient for being deep and creative, it is something else. Curiosity can be even defocussing, time consuming, and counterproductive in the short-term. This plays into the game of hyperspecialization, which is essentially the result of a sort of short-term utilitarianism, something unconscious which is implicitly encouraged by the selective educational and academic systems.
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