Topological Complexity of Smooth Random Functions: École d’Été de Probabilités de Saint-Flour XXXIX-2009

The 2007 monograph has been very well received, but does not make for easy reading. The current notes, while not as exhaustive, are much more readable. As such, they provide a comparatively easy entry into a difficult, but important, area of research This is the main contribution of these notes… There are no real competitors to these notes, beyond our 2007 book. Recent reprintings of Adler’s `Geometry of Random Fields’ (1980) by SIAM and Vanmarke’s `Random Fields: Analysis and Synthesis” (1983) are not competitors. Both are terribly out of date. Includes supplementary material: sn.pub/extras