Singularities of Differentiable Maps

Abstract

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RG fixed points and flows in SQCD with adjoints

“…The names given to the fixed points in (1.2) are motivated by Arnold's [17] ADE classification of singularities, which precisely coincides with the possible relevant deformation superpotentials, listed as A k , D k+2 and E k in (1.2). Our method for obtaining the above superpotentials was based on a detailed analysis of the anomalous dimensions of operators at each of the RG fixed points, and when the associated Landau-Ginzburg superpotentials can be relevant and drive the theory to a new RG fixed point.…”

Exceptional SW geometry from ALE fibrations

“…In these approaches, the curves are given in terms of the appropriate simple singularities W ADE [6], and are generically of the form y 2 = W 2 (x; u j ) − µ 2 , (1.1) with µ = Λ h ∨ , where h ∨ is the dual Coxeter number of G, and Λ is the quantum scale.…”

Uniqueness of thermodynamic projector and kinetic basis of molecular individualism

“…If we assume that the whole picture is hidden insight a multidimensional Fokker-Planck equation for a large molecule in a flow, then we can use this hint in such a way: when the flow strain grows there appears a sequence of bifurcations, and for each of them a new unstable direction arises. For qualitative description of such a picture we can apply a language of normal forms [66], but with some modification.…”

“…If one needs another class of asymptotic, it is possible just to change the choice of the basic peak. All normal forms of the critical form of functions, and families of versal deformations are well investigated and known [66].…”