AbstractGeometric inequalities reveal relation between different geometric quantities, such as volume, surface area, width, diameter, etc. By the correspondences between convexity and positivity, such as mixed volumes of convex bodies and intersection numbers of divisors, we present a series of new geometric inequalities inspired by positivity results from algebraic and analytic geometry.Speake...
摘 要:Rapidly oscillating functions associated with Lagrangian submanifolds play a fundamental role in semiclassical analysis. In this talk I will describe how to associate classes of semiclassical oscillating functions to isotropic submanifolds of phase space, and show that these classes are invariant under the action of Fourier integral operators (modulo the usual clean intersection conditio...