|XXXVII Workshop on Geometric Methods in Physics||1-7.07.2018|
|VII School on Geometry and Physics||25-29.06.2018|
Functional Analysis techniques in Optimization and Metrization problems
In the context of infinite dimensional Lie groups (and their homogeneous spaces, such as Grassmannians or positive operators) it is not uncommon to find natural optimization problems posed in terms of tangent metrics, or Lagrangians, that are not necessarily Riemannian. Therefore the task of finding and characterizing optimal paths (minimizers of the Lagrangian) must be approached using functional analysis techniques that include -but are not limited to- convex analysis, operator inequalities, and representation theory. In this short course we will give an introduction to this rich subject that intertwines functional analysis, differential geometry and operator theory. We will go through some general tools of the theory and explore relevant examples of the literature.
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