Title: Some Aspects of Krylov Complexity

Abstract: A review of the concept of Krylov Complexity(K- Complexity) will be presented. One feature of K-Complexity is that its definition does not involve a tolerance parameter.

I will describe some general properties of K-Complexity, its behavior when interpolating among various types of systems: free, strongly integrable and chaotic ones. Finally for a certain low dimensional system in a certain state I will describe an explicit derivation of the geometric bulk dual of K complexity.

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