Abstract: Let G be a simple graph and k a positive integer. Two important graph operations are the k-th graph power of G and the complement graph of G. We explore a permutation between both operations and how it affects the independence number of the resultant graphs.

We will discuss local aspects of Banach space theory arising in finite-dimensional Banach spaces of analytic polynomials. The lecture will focus on how classical constants, such as projection constants, unconditional basis constants, and Gordon-Lewis constants, reflect the geometry of these polynomial spaces. I will explain the main ideas behind recent estimates and indicate how they connect local Banach space theory with complex analysis, probability, and combinatorial methods. The lecture is based on joint works with A. Defant, D. Galicer, M. Mansilla, and S. Muro.

Please see the attached PDF for the abstract.

https://drive.google.com/file/d/1V1smOS2b67Hm6UyL2hMkJRqDLSXhL7BH/view?usp=sharing