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

Abstract:  The identity checking problem asks whether an identity holds in a given semigroup. In this talk, we discuss the identity checking problem for diagram monoids, focusing on twisted partition monoids. We present a structural approach based on an embedding of the twisted partition monoid into a larger regular monoid satisfying the same identities. Using this approach, we show that for every n ≥ 5, the identity checking problem in the twisted partition monoid (P_n^\tau) is co-NP-complete.