Abstract
A major period in the development of homological algebra is marked by the use of derived and triangulated categories. Though initially categories of this type were only used as a formal tool to ensure the correct domains of definition for various derived functors, motivated by Gelfand-Manin's book and pioneering work of Kashiwara, Mukai, Neeman, Bondal, Orlov and others, in the last thirty years their status has grown to that of fundamental objects in their own right. In concrete settings, triangulated categories are known to carry deep algebraic and geometric information, and have been used to solve classical problems in algebraic geometry, ring theory and representation theory. Recently Genovese, Lowen and Van den Bergh developed a new method to study triangulated categories with t-structures using so-called derived injectives. This was in particular used to develop the deformation theory of such triangulated categories and tackle the illustrious "curvature problem". In this project we discuss a number of related problems about triangulated categories with t-structures which may also be approached through the category of derived injectives.
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