Compactifications configurations and cohomology : conference on compactifications configurations and cohomology : october 22 24 2021 : Northeastern University Boston Massachusetts This volume contains the proceedings of the Conference on Compactifications Configurations and Cohomology held from October 22–24 2021 at Northeastern University Boston MA. Some of the most active and fruitful mathematical research occurs at the interface of algebraic geometry representation theory and topology. Noteworthy examples include the study of compactifications in three specific settings algebraic group actions configuration spaces and hyperplane arrangements. These three types of compactifications enjoy common structural features including relations to root systems combinatorial descriptions of cohomology rings the appearance of iterated blow ups the geometry of normal crossing divisors and connections to mirror symmetry in physics. On the other hand these compactifications are often studied independently of one another. The articles focus on new and existing connections between the aforementioned three types of compactifications thereby setting the stage for further research. It draws on the discipline specific expertise of all contributors and at the same time gives a unified self contained reference for compactifications and related constructions in different contexts.