Categorical Dualities in Logic and Algebra

This course is an introduction to categorical duality theories between algebra and topology in various mathematical contexts, including Stone Duality between distributive lattice and spectral spaces and between Boolean algebras and Stone spaces, the Stone-Gelfand-Yosida theory on dualising the category of compact Hausdorff spaces, and Pontyagin Duality for Abelian groups. The course provides categorical and algebraic tools and methods of sufficient generality for the study of the mentioned duality theorems in a uniform conceptual framework.

Understanding of the theory of dual concrete adjunctions and its conceptual significance; development of specific detailed expertise on several classical duality theories.