Title: Dualities in algebraic logic

Abstract: Algebraic logic is, in short, the study of logic by universal algebra means. A key tool in the field is provided by categorical dualities that extend Stone's representation theorem for Boolean algebras and provide many interesting links between the worlds of algebra and topology. In the talk I will review a well-known, simple instance of such a duality, in the setting of modal logic. After a gentle introduction of the main constructions, which go back to the seminal work of Jonsson and Tarski, I will discuss some examples showing how concepts on one side of the duality are represented on the other side: subdirect irreducibility and the Vietoris construction.
  Time permitting I will finish the talk by discussing modal duality from the perspective of coalgebra, the general theory of state-based evolving systems.