Past Analytic Topology in Mathematics and Computer Science

1 February 2012
Ramon Jansana

 I will first present Priestley style topological dualities for 
several categories of distributive meet-semilattices
and implicative semilattices developed by G. Bezhanishvili and myself. 
Using these dualities I will introduce a topological duality for Hilbert 
the algebras that correspond to the implicative reduct of intuitionistic logic.

  • Analytic Topology in Mathematics and Computer Science
27 January 2012
Leonardo Cabrer

Dualities of various types have been used by different authors to 
describe free and projective objects in a large
  number of classes of algebras. Particularly, natural dualities provide a 
general tool to describe free objects. In
  this talk we present two interesting applications of this fact. 
  We first provide a combinatorial classification of unification problems 
by their unification type for the
varieties of Bounded Distributive Lattices, Kleene algebras, De Morgan 
algebras. Finally we provide axiomatizations forsingle
and multiple conclusion admissible rules for the varieties of Kleene 
algebras, De Morgan algebras, Stone algebras.

  • Analytic Topology in Mathematics and Computer Science
30 November 2011
Umberto Rivieccio
I will give an overview of some of the most interesting algebraic-lattice theoretical results on bilattices. I will focus in particular on the product construction that is used to represent a subclass of bilattices, the so-called 'interlaced bilattices', mentioning some alternative strategies to prove such a result. If time allows, I will discuss other algebras of logic related to bilattices (e.g., Nelson lattices) and their product representation.
  • Analytic Topology in Mathematics and Computer Science