Woensdag 23 april 2008

Spreker: Bas Spitters (Radboud Universiteit)

Titel: The point of pointless topology

Tijd: 11:00 - 12:00

Plaats: HG00.062

Vanaf kwart voor 11 is er koffie en thee in de binnenstraat (voor de zaal).

Abstract

Traditionally, a topological space is defined as a set of points together with a certain distributive lattice of subsets. It turns out that most of the theory can be developed using the lattice only. Logically, this may be seen as a move from models to theories or as the move from individual choice sequences to spreads in intuitionism. In this way, avoiding points allows us to eliminate the axiom of choice from many proofs. This is crucial in our recent work where we apply topos theory to the foundations of quantum theory, but also connected to the implementation of the algebraic closure of a field in MAGMA, the use of modal logic in security and localization in algebraic geometry.

This lecture will be student-friendly as it assumes only very basic knowledge of topology and lattice theory.