Annelies Gerber: 

"Mathematical models for propositional proof systems and complexity"

Abstract: One of the intentions of this research is to examine how
propositional proof systems can be mathematically characterised.
Some known mathematical structures may already implicitly contain
proofs of particular proof systems.

Mathematical Models need to contain the minimal information
necessary to reconstruct a proof. This is linked to the
computational complexity of the corresponding proof and the
related decision problems. Using mostly notions from Euclidean
geometry we give some examples and results for particular
resolution strategies.