In its board meeting on June 30, the Austrian Science Fund FWF has approved Erhard Aichinger's grant application "Equations in Universal Algebra". The proposal lists a number of open problems on solving equations in general algebraic structures: the complexity of algorithms to solve equations, the logical connection between different equations, the shape of the solution sets, and a comparison of various concepts of solvability. These questions mainly fall into universal algebra and equational logic, but the answers might also contribute to circuit complexity and theoretical computer science.
The project includes several topics that are suitable for a Master's Thesis. Interested candidates are asked to contact Erhard Aichinger.