The topic of this project is the study of groups from a variety of perspectives: algorithmic, combinatorial, geometric and algebraic. The common thread of this work will be solving equations in groups, and understanding what kind of role the nature of the solutions obtained plays in determining the properties of the groups. We will solve problems in areas that range from fixed point theory in free groups and the Post Correspondence Problem in free groups, to properties of a large class of relatively hyperbolic groups. The topic we suggest and the specific questions are of interest to both mathematicians in group theory, geometry and logic, and to computer scientists. Thus the work we propose will bring many different communities together, and will employ techniques from diverse fields.
Call for proposal
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