Executive Summary : | The proposed proposal aims to explore the concept of twisted conjugacy in various types of groups, which originated in Nielsen Reidemeister fixed point theory and has been studied in number theory and representation theory. The first problem is to generalize previous work on the R∞-property of SL_n(R), where R is a ring of S-integers in F_q(t). The second problem is to study the R∞-property of S-arithmetic subgroups of SL_n(F_q(t)), contributing to the problem of classifying lattices in semisimple connected algebraic groups over local fields of positive characteristics. The third problem is to investigate the R∞-property of one-relator groups with center, a crucial class of groups in various mathematical fields. The final project, in collaboration with Prof. Enric Ventura, focuses on algorithmic aspects of the twisted conjugacy problem for Baumslag-Solitar groups, aiming to determine if the conjugacy problem for certain extensions of these groups is solvable. |