Is a wife's engaging in personal conversations with a male colleague at work considered nushuz (rebellion/disobedience), and what is the Islamic legal ruling concerning this? Would the husband be sinful if he divorces her, or would he be considered a dayyuth (one who lacks protective jealousy over his womenfolk) if he reconciles with her without an apology from her?

The wife must obey her husband in refraining from speaking with non-mahram men without necessity, and she is not entitled to violate his jealousy over her. This is among the requirements of a man's guardianship (qawamah). Some jurists have explicitly stated the permissibility of disciplining the wife with a beating if she speaks to a non-mahram man. There is a difference of opinion among jurists regarding desertion outside the home. There is no sin upon the husband if he divorces his wife for these reasons, but we advise reconciliation and holding onto her. If the wife stops speaking with the man, there is no blame in forgiving her, and that is not considered cuckoldry (dayathah). The husband is advised to teach his wife the limits of the Sharia and strengthen her connection with Allah.