The short answer here is that chat suspensions are global (there are some other chat servers, but your suspension is on the one where both Mathematics and Ask Ubuntu chatrooms reside).
When one is suspended on the site of one's chat "parent user" (your chat parent user is your Mathematics account), one is suspended in chat also.
It is unclear why your chat suspension is so long, while your site suspension is only for another 5 days. I have not been able to find out exactly what happened. I will updateI will update this if I do. But Catija's answer has addressed this if I do.
After some investigation and discussion, I did not find any grounds for such a long suspension.
After your suspension on the Math Stack Exchange ends, I would suggest that the chat suspension should also be ended.
By the way, as a suggestion, when trying to resolve a conflict, I recommend doing your best to present a clear picture (with, like, links and stuff if needed) of the situation without judgements; this will in general be more effective, as you avoid the risk of people feeling attacked, which often leads to further escalation.