I applied for a tenure track job recently. There were two deadlines mentioned in their advertisement (on mathjobs), one was Oct 1 and the other was Oct 15. I did not notice the Oct 1st one and applied on Oct 15. I never received a call from them, so out of curiosity, I looked at their job ad and found out about the two deadlines. Can I email the hiring committee chair and let them know about this situation and ask whether or not my application is being considered? If so, what would be the appropriate language? I do not want to come across as someone who wants to take advantage of it. I genuinely overlooked the earlier deadline.
You can send an email but I suggest to put effort for searching other positions that are currently open and accept applications, instead of trying to recover the one that probably would lead to dead end. I don't wanna be so pessimistic but you should become used to not hearing back from whatever job that you applied regardless of if your application is strong or weak, or if it is submitted within deadline or not, or it has all the required documentation or not, etc. Unfortunately it's the way it works for pretty much everyone these days inside/outside of academia.