Is my boyfriend's ex-gf a threat to our relationship?

[M]

My boyfriend and I have been dating for 8 months and get along great. We're both 22 years old, and go to the same university. My boyfriend still talks to his ex-gf and they also work together - so they see each other frequently. When the ex gf became aware of our relationship, she started becoming more active on my boyfriend's facebook profile - commenting on EVERY single thing in attempts of ticking me off. My boyfriend tells me he makes an effort to constantly talk about me in front of her so she understands my position in his life, but she has told him that she prefers him not sharing his relationship stories with her. She's extremely jealous of me, and is constantly nagging to him about how he isn't giving her enough attention anymore, and isn't seeing her much either. I trust my boyfriend wholeheartedly, and he has also told me how he doesn't really care to see her as much anymore. My question is, is the ex-gf a threat to my relationship? She's clearly envious but is this something I should be concerned about?