What is she thinking? Can somebody please help explain?

Hey, I'm new here.

I need your help :)

so there is this person that i like, from what i know and from my peers, I think she likes me too. We see each other about 3 to 4 times a week,each last about 2 hours.

We don't talk much to one another. We've never talked about personal stuff, but rather professional related topics. what limits us from do so is the fact that she is older than me. Her position and mine should not be put into context. We are so far apart in terms of that.

Lately, I have not seen her around, since i have switched classes. Surprisingly, and random i see her around in places, where i usually don't see her around e.g library, canteen (on the table where i usually sit) or on the bus at the end of the day. Does she want to see me? is she missing me maybe? i honestly don't know.

This morning i walked passed the library, she hurried out from the library. We almost bump into one another. She had her arms out, as if expecting a hug. I took a step back, knowing that hugging her would get both of us into trouble and maybe spread some gossips (this was near the hallway btw, so there were tons of people around). We stood there fore like a minute and did nothing apart from saying 'good morning' etc. Until i decided to break it off and walked away.

I personally think its not just me. Other friends confirmed that thought too.

I am a student, not underage. It is my first year at Yale. I think it pretty clear already who the person i referred to above is.

Let me know what you think
xx