Dear WhenHeIsClose,
I was caught looking at porn on my company computer (not to mention company time) when I had a summer job a couple years ago. I was fired immediately, and then I went home and told my wife what happened. I told her about the porn/masturbation habit that I had since I was a teenager, which I had been keeping secret from her for the first few years of marriage.
I am not sure exactly who was the one who walked by my desk and saw what I had on the screen. Was it my boss? Was it a coworker? Was it someone from a different department who happened to walk by? Was it my friend from yeshiva who had helped find the position at that company? Was it a goy? Did everyone in the department there eventually find out why I left, resulting in a huge chillul Hashem? These are some of the questions that floated through my mind (and still do sometimes), but I will probably never find out the answer. But the truth is, what difference does it make?
The company did have a filter (clearly not 100% effective for someone like me), and monitoring software of some sort, but I think they only checked the logs of that stuff if they had a reason to be suspicious. It was not enough to make me not take the risk of porn-hunting, though.
If you are able to get a good filter and monitoring software on your work laptop (we have K9 and Spector Pro on our home laptop, and they work well), go for it! Can your mentor be the one who holds the password and sees the monitoring logs?
Even with that, I would still try to use every tool at my disposal to prevent yourself from getting into the same mess that I got into. It's not pretty, getting fired.
I wish you much hatzlacha, my friend.
TTS