help me to choose the right variant - at univeristy vs. at the university

Hello! I need help with the following sentence. I'm not sure whether I should use a definite article before the word university. Or probably I should use 'my'. Here's the sentence:

What do you think of young teachers? There are some (or we have some) at my university.

I think that the absence of 'the' or 'my' would make little sense in this sentence. I'd use a definite article if I'd already referred to this university before this sentence. And I'd use 'my' if this university were referred to in the text for the first time. I have doubts about the usage of 'my' here because I'm afraid that it will make a reader think that I am the owner of this university.

Thank you for taking the trouble to englighten me on this.

P.S. I'd be very grateful if anyone could also point out the errors I made in this post.