Leaning forward when you talk reinforces that you want to get closer to her, even if that effect will probably only be subconscious. Like Loading Conviction of online solicitation of a minor is a felony. Many schools have programs that encourage students to have meals with professors as a way to interact outside the classroom. Texting Your Way into Trouble:
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Professor-Student Relationships: What You Need to Know
Go ahead and respond with your interests to see if there is further compatibility. They now live together. Students dating lecturers: Pay attention for clues about her personal life.