Can a married man have serious feelings for a younger woman and act on it?

Anonymous
A married man who is 30 years older than me has shown me consistent signs of interest (what kind of?) over the past year.
Some of them were harmless: asking me about my personal life, telling stories from his, making jokes, complimenting me, teasing me etc.,
some were a little more on the sensual side: coming very close to me, touching my hands, shoulders and back, asking if I have a boyfriend, checking me out when I look away.
I let it all happen because I never thought that he'd mean it seriously.

Now the situation is that I study under him in my professional field and will be doing so for the upcoming four years at least. Yet he still continues doing these things. By taking me as his student he shows that he takes me seriously, as his time and reputation is too precious to fool around with his students.
He is in a high position and chooses from hundreds of students who want to study under him. He is very professional and serious about his work and I believe that it means a lot to him as a person.
He has shared personal stories with me that he trusts me to keep for myself and has told me that I am near his heart basically. But he always treats me with respect and never makes me feel uncomfortable.
My question is, would a refined, ambitious and competent man like him really risk being seen as overly flirtatious, given the fact that he knows my family, background and we know a lot of the same people in our field?
I just can't imagine him risking his reputation. I could "tell on him" if I wanted to, after all.
Could he have serious feelings for me (I don't care about how naive that might sound)?
Or could he really be a skirt-chaser (which I just can't picture him as, he is quite honest)?

Thanks for your opinions!
Can a married man have serious feelings for a younger woman and act on it?
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