I asked for a graduate student position from a professor. He replied "welcome". What does that mean?
I'd be a bit wary of working with this person if this is really them and is really their communication style.

20 minutes is plenty of time to determine a student is not a fit and to politely deny them. 20 minutes is not really enough time to commit to supervising a student.

This level of communication might be typical from some professors, but I think those are the worst to have as advisors:


  "What do you think of my research ideas?"


"Good"


  "Where should we try to submit this paper?"


"Journal"


  "I'm worried I'm not making progress towards my thesis"


"Ok"



I would look at the admissions process for this university. If the process is such that you need to have some professor's sign off to apply, then maybe that's all they are trying to convey: that you get their sign off, and they aren't putting more effort in because the application process tends to winnow students.

In that case, clarify they are willing to sponsor your application, and go ahead and apply, but make sure you get a chance to meet further with this person before you take them as an advisor, and continue to apply elsewhere: you should not take this as a sure thing by any means, nor should you be sure yourself. If there are other people there you are interested in working with, by all means contact them.

Good luck.