Longman Dictionary of Contemporary English classifies the noun 'welcome' as 'singular', which is not the same as 'uncountable'. A singular noun needs a determiner (such as an indefinite article), an uncountable noun does not.What confuses me that "welcome" is not a countable, and I haven't found any explanation why " A warm welcome" have been used in many places.
Thank you for your kind explanation~You could say, "A warm welcome to Professor [name]."
I don't think there is anything wrong with it, but it's not what I would say.
To me, this version is more like an announcement -- we giving Professor [name] a warm welcome. However, the professor will understand that you are addressing the welcome to hi or her.
The version, "Welcome, Professor [name]." addresses the professor directly, and sounds warmer. You could say when someone comes to your house as well as in formal occasions.
Nonetheless, you could use either one, according to your preference.