I have never heard of Houston University. There is a University of Houston which you should use the definite article to refer to as "the University of Houston" because it is how the school is named. Also, it should be "a professor at ABC University"
I am going to pilfer Hellion's answer on ELU as it is hard to improve upon. And since this is ELL not ELU we can't really duplicate your question to that answer. Plus, I didn't find a good duplicate target on ELL either. So here it goes:
My personal rule of thumb would be that if the school name includes an "of", use "the": The University of Minnesota, The College of St. Catherine, The Massachusetts Institute of Technology, etc. (And when abbreviating one of these names, use "the" only if the "of" is present in the abbreviation: "I attend the University of California at San Diego" → "I attend UCSD"; but "I attend the University of Minnesota" → "I attend the U of M".)
But if the school name does not include an "of", and especially if its name consists of a proper noun prepended to a school type, do not use "the": Carleton College, South Dakota State University, Rensselaer Polytechnic Institute, etc.
This is a good rule of thumb to go by, but you should know that there will always be exceptions. A comment on ELU points to the Ohio State University which is commonly known simply as "Ohio State".
Also note that a lot of colleges and universities outside the Anglosphere have English names. Their naming doesn't necessarily follow the above rule. Always look it up and check their website if you are writing something formal that makes mention of a university. That's the way to go.