Why computer science papers rarely use advanced mathematics?
There are many reasons that you may not see a lot of complex mathematics in the papers you are reading.

First, the tools used depend on the task at hand. If a task is simple, a simple tool might be adequate. Also, if the task runs on a simple system, a simple tool is often best. 

Second, usually in Computer Science, the goal is usually to make things usable to a layprogrammer; therefore, it would be detrimental to make something depend on an advanced or abstract concept that few people understand. Often, the proofs sections of algorithms papers have much more advanced mathematics than the rest of the paper; the assumption is that anyone who wants to verify the correctness of the algorithm or its complexity can invest the time in understanding the proof, but that that is not essential to use the results.

Finally, some of this has to do with a lack of familiarity; people who spend their lives reading and writing computer science papers might never have the time to learn about new, highly complex mathematics. Actually, a great way to expand the field is to introduce a concept that many mathematicians understand in a way that it is accessible to and usable by computer scientists. (For instance, I have a friend whose PhD work applied known concepts of Control Theory to problems in Motion Planning. He did very little new work, but he did advance Motion Planning.)