Why should you choose me as a PhD adviser?
Well, for a start, don't choose me unless you want to participate in all phases of research and publication. I'm currently in a College of Engineering, but I'm a scientist, not an engineer. Engineers tend to know exactly what they are doing. If you have an engineer as a PhD adviser, he or she will put you on a project and tell you exactly what to do. You will get your hand held, which is a good thing. But when you graduate and leave, you won't necessarily know how to work on your own. If you work successfully with me, I will make sure you have the ability to work independently after graduation.
My philosophy of research is like the quote from Werner von Braun: "Research is what I'm doing when I don't know what I'm doing". I like to futz around on a number of different projects at once, not all of which will lead to publications or funding.
If you want to be my PhD student and you don't know what problem to work on, I'll start you out by reading papers and books to get background knowledge in whatever it is I'm currently thinking about. Eventually you'll discover something that you think you can do better than what you've read. Put enough of those things with a common theme together, and you've got a PhD thesis.
I'll teach you how to measure the importance of your contribution. It can be the first solution of a problem, or the best solution. In either case, you'll need to do a literature search to find out what research has been done before in this and related areas, and you'll need citations to those papers in your work to demonstrate that you are a contributing member of the scientific community. You will enter the "web of research", the interconnected network of papers connected by citations.
If your solution is the best, you'll need to set up the metrics by which you determine "best", and justify your claim. Is your solution of higher quality, or faster perhaps? Those claims can be justified either theoretically or experimentally. Experiments can be by simulation, or with a human audience. Either way, it is that measurement of the outcome that distinguishes academic research from the kind of development things that are done outside academia and are often erroneously called "research".
After you've done the research, there's the writing up of the thesis, the writing of the papers, the submission of the papers, dealing with refereeing and manuscript requirements. There's the giving of talks on your work at conferences and workshops. I'll give you advice on how to do that. (While we're on the subject, your name will come first in the author list of any publications we write together.)
I may even get you involved in writing funding proposals too.
Oh, and it may come as a surprise to you, but there will come a point when you will know more about your chosen subject than I do. That is as it should be.
I have high standards, which may scare you a little. I've had 5 PhD students, which is admittedly not many for 22 years in academia. I put high value on significance of research though, not just on the number of publications generated. What use is it writing 200 papers if nobody cites them?
My PhD antecedents go back a long way, you can read about them here.
For more information about the kind of research that I do, look at my publication list, and also look at the scientific papers that have cited my publications here.
For more information about me, you can always Google me to find out more.