Introduction: Getting 'results' from tutoring, and education in general, requires one to understand the complexity of various learning styles and it is imperative that an educator be adaptive and eclectic in their approach. Each individual brings their own personality to tutoring sessions. Training and experience in the mental processes involved in learning, and the various stages of understanding a topic, mean that an educator must not only know their subject very well, but we must also know people very well. Further, we must continue to educate ourselves in our field. Continuing education is fundamental to an educator succeeding in helping students develop their own relationship with the material. Often educators are expected to implement new standards that they themselves have note been properly educated in, common core standards for example. These standards are sometimes very positive, but prove to be ambitious as education of the teachers is not taken into account. We as educators must push ourselves and continue to learn throughout our careers, otherwise we fail our students and end up confusing them by trying to explain concepts we don't completely understand. Learning advanced mathematics that gives insight into why we have such standards, and why we require students to learn what they are expected to learn, is something I continue to do every day. My training as a professional educator, being involved in new research in mathematics, constructing new math and publishing articles, continuing to educate others, writing expository articles and books, and constantly finding new and more effective ways to teach mathematics to students, means that I am particularly effective.
My main research interests are: Representation theory; noncommutative algebra; algebraic geometry; homological algebra; invariant theory; algebraic groups; and Lie groups. Math is definitely one of the two most important things in my life, the second being my partner. Of course, working on actual math is but a small part of being a mathematician or a student of mathematics, but I enjoy the other aspects of it as well. Teaching is always very rewarding, grading maybe not so much. Being in a department where I can skate around on my roller skates is nice. I prefer an environment with people who can have fun but who love math and really know how to work when it's time for work. Math is often a communal sport, and I definitely enjoy working with others on problems and research. Quiet time alone with math is also very nice though. I also enjoy helping my colleagues and getting them excited about things I'm working on.
