My research ranges over a fair number of topics but usually involves group theory in some form. To date, my work has focused mostly on topics arising from Lie groups and their discrete subgroups. As Lie groups are important to many areas of mathematics, my work has addressed problems/topics in algebraic/analytic number theory, algebraic geometry, geometric topology, geometric group theory, geometric analysis, representation theory, spectral geometry, asymptotic behavior of functions (counting functions of various types mostly), finite simple groups, dynamics, and profinite objects. I am by no means an expert in all of these areas but have current mathematical interests in these areas (and more). I enjoy collaborating and currently have PhD students working in several of these areas.
Those interested in my past work can access it through the files below that document my research work and my professional activities. If you have any questions about my work or questions that you think might interest me, feel free to email me. I reply as quickly as I can but am sadly not as fast I wish I could be in replying to emails.
Picking a mentor as either an undergraduate or graduate student is not an easy task. I am a mentor of students in both groups and view this as one of my most important jobs; professional mentorship involves both academic and administrative tasks. If you are interested in speaking with me, it is best to contact me via email. I cannot promise to mentor everyone that wishes for me to. I view my jobs as helping you find the best mentor. This is not always me (nor should it be).
All completed papers that are ready for public consumption can be found of the ArXiv which can be found HERE. My Google Scholar Profile can be found HERE. The three files below summarize my research and professional activities. The full bibliography includes abstracts for each of my papers and my CV (both versions) provide links to some version of each of the papers that have been published.