Dr. Buhl performs research on the mathematical structures that arise from String Theory in physics. The mathematical objects that he studies include infinite-dimensional Lie algebras, vertex algebras, and vertex operator algebras. In particular, his research attempts to explain fundamental aspects of the representation theory of these objects.
Geoff enjoys teaching a variety of mathematics courses. His favorite courses to teach are Math 300-Discrete Mathematics and Math 350-Differential Equations. Differential Equations is a favorite because it is a course that gives students their first introduction to abstract concepts and proof techniques. In his Differential Equations course, Dr. Buhl incorporates a variety of biological concepts and models to help student develop an intuition about how differential equations model natural phenomena.
In addition to degrees from UC Santa Cruz and the University of Michigan, Dr. Buhl has studied mathematics at a variety of institutions. Before coming to Channel Islands, he was a National Science Foundation Postdoctoral Fellow at Rutgers University. He has also performed mathematical research at the Fields Institute in Toronto as a graduate research and at the College of William and Mary as an undergraduate.