Undergraduate Research Faculty Profiles

My research focuses on algebraic groups, finite groups, and applications of group theory. A common theme involves generation problems for algebraic groups. I am interested in finding precise conditions which determine when a collection of elements (given up to conjugacy) generate a Zariski dense subgroup. Isolating such conditions has surprising applications in probabilistic group theory, and the representation theory of algebraic groups.

Dr. Christian Geske received his PhD from University of Wisconsin–Madison in 2019. His research interests revolve around algebraic topology and in particular singularity theory. If you are an undergraduate who has already taken an abstract algebra course and a topology course, then you might consider a theoretical mathematics project with Dr. Geske centered on the study of topological singularities. You could explore aspects of the classification of isolated singularities like the study of the Milnor fiber, or perhaps dive into the relationship between singularities and knot theory.

Dr. Cymra Haskell was awarded her PhD in Mathematics from Stanford University in 1992 and completed post-doctoral fellowships at the University of Texas at Austin and the State University of New York at Stony Brook before coming to the University of Southern California (USC) in 1998. Her research is in the area of ergodic theory and applied mathematics. Her primary focus today is on mathematics education and increasing diversity in mathematics.