Pure Mathematics Graduate Student
Department of Mathematics, Florida State University
M.A., Florida State University, USA, 2014
M.A., Bowling Green State University, USA, 2012
B.A., Valdosta State University, USA, 2010
B.S., Valdosta State University, USA, 2009
Detailed description of research
I'm currently studying the (quote-unquote) consequences of depth-one, taut codimension-one foliations on 3-manifolds, particularly transverse topological structures (e.g., transverse laminations) induced by the existence of such foliations.
I'm interested in manifolds admitting hypercomplex structures, particularly in deriving analogues of complex manifold theory and attempting to get an idea of what makes manifolds with hypercomplex structures (which are pretty rare in general) special...
I'm also interested the theory of Clifford-valued functions and of complex analytic analogues of such functions, particularly on manifolds. This involves the study of Dirac operators (and generalizations thereof) which itself hinges on understanding spin manifolds and various geometric aspects (connections, spinor bundles, etc.) related thereto.