Ralph Agyei Twum (BSc (Ghana), MS PhD (Howard) )

Academic Qualifications
BSc. Computer Science and Mathematics, University of Ghana, 2003
MS. Mathematics, Howard University, 2007
PhD Mathematics, Howard University, 2012

Research interest 
I primarily study representations of Lie algebras. I am interested in the applications of known results in the finite-dimensional case to infinite-dimensional generalizations. I use the tools of Diffeology to see if these results can be extended. I am also interested in other areas of algebra like Higher Category Theory.

Current research/project(s)
I am currently studying two things:
1. Important results on induced representations – the Borel-Weil theorem and its extension by Bott, the Beilinson-Bernstein localization conjecture, and Kazhdan-Lusztig theory. All of these pose important questions (either in fields of characteristic p, or in the infinite dimensional case). It would be interesting to see if changing the category from that of smooth manifolds to diffeological spaces surmount some of these issues.
2. How can representations of the generalized symmetric group be used to find solutions to simple games involving permutations? An example is the “icosoku” game