Benjiman C. Tharp
Research
I am primarily interested in diagram algebras (and diagram categories)
and their relationships with other mathematical objects such as Lie
superalgebras. Diagram algebras have become objects of study in
theoretical physics and are quite interesting on their own. For
example, the Brauer algebra naturally contains (as a subalgebra) the symmetric group algebra and, as a result, the intriguing combinatorics of Young tableaux
play an important role in its representation theory. I
am currently studying the representation theory of a variation of the
Brauer algebra (developed in joint work with my advisor) called the
marked Brauer
algebra. While it bears some outward similarities with the
ordinary Brauer algebra, the combinatorics associated with its
representation theory are quite different. For further details,
see my research statement.
Publications
Some Useful Software
I
use a variety of computer programs to simplify the task of computing
examples for both teaching and research. Some of my favorite
open-source programs are:
- Maxima
- a computer algebra system, good for calculus computations, matrix
calculations, etc. which is comparable to Mathematica or Maple
- GAP - a
program suite which is useful for more algebraic calculations (e.g.
what is the center of a ring given by generators and relations?) which
is comparable to Sage or Magma
- FreeMat - a free and open-source alternative to MATLAB which maintains a decent amount of compatibility with MATLAB functions
- Inkscape - great for drawing the diagrams which appear frequently in my research
Other Interesting Links