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I'm a sixth year graduate student at Northeastern University working on determining rings of semi-invariants for representations of associative algebras. More precisely, I have been working with gentle string algebras--a particular case of associative algebras whose representation spaces can be viewed as products of varieties of complexes. My first paper on the subject was posted June 7, 2011 on arXiv: http://arxiv.org/abs/1106.0774v1 . This paper focused primarily on the combinatorics involved in determining rings of semi-invariants for these representation spaces by exploiting the description of their coordinate rings by DeConcini and Strickland. My second paper was posted in November on arxiv: http://arxiv.org/abs/1111.5064. This paper details the construction of the generic modules in the (irreducible components) of the aforementioned representation spaces. As an upshot of this construction, I have been able to show that certain GIT quotients for these spaces are products of projective spaces. This confirms a general conjecture of Weyman for the case of gentle string algebras. My full CV and research statement are at the other end of the preceeding links.
Various Considerations
My primary research interests include representation and invariant theory (perhaps more succinctly quiver invariant theory), as well as Auslander-Reiten theory. On the side, I enjoy reading about cluster algebras, preprojective algebras, Schubert calculus, and cyclic sieving.