the moduli space of Riemann surfaces with boundary with an additional structure called a
grading. *Joint work with R. Tessler.
Suppose you have a finite group G and you want to study certain related structures (e.g., random walks, Cayley graphs, word maps, etc.). In many cases, this might be done using sums over the characters of G. A serious obstacle in applying these Fourier type formulas is lack of knowledge on the low dimensional representations of G. In fact, numerics shows that the "small" representations tend to contribute the largest terms to these sums, so a systematic knowledge on them might assist in the solution of important problems.