Mathematics Colloquia and Seminars

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Combinatorial representation theory has made remarkable progress in our understanding of groups, algebras, and their many applications. However, there are still many examples of algebraic structures -- such as the group of unipotent upper-triangular matrices over a finite field U_n -- where a complete understanding of the representation theory is provably unknowable. This talk explores an alternative to a complete understanding by developing a notion of an approximate representation theory (or super representation theory). We will show that for a family of groups that generalize U_n, the natural approximation not only is understandable, but we even obtain character formulas. Along the way, I will also mention some of the many open questions in this new area of research. This is joint work with P. Diaconis.