Mathematics Colloquia and Seminars

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Description

Left regular bands (or LRBs) are a special family of finite, noncommutative semigroups which arise surprisingly frequently in algebraic combinatorics and discrete geometry. The representation theory of their semigroup algebras is rich but tractable and has close connections to an area of combinatorics called "poset topology."

Many of the LRBs in the literature come equipped with natural symmetry groups. In such cases, one can study the invariant subalgebra of the semigroup algebra. Solomon's descent algebra arises as one such invariant subalgebra.  In this talk, we will discuss joint work with Benjamin Steinberg which approaches understanding the representation theory of these invariant subalgebras through group-equivariant poset topology.