Alexander Miller
In this talk we introduce combinatorial structures called differential posets. The prototypical (1-)differential poset is Young's lattice, which describes the branching of irreducible representations for the symmetric group. Our focus will be on certain operators over Z[t] in these posets that conjecturally have a Smith form, conjecturally easily computed from their completely understood eigenvalues. We will state results thus far, and will also introduce the notion of dual graded graphs, generalizing differential posets. There is no assumption of combinatorial knowledge, and you should leave the talk ready to work on the presented problems. This talk should be valuable to those interested in algebra, combinatorics, and...math!
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