Details — Mathematics Faculty Lecture by Dr. Lauren Williams — November 30
| Date: 11/30 | Time: 4 pm |
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As part of the Mathematics Faculty Lecture Series, Dr. Lauren Williams from Mercyhurst University will give a talk “The combinatorics of invariant polynomials on tensors under a product of orthogonal groups” on Thursday, November 30, at 4 p.m. in Arter 105.
Abstract:
We will begin with an overview of permutations, Young tableaux, and their connections to representation theory. We will then compute a formula for the number of fixed point free transpositions that commute with a given permutation. If we let K be a product of r complex orthogonal groups, and let V be the r-fold tensor product of defining representations of each orthogonal factor, we will use our formula to find the dimension of the K-invariant algebra of degree d homogeneous polynomial functions on V in the stable case where the dimension of each factor is at least d. We will also describe a bijection between these invariant polynomials and the isomorphism classes of certain r-regular graphs on d vertices, and their interpretation as phylogenetic trees. Finally, we will consider the inherent difficulty of attempting to compute similar formulas for the non-stable cases.
There will be refreshments in Arter Hall Lounge (104) immediately following the talk.