# MS-1 Linear Algebra Aspects of Association Schemes (Association Schemes)

### Organizers: Allen Herman (Regina) and Bangteng Xu (Eastern Kentucky)

Research on association schemes has continued to evolve in the last decade, led by advances in both the combinatorial and representation-theoretic directions that rely heavily on linear algebraic techniques. This mini-symposia will highlight the applications of linear algebra in this field, featuring talks by invited speakers on characterizations of table algebras of low rank, on new characterizations of P- and Q-polynomial association schemes, on new applications of Terwilliger algebras of association schemes, and on new descriptions of the algebraic properties of distance regular and strongly regular digraphs.

### Speakers

**Harvey Blau**, *Reality-based algebras with a 2-dimensional representation*

**Brian Curtin**, *Co-split Leonard Systems*

**Christopher French**, *Realizations of nonsymmetric hypergroups of rank 4 as association schemes*

**Mitsugu Hirasaka**, *On meta-thin association schemes with certain conditions*

**Siwaporn Mamart**, * Merging in bipartite distance-regular graphs*

**Alyssa Sankey**, *Covering configurations derived from weighted coherent configurations*

**Gurmail Singh**, *C-algebras arising from integral Fourier matrices*

**Sung-Yell Song**, *Partial geometric designs obtained from association schemes*

**Supalak Sumalroj**, *The nonexistence of a distance-regular graph with intersection array {22,16,5;1,2,20}*

**Paul Terwillinger**, *Leonard triples of q-Racah type and their pseudo intertwiners*

**Jason Williford**, *Q-polynomial association schemes with at most 5 classes.*

**Bangteng Xu**, *Pseudo-direct sums and wreath products of loose-coherent algebras with applications to coherent configurations*