Representations of association schemes and their applications

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Association schemes are certain special decompositions of complete graphs, and provide a unified framework to experimental designs, error-correcting codes, combinatorial designs, and so on. I worked on developing applications of new tools such as semidefinite programming and the Terwilliger algebra, which is a noncommutative semisimple algebra associated with each vertex of an association scheme. In particular, I obtained (among other results) the so-called Fisher-type inequality for relative t-designs as well as a new intersection theorem in extremal set theory. These results should demonstrate the power of these new tools.