Frederic Vanhove「Problems related to geometry and (P-and Q)-polynomial schemes 」
Many geometric structures yield one or more association schemes. Quite often, these schemes are symmetric and even $P$- or $Q$-polynomial. In this talk, I will first introduce the basic notions from algebraic combinatorics (like association schemes and distance-regular graphs) and a few geometric structures (like projective and polar spaces). Then, I will show several examples where one area contributes to the other, using design theory, the $Q$-polynomial property and stronger versions of the latter, and I will describe how this is connected to my own research. The talk should not require earlier knowledge of association schemes or finite geometry.