Resolutions of $t$-designs were studied as early as 1847 by Reverend T. P. Kirkman who proposed the famous 15 schoolgirls problem. A large set of $t-(v, k, \lambda)$ designs is a partition of the complete design $\left( \overset{\displaystyle X}{k} \right)$ into block-disjoint $t-(v, k, \lambda)$ designs. We discuss prolific families of semiregular large sets of 2-designs and 3-designs arising from the 2-homogeneous half-affine groups acting on $q = p^{a}$ points, and the 3-homogeneous $PSL_{2}(q)$ acting on the projective line. Time permitting, we discuss orthogonality of large sets, present the entertaining Kramer's $7 \times 7 \times 7$ Steiner cube, and offer some tantalizing open problems.

This is joint work with Chuck Cusack, Michael Hurley and Oscar Lopez.

Bio: Spyros is Professor Emeritus in the Department of Mathematical Sciences at Florida Atlantic University. With a Ph.D. from Birmingham, his interests lie at the intersection of nite group theory, combinatorial design theory, and cryptography. Spyros is a fan of good food, good friends and good theorems.