There is no pre-seminar.

An incomplete pairwise balanced design is equivalent to a pairwise balanced design with a distinguished block, viewed as a `hole'. If there are $v$ points, a hole of size $w$, and all (other) block sizes equal $k$, this is denoted IPBD$((v;w),k)$. In addition to congruence restrictions on $v$ and $w$, there is also a necessary inequality: $v >(k-1)w$. In this talk, I will discuss two new existence results for IPBD$((v;w),k)$: one in which $w$ is fixed and $v$ is large, and the other in the case $v > (k-1+\epsilon) w$ when $w$ is large (depending on $\epsilon$). This talk is intended for a general audience. I will include an introduction to design theory and discuss current research techniques for investigating existence problems in design theory.

The pre-seminar will be an intro to design theory with more details and examples aimed at grad students.