I will describe my research project on statistical analysis of networks
and how a simple question related to osteoporosis lead me to learn about
percolation, combinatorics of lattice paths, the asymptotic theory of
determinants, q-series, and algebraic geometry. I will describe various
open problems in those areas and how they relate, and I will present
some partial results. The talk will be non-technical and accessible with
little else than basic calculus, linear algebra, and elementary
probability theory. 