A number of recent experiments have shown that several organisms
that reproduce by fissioning (e.g. E. coli bacteria)
don't share the cellular damage they have
accumulated during their lifetime equally among their offspring. Using
a stochastic PDE model, David Steinsaltz and I have shown that under quite
general conditions the optimal asymptotic growth rate for a population
of fissioning organisms is obtained when there is a non-zero but moderate
amount of preferential segregation of damage -- too much or too little
asymmetry is counter-productive. The proof uses some new results of ours
on quasi-stationary distributions of one-dimensional diffusions and
some Sturm-Liouville theory. The talk is intended for a probability
audience and I won't assume any knowledge of biology.

Many Hodge integral identities, including the ELSV formula of Hurwitz numbers and the lambda_g conjecture, are various limits of the formula of one-partition Hodge integrals conjectured by Marino and Vafa. Local Gromov-Witten invariants in all degrees and all genera of any toric surfaces in a Calabi-Yau threefold are determined by the formula of two-partition Hodge integrals. I will describe proofs of the formulae of one-partition and two-partition Hodge integrals based on joint works with Kefeng Liu and Jian Zhou.

I shall report some recent progress on the quasi-local mass associated to any space-like surface in space-time. The relation to isometric embedding problems shall also be discussed.