When high-energy particles pass through matter (cosmic rays
through the atmosphere, high-energy partons through quark-gluon
plasmas, whatever), they lose energy by showering via hard
bremsstrahlung and pair production.  At very high energy, the quantum
duration of each splitting process, known as the formation time,
exceeds the mean free time for collisions with the medium, leading to
a significant reduction in the splitting rate known as the
Landau-Pomeranchuk-Migdal (LPM) effect.  This interference effect was
worked out theoretically in the 1950s for QED and the 1990s for QCD
and applies individually to each splitting in a shower.  In the past
few years, there has been a flurry of work on the problem of whether
consecutive splittings in a shower can also interfere with each other.
I will review the LPM effect, explain why the question of interference
between different splitting is interesting, and present the current
state of theoretical work towards analyzing this problem.  Time
permitting, I will very briefly discuss similarities and
dissimilarities to related calculations of small-x deep-inelastic
scattering physics.