  Underdoped Mott insulators provide us with a challenge of many-body physics.
Recent renewed understanding is discussed in terms of the evolution of pole and
zero structure of the single-particle Green's function. Pseudogap as well as
Fermi arc/pocket structure in the underdoped cuprates is well reproduced from
the recent cluster extension of the dynamical mean-field theory. Emergent
coexisting zeros and poles set the underdoped Mott insulator apart from the
Fermi liquid, separated by topological transitions. Cofermion proposed as a
generalization of exciton in the slave-boson framework accounts for the origin
of the zero surface formation. The cofermion-quasiparticle hybridization gap
offers a natural understanding of the pseudogap and various unusual Mottness.
Furthermore the cofermion offers a novel pairing mechanism, where the cofermion
has two roles: It reinforces the Cooper pair as a pair partner of the
quasiparticle and acts as a glue as well. It provides a strong insight for
solving the puzzle found in the dichotomy of the gap structure.
