A weakly interacting gas of bosonic atoms moving in the periodic
potential of an optical lattice goes through a phase transition at a
sufficiently low temperature. This phase transition is characterized
by the macroscopic occupation of the single particle ground state and
called as Bose-Einstein condensation. This Bose-Einstein condensate
is, however, sensitive to particle interactions. When the interaction
between particles becomes strong, the Bose-Einstein condensate can
freeze into a Mott insulator.

When the Bose gas is placed inside an optical resonator, atom-light
interaction may create an infinite range interaction between the atoms
and may cause, in certain geometries, another interesting phase
transition: the formation of a charge-density wave. The charge-density
wave combined with Bose-Einstein condensation is called as super solid.

During the talk, we discuss the Bose gas inside an optical resonator,
paying special attention to another very important feature: the
driven-dissipative nature of the cavity. The photons eventually escape
the cavity resulting in a quantum noise for the atomic dynamics.

All the cells of a multicellular organism are the product of cell divisions organized into a single binary tree. Cell divisions are, however, accompanied by replication errors, which result in somatic evolution and can potentially lead to aging, tissue deterioration, and cancer. Using mathematical models we show that a well orchestrated pattern of cell divisions during tissue development and maintenance can dramatically slow down somatic evolution and can ensure a long lifespan for large multicellular organisms.