Kapouleas and Yang have constructed, by gluing methods, sequences of
minimal embeddings in the round 3-sphere converging to the Clifford
torus counted with multiplicity 2. Each of their surfaces, which
they call doublings of the Clifford torus, resembles a pair of
coaxial tori connected by catenoidal tunnels and has symmetries
exchanging the two tori. I will describe an extension of their work
which yields doublings admitting no such symmetries as well as
examples incorporating an arbitrary (finite) number of tori, that
is Clifford torus triplings, quadruplings, and so on.

From a complex analytic perspective Teichmüller space - the universal
cover of the moduli space of Riemann surfaces - is a contractible
bounded domain in a complex vector space. Likewise, Bounded Symmetric
domains arise as the universal covers of locally symmetric varieties
(of non-compact type). In this talk we will study isometric maps
between these two important classes of bounded domains equipped with
their intrinsic Kobayashi metric.

Based on the compactness of the moduli of non-collapsed Calabi-Yau
spaces with mild singularities, we set up a structure theory for
polarized K\"ahler Ricci flows with proper geometric bounds.
Our theory is a generalization of the structure theory
of non-collapsed K\"ahler Einstein manifolds.
As applications, we prove the Hamilton-Tian conjecture and the partial-
C0-conjecture of Tian. This is a joint work with Xiuxiong Chen.