Growth is involved in many fundamental biological processes such as
morphogenesis, physiological regulation, or pathological disorders.
It is, in general, a process of enormous complexity involving
genetic, biochemical, and physical components at many different
scales and with complex interactions. In this talk, I will consider
the modeling of elastic growth in elastic materials and investigate
its mechanical consequences. First, starting with simple system in
one two and three dimensions, I will show how to generalize the
classical theory of exact elasticity to include growth. Second, we
will see that growth affects the geometry of a body by changing
typical length scales but also its mechanics by inducing residual
stresses. The competition between these two effects can be used to
regulate the physical properties of a material during regular
physiological conditions. It can also lead to interesting spontaneous
instabilities in growing materials as observed in simple physical
systems.

I will introduce some basic concepts and methods from nonlinear time series analysis and discuss applications that may hold implications for a diverse body of scientific groups: from scientists who study physical ocean processes such as El Nio events to environmental managers charged with overseeing and sustaining ecosystem resources such as fisheries. Of particular interest is the fact that the concepts and methods relate to many disciplines involving complex webs of mutually interacting parts, such as ecosystems and world financial markets, which have the potential for unexpected collapse and irreversible change.

One of the most interesting questions in the operator space
theory was ``What are the possible operator algebra products a given
operator space can be equipped with?''. In my Ph.D. thesis, I answered
this question using quasi-multipliers and the Haagerup tensor product.
Quasi-multipliers of operator spaces were defined by Paulsen in late
2002 as natural variations of one-sided multipliers of operator spaces
which had been introduced by Blecher around 1999. However, the
significant relation between quasi-multipliers and operator algebra
products was discovered and proved by myself in early 2003. Since many
people seem to be interested in this topic, in my talk I present this
theorem as well as more recent results in a self-contained manner from
basic definitions with examples. So mathematicians in any fields
(especially, pure algebra) and graduate students are welcomed to attend.

In a celebrated paper, Dyson shows that the spectrum of a random Hermitian matrix, diffusing according to an Ornstein-Uhlenbeck process, evolves as non-colliding Brownian motions held together by a drift term. The universal edge, bulk and gap scalings for Hermitian random matrices, applied to the Dyson process, lead to novel stochastic processes, Markovian and non-Markovian; among them, the Airy, Sine and Pearcey processes. The integrable theory around the KdV and KP equations provides useful information on these new processes.