\indent A``geometric'' construction of $SU(2) (2+1)-$dimensional TQFTs associates to a surface the vector space spanned my multi-curves modulo local relations. The relevant local relations are defined by the Jones-Wenzl projectors. This talk will outline an approach to categorification of this picture construction of TQFTs, in particular categorification of the Jones-Wenzl projectors, and it will explain how the evaluation at a root of unity may be viewed as a localization of a category. (Joint work with Ben Cooper).

\indent We will discuss the notion of arithmetic matroid, whose main example is provided by a list of elements of a finitely generated abelian group. Guided by the geometry of toric arrangements, we will present a combinatorial interpretation of the associated arithmetic Tutte polynomial, which generalizes Crapo's formula for the classical Tutte polynomial.

\indent The aim is to show a convergence theorem of the Kahler-Ricci flow: if the initial metric is sufficiently close to a shrinking
Kahler-Ricci soliton with respect to a holomorphic vector field, then
the modified Kahler-Ricci flow by this holomorphic vector field will
converge to a shrinking Kahler-Ricci soliton.

\indent In chemical systems, one studies the concentrations of chemical species over time. Of particular interest are steady-state concentrations, and more specifically, when systems admits multiple equilibria. Recent results of Helton partially characterize this possibility in terms of the sign pattern of the stoichiometric matrix, where the stoichiometric matrix describes the chemical species' interactions.

\indent Many biological and physiological processes involve
self-regulating mechanisms that prevent too much growth while ensuring against extinction: the rate of growth is somewhat random (``noisy"), but the distribution depends on the current state of the system. Cancer growth and neurological control mechanisms are just a few examples. In finance, as well, markets self-regulate since people want to "buy low" and "sell high".

\indent Some questions that we'd like to answer are: does the system have a well-defined average? In more technical terms, we want to know if the system is ergodic. How does this long-term average compare to the long-term behavior of the deterministic (not random) system? What can we say about the distribution of ``survival times", i.e. the distribution of times until the system reaches a particular value?

\indent In this talk we will look at (and listen to) a simple example of a noisy, discrete dynamical system with parametric noise and explore ways to answer these questions analytically. We prove ergodicity for a class of growth models, and show that the randomness is harmful to the population in the sense that the long-term average is decreased by the presence of noise. When systems obeying noisy growth laws are connected together as a coupled lattice, the long-term effects of the
noise can have damaging effects on the organism as a whole, even though local interactions might favor growth in a particular area. We will present simulations that highlight the effect of both the noise and the local coupling on the survival of the organism.