In 1980s, Yau conjectured that the existence of Kaehler Einstein metric on Fano manifold is related to an algebraic geometric  condition of ``stability''.  The recent work with Donaldson, Sun Song confirmed this conjecture.  In the talk, we will  review history of this problems as well as this subject, and we also will review earlier work of  G. Tian and others on this problems.  We will outline the strategy of proof, which involves deforming through metrics  with cone singularities.  If time permits, we will give more details about various aspects of the proof. Tea at 3:30 pm in SC 1425.

After reviewing some results on genericity and generic computability in group theory, I will discuss the rich interaction of generic computability and the general theory of computation and then discuss coarse computability and coarse degrees.

Eighty years after the beginning of the general theory of computability, ideas from the "asymptotic point of view" prevalent in several areas of mathematics have begun to interact with computability theory. This will be a very general talk, developing the necessary ideas from scratch. I will try to give an idea of how this point of view leads to new questions and new answers. Tea at 3:30 pm in SC 1425

Two day workshop, March 22-23, 2013. For a list of invited speakers, please visit: http://www.math.vanderbilt.edu/~suvaini/Workshop-2013/

Boolean networks, neural networks and reaction-diffusion automata share a common structure which we identify as a special class of a new notion of dynamical systems on graphs for which we present a Lyapunov function type concept which implies phase-locking of the dynamics.  For dynamical systems with 'time' being a monoid instead of the integers or the reals, we define a notion of chaos which extends Devaney's classical chaos notion and we prove a theorem that sensitive dependence of initial conditions is a consequence of the two other properties in the definition. The common theme of the two topics is the intention to push the limits of dynamical systems theory in order to investigate how coupling or feedback motifs influence macroscopic behavior and discuss the role of time being a line.

Two day workshop, March 22-23, 2013. For a list of invited speakers, please visit: http://www.math.vanderbilt.edu/~suvaini/Workshop-2013/