Past

 

We consider as a starting point a problem raised by Kunen and Tall as to whether

the real continuum can have non-homeomorphic versions in different submodels of

the universe of all sets. Its resolution depends on modest large cardinals.

In general Junqueira and Tall have made a study of such "substructure spaces"

where the topology of a subspace can be different from the usual relative

topology.

  We will shortly review the known bounds on the angular momentum J in terms of mass m assuming a negative cosmological constant, and describe in more detail Brill's proof of the axisymmetric positive energy theorem, and Dain's upper bound on angular momentum J for vacuum initial data sets with an axial Killing vector and with two asymptotically flat regions.

  We start from the stochastic Ising model(or Glauber Dynamics) and have a short review of some important topics in Particle Systems such as ergodicity, convergence rates and so on. Then an abstract nonlinear model will be introduced by an evolution differential equation. We will build the existence and uniqueness theorem, and give some nice properties such as convergence exponentially and monotonicity for the abstract systems. To apply our abstract theory, we will study a family of nonlinear interacting particle systems generalized from Glauber Type Dynamics(we call them nonlinear Glauber Type Dynamics) and prove that such generalization can be done in infinitely many ways. For nonlinear Glauber Type Dynamics, we have two interesting inequalities related to Gibbs measures. Finally, we will concentrate on one specific nonlinear dynamics, and provide the relation between nonlinear system and the linear one, and that between Gibbs measures and tangent functionals to a nonlinear transfer operator.

 

We will see how Dynkin's isomorphism emerges from the "loop soup" introduced by

Lawler and Werner.

/notices/events/abstracts/applied-analysis/ht07/otto.pdf