we study reaction-diffusion equations $u_t = l u + f(u)$ with homogeneous reactions f and diffusion operators l arising from the theory of levy processes, with emphasis on propagation phenomena. the classical diffusion case (l = laplacian) has been well-studied, including questions about traveling fronts, wavefront propagation, existence of spreading speeds, etc. after a brief review of the one-dimensional theory, we will concentrate on the case of nonlocal diffusions in several dimensions. we will discuss questions concerning long time dynamics of solutions, including spreading vs. quenching and existence of spreading speeds.

initial data in general relativity must satisfy certain underdetermined differential equations called the constraint equations. a natural problem is to find a parameterization of all possible initial data. a standard method for this is called the conformal method. in this talk, we'll discuss the successes and failures of this method, and future directions for research.

we consider a reduced rank vector autoregressive model where one or several of the roots of the determinant of the characteristic polynomial have modulus stricter than one. we prove a noncausal johansen-granger representation for such time series and discuss how the parameters can be estimated. the asymptotic distribution of the trace statistic is also considered. some monte carlo simulations and a small illustration are presented.

since the discovery of the jones polynomial in the 1980's, it is
well-known that subfactors of von neumann factors are intimately
related to quantum topology. a subfactor is said to have infinite
representation theory, if its standard representation generates
infinitely many non-equivalent irreducibles. such subfactors are
quite hard to come by, and very few methods are known to produce
interesting examples. i will highlight one such procedure, due to
vaughan jones and myself. the construction yields new c$^*$-tensor
categories and solutions of the quantum yang-baxter equation. if
time allows, i will also talk about invariants for subfactors
beyond the standard invariant.

we will start with a discussion of a hierarchy for convex optimization problems based on the classes of convex cones used in representations. then, we will move to reviewing some of the recent developments in primal-dual interior-point algorithms for convex optimization problems in the context of this hierarchy. we will make connections to various areas of mathematics and mention some open problems.