In my ongoing work with J. Quastel we consider spatially periodic growth models built from weakly asymmetric exclusion processes with finite jump ranges and general jump rates. We prove that at a large scale and after renormalization these processes converge to the Hopf-Cole solution of the KPZ equation driven by Gaussian space-time white noise. In contrast to the celebrated result by L. Bertini and G. Giacomin (in the case of the nearest neighbour interaction) and its extension by A. Dembo and L.-C.
Sala Seminari (Dip. Matematica)
"Una varietà complessa è una varietà il cui modello locale è C^n, invece che R^n. Tra le varietà compatte, l'esempio più semplice è probabilmente la sfera S^2 vista come spazio proiettivo complesso CP^1. Quali altre sfere ammmettono una struttura complessa? A tutt'oggi non è chiaro se esistono strutture complesse su S^6.
Given an n-dimensional hyperbolic manifold M, it is reasonable to ask whether or not it can be realized as a totally geodesic, embedded submanifold of an (n+1)-dimensional hyperbolic manifold. If this is true, we say that M geodesically embeds. Determining whether or not a hyperbolic manifolds geodesically embeds is, in general, quite difficult.
However, if we restrict our attention to the case of arithmetic manifolds of simplest type, (a class of manifolds constructed using tools from number theory), we can show that, in many cases, they do indeed embed geodesically.
Let N/K be a normal tame extension of number fields and let G := Gal(N/K)
be its Galois group. It is common knowledge that, under these conditions,
[O_N] lies in the locally free class group Cl(O_K[G]). What can be said about
the existence of a normal integral basis for the extension N/K, by knowing
the structure of the group Cl(O_K[G])? In some cases this problem is easily
settled via cancellation law.
There is also a rank notion for locally free modules over orders. Which