Talk

 We study principal bundles for strict Lie $n$-groups over simplicial manifolds. Given a Lie group $G$, one can construct a principal $G$-bundle on a manifold $M$ by taking a cover $U$ of $M$, specifying a transition cocycle, and then quotienting $U\times G$ by the equivalence relation generated by the cocycle. We demonstrate the existence of an analogous construction for arbitrary strict Lie $n$-groups. As an application, we show how our construction leads to a simple finite dimensional model of the Lie 2-group String($n$).

Zipf's law was discovered as an empirical probability distribution
governing the frequency of usage of words in a language.  Later
it was observed in many other situations. As Terence Tao recently remarked,
it still lacks a convincing and satisfactory mathematical explanation.

In this talk I suggest that at least in certain cases, Zipf's law can be explained as
a special case of   the  a priori distribution introduced and studied by L.~Levin.
The Zipf ranking corresponding to diminishing frequency appears then as the

It is a well known fact that a holomorphic Jacobi form $\phi$ splits into the so called theta--decomposition, and that the associated theta coefficients (essentially the Fourier coefficients of $\phi$) are modular forms. Although a similar decomposition is not possible if $\phi$ is meromorphic, in their recent paper Dabholkar, Murthy, and Zagier extended this construction providing a canonical decomposition of $\phi$, defining the so called canonical Fourier coefficients of $\phi$, and describing their modular property in the case of poles of order at most 2.