Higher rank Teichmüller theory is the study of certain connected components of character varieties of surface groups in higher rank semisimple Lie groups, with the property that all elements in these components correspond ...

Arithmetic groups arise naturally in many fields such as number theory, algebraic geometry, and analysis. Mapping class groups arise in both low dimensional topology and geometric group theory. They have been studied ...

We characterize the uniform limits of Dirichlet polynomials on a right half plane. We extend the approximation theorems of Runge, Mergelyan and Vitushkin to the Dirichlet setting with respect to the Euclidean distance and ...

The recent developments in hyperbolic geometry and flat geometry in real dimension $2$ formed the core of the workshop, with an emphasis on enumerative aspects. A particularly important role in this regard was played by ...

For compact sets $K\subset \mathbb C^{d}$, we introduce a subalgebra $A_{D}(K)$ of $A(K)$, which allows us to obtain Mergelyan type theorems for products of planar compact sets as well as for graphs of functions.

We study harmonic mappings of the form $f(z) = h(z) - \overline{z}$, where $h$ is an analytic function. In particular we are interested in the index (a generalized multiplicity) of the zeros of such functions. Outside the ...

In recent years a number of challenging research problems have crystallized in the analytic theory of Dirichlet series and its interaction with function theory in polydiscs. Their solutions appear to require unconventional ...

The goal of this mini-workshop is to gather specialists of the dimer, Ising and spanning tree models around recent and ongoing progress in two directions. One is understanding the connection to the spectral curve of these ...

Let $f_1,..., f_p$ be entire functions that do not all vanish at any point, so that $(f_1,..., f_p)$ is a holomorphic curve in $\mathbb{CP}^{p-1}$. We introduce a new and more careful notion of counting the order of the ...

The program “New Trends in Teichmüller Theory and Mapping Class Groups” brought together people working in various aspects of the field and beyond. The focus was on the recent developments that include higher Teichmüller ...