Automorphic mappings in $R^n$

The Existence of Automorphic Quasimeromorphic Mappings

We give a complete characterization of all Kleinian groups G, acting on hyperbolic space Hn, that admit non-constant G-automorphic quasimeromorphic mappings, for any n ≥ 2. We also address the related problem of existence of qm-mappings on manifolds and prove the existence of such mappings on manifolds with boundary, of low differentiability class.

Pseudospectra in Automorphic Scattering

Topics in Automorphic Forms

Automorphic Forms

We apply a theorem of J. Lurie to produce cohomology theories associated to certain Shimura varieties of type U(1, n−1). These cohomology theories of topological automorphic forms (TAF ) are related to Shimura varieties in the same way that TMF is related to the moduli space of elliptic curves. We study the cohomology operations on these theories, and relate them to certain Hecke algebras. We c...

Self-Affine Tiles in Rn

A self-affine tile in R is a set T of positive measure with A(T) = d ∈ $ < (T + d), where A is an expanding n × n real matrix with det (A) = m on integer, and $ = {d 1 ,d 2 , . . . , d m } ⊆ R is a set of m digits. It is known that self-affine tiles always give tilings of R by translation. This paper extends the known characterization of digit sets $ yielding self-affine tiles. It proves seve...