A local-global question 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...

Topics in Automorphic Forms

Automorphic forms: a physicist’s survey

Automorphic forms play an important rôle in physics, especially in the realm of string and M-theory dualities. Notably, the hidden symmetries of 11-dimensional supergravity compactifications, discovered by Cremmer and Julia, motivate the study of automorphic forms for exceptional arithmetic groups En(Z) (including their n ≤ 5 classical A andD instances). These Notes are a pedestrian introductio...

k-hypermonogenic automorphic forms

In this paper we deal with monogenic and k-hypermonogenic automorphic forms on arithmetic subgroups of the Ahlfors-Vahlen group. Monogenic automorphic forms are exactly the 0-hypermonogenic automorphic forms. In the first part we establish an explicit relation between k-hypermonogenic automorphic forms and Maaß wave forms. In particular, we show how one can construct from any arbitrary non-vani...

Overconvergent Algebraic Automorphic Forms

I present a general theory of overconvergent p-adic automorphic forms and eigenvarieties for connected reductive algebraic groups G whose real points are compact modulo centre, extending earlier constructions for forms of GLn due to Buzzard, Chenevier and Yamagami. This leads to some new phenomena, including the appearance of intermediate spaces of “semiclassical” automorphic forms; this gives ...