Simon Wadsley

I'm a mathematician at the University of Cambridge currently working on rigid analytic spaces and p-adic representation theory. My work focuses on developing the theory of D-modules in the p-adic setting, studying Iwasawa algebras and their representations, and exploring representations of p-adic Lie groups via non-commutative algebra.

A major theme in my research has been establishing fundamental results about D-modules on rigid analytic spaces, including proving analogues of classical results like Kashiwara's equivalence and Bernstein's inequality in the p-adic setting. I have also done work on irreducible representations of compact p-adic analytic groups and their canonical dimensions.

More recently, my research has involved studying equivariant line bundles on Drinfeld's p-adic upper half plane and their global sections. This connects to the broader program of understanding locally analytic representations of p-adic Lie groups through geometric methods.

Publications

Global sections of equivariant line bundles on the $p$-adic upper half plane

K. Ardakov, S. Wadsley

Equivariant line bundles with connection on the p-adic upper half plane

K. Ardakov, S. Wadsley

$\widehat {\mathcal {D}}$-modules on rigid analytic spaces III: weak holonomicity and operations

K. Ardakov, Andreas Bode, S. Wadsley

Compositio Mathematica 2019

\wideparen{𝒟}-modules on rigid analytic spaces II: Kashiwara’s equivalence

K. Ardakov, S. Wadsley

Journal of Algebraic Geometry 2018

PROPs for Linear Systems

PROPs for Linear Systems

S. Wadsley, N. Woods

D-modules on rigid analytic spaces II: Kashiwara's equivalence

K. Ardakov, S. Wadsley

⌢𝒟-modules on rigid analytic spaces I

K. Ardakov, S. Wadsley

Journal für die Reine und Angewandte Mathematik 2014

Verma modules for Iwasawa algebras are faithful

K. Ardakov, S. Wadsley

On irreducible representations of compact $p$-adic analytic groups

K. Ardakov, S. Wadsley

Euler characteristics, Akashi series and compact $p$-adic Lie groups

S. Wadsley

Euler characteristics and compact p-adic Lie groups

S. Wadsley

Γ-invariant ideals in Iwasawa algebras

K. Ardakov, S. Wadsley

Gamma-invariant ideals in Iwasawa algebras

K. Ardakov, S. Wadsley

A BERNSTEIN-TYPE INEQUALITY FOR LOCALIZATIONS OF IWASAWA ALGEBRAS OF HEISENBERG PRO-p GROUPS

S. Wadsley

On the Cartan Map for Crossed Products and Hopf–Galois Extensions

K. Ardakov, S. Wadsley

K0 and the dimension filtration for p‐torsion Iwasawa modules

K. Ardakov, S. Wadsley

Characteristic elements for -torsion Iwasawa modules

K. Ardakov, S. Wadsley

Homogeneity and rigidity of the Brookes–Groves invariant for the non-commutative torus

S. Wadsley

Polyhedrality of the Brookes–Groves invariant for the non-commutative torus

S. Wadsley