Alexander Paulin

Lecturer of Mathematics
School of Mathematical Sciences
University of Nottingham
University Park
Nottingham
NG7 2RD
United Kingdom
alexander[dot]paulin[at]nottingham[dot]ac[dot]uk

Personal

Curriculum Vitae

Teaching

Teaching Statement

Undergraduate Courses

Graduate Courses

Research

My research is in number theory and geometry. In the late 1960s Robert Langlands proposed a series of deep and elegant conjectures linking arithmetic, geometry, analysis and representation theory. Since its inception this program has, thanks to the work of mathematicians such as Pierre Deligne, Vladimir Drinfeld, Alexander Beilinson and Robert Langlands himself, evolved in many directions and now permeates much of mathematics. My work predominantly explores the p-adic and geometric aspects of the Langlands program and is highly interdisciplinary, involving number theory, arithmetic geometry, algebraic geometry, p-adic analytic geometry, D-module theory, p-adic D-module theory, p-adic Hodge theory, affine Kac-Moody Algebra theory, stack theory and higher category theory.

Research Summary

Papers and Preprints

Local to Global Compatibility on the Eigencurve, Proc. London Math. Soc. (2011) 103 (3): 405-440.

Geometric Level Raising and Level Lowering on the Eigencurve,manuscripta mathematica (9 June 2011), pp. 1-29.

A Linear p-adic Geometric Langlands Correspondence, submitted.

A Riemann-Hilbert Correspondence on Smooth Algebraic Stacks, in preparation.

Arithmetic D-modules on Algebraic Stacks, in preparation.

The Radon Transform for Arithmetic D-modules, in preparation.

Moduli of F-isocrystals, in preparation.

The Hitchin fibration in the Setting of Formal and Rigid Geometry, in preparation.