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 Hodge theory, motive theory and higher category theory.

p-adic Automorphic Forms

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

A. Paulin. Geometric Level Raising and Lowering on the Eigencurve. Manuscripta Mathematica (2012) 137, (1-2): 129-157.

p-adic Geometric Langlands

A. Paulin. A p-adic Geometric Langands Correspondence for GL_1.
[preprint pdf]

Higher Category Theory and Geometry

A. Paulin. The Riemann-Hilbert Correspondence for Algebraic Stacks.
[preprint pdf]