Regular biography
Patrick Allen is an Associate Professor in the Department of Mathematics and Statistics at McGill University. His research focuses on Number Theory, with specific interests in Galois representations and Automorphic forms. Allen's work contributes to the broader field of mathematical research, particularly within the areas of Number Theory. His academic profile can be accessed through the McGill University Mathematics and Statistics department website.
Scholar-generated biography
Patrick B. Allen is an Associate Professor at McGill University specializing in Number Theory. His research focuses on automorphy, Galois representations, and modular forms, with a particular emphasis on the interplay between number theory and representation theory. He investigates properties of automorphic forms, deformation rings, and congruences, contributing to the understanding of modularity lifting theorems and the behavior of Galois representations over CM fields. His work also explores linear recurrence sequences, Selmer groups, and the arithmetic of elliptic curves. Allen's research bridges algebraic number theory and automorphic forms, offering insights into the structure of Galois representations and their applications in arithmetic geometry.