Contact Information
340 Illini Hall, MC-382
1409 W. Green Street
Urbana, IL 61801
Research Description
I am interested in algebraic number theory; in partuclar, the connection between Galois representations and automorphic forms. I am especially interested in the conjectures of Fontaine–Mazur and Langlands, and their interaction with the deformation theory of Galois representations, p-adic automorphic forms, and Selmer groups.
Education
PhD, UCLA, 2012
External Links
Recent Publications
Allen, P. B. (2019). On automorphic points in polarized deformation rings. American Journal of Mathematics, 141(1), 119-167. https://doi.org/10.1353/ajm.2019.0003
Allen, P. B. (2016). Deformations of polarized automorphic galois representations and adjoint selmer groups. Duke Mathematical Journal, 165(13), 2407-2460. https://doi.org/10.1215/00127094-3477342
Allen, P. B., & Calegari, F. (2014). Finiteness of unramified deformation rings. Algebra and Number Theory, 8(9), 2263-2272. https://doi.org/10.2140/ant.2014.8.2263
Allen, P. B. (2014). Modularity of nearly ordinary 2-adic residually dihedral Galois representations. Compositio Mathematica, 150(8), 1235-1346. https://doi.org/10.1112/S0010437X1300780X
Allen, P. B. (2007). On the multiplicity of linear recurrence sequences. Journal of Number Theory, 126(2), 212-216. https://doi.org/10.1016/j.jnt.2006.11.013