John F Bergdall
Welcome to my webpage. I am a postdoctoral researcher at Michigan State University. My position presents me the opportunity to combine teaching, personal research and active participation in seminars. Prior to arriving at MSU, I was a postdoctoral fellow at Boston University, partially supported by the National Science Foundation.
This semester I am teaching MTH 133: Calculus II.
You may want to view my CV. (Last update: March 14, 2018)
My research is in number theory. I am ultimately interested in all aspects of the Langlands program, but my focus at the moment is on the theme of p-adic variation. Below you will find my writings along with a short abstract for each article.
For articles which have appeared in peer-reviewed journals, the arXiv versions may differ slightly from the published versions (especially in the numbering of statements). I have tried to provide links to the official journal versions if possible.
Slopes of modular forms and the ghost conjecture, II
To appear in Transactions of the American Mathematical Society.
Smoothness of definite unitary eigenvarieties at critical points
To appear in Journal für die reine und angewandte Mathematik.
Slopes of modular forms and the ghost conjecture
To appear in International Mathematics Research Notices.
An adjunction formula for the Emerton-Jacquet functor
Israel J. Math., 223(1):1-52, 2018.
A remark on non-integral p-adic slopes for modular forms
C. R. Acad. Sci. Math. Sci. Paris, 355(3):260-262, 2017.
Paraboline variation of p-adic families of (φ,Γ)-modules
Compositio Math., 153(1):132-174, 2017.
Arithmetic properties of Fredholm series for p-adic modular forms
Proc. Lon. Math. Soc., 113(3):419-444, 2016.
Ordinary modular forms and companion points on the eigencurve
J. Number Theory, 134(1):226–239, 2014.
On p-adic L-functions for Hilbert modular forms
Upper bounds for constant slope p-adic families of modular forms
Slopes of modular forms and the ghost conjecture (unabridged version)
Joint with Robert Pollack.
Note: This manuscript is a combined version of the two papers we have written with the title "Slopes of modular forms and the ghost conjecture." It is here for historical purposes only.
Website: Slopes of modular forms
Joint with Robert Pollack.
Note: The authors are not professional coders. Use at your own risk!
Ordinary representations and companion points for U(3) in the indecomposable case
On the variation of (φ,Γ)-modules over p-adic families of automorphic forms
Ph.D. thesis, Brandeis University, 2013.
Note: Some material, especially Chapter 4, is generalized and subsumed by the paper Paraboline variation of p-adic families of (φ,Γ)-modules posted above. The rest is contained in Smoothness on definite eigenvarieties at critical points.
: Dirichlet's theorem on primes in arithmetic progressions (no website, but exercises sheets are available here
Wells Hall, Room C237
M 1:30-3:00, W 4:00-5:30
Dept. of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824