John Bergdall

Assistant Professor
Bryn Mawr College


My research focuses on p-adic automorphic forms and Galois representations. Below I list the written products of my research. If you are interested in viewing recorded talks I have given, you can find some at the bottom of this page.


Preprints are listed chronologically by their first appearance, newest at top, regardless of revisions. All links provided point to the arXiv.


All linked titles refer to arXiv versions. Journal links, by digital object identifier (doi), are given in the far right column when available. It happens that some of the journal versions of differ from the final arXiv versions.

To appear in the Journal of the Inst. of Mathematics Jussieu.
To appear in Memoirs of the Amer. Math. Soc.
Selecta Mathematica, 25(4):Art. 59, pp. 24, 2019.
Trans. Amer. Math. Soc., 372(1):357–388, 2019.
J. reine angew. Math., 759:29--60, 2020.
Int. Math. Res. Not., 2019(4):1125-1244, 2019.
C. R. Acad. Sci. Math. Sci. Paris, 355(3):260-262, 2017.
Israel J. Math., 223(1):1-52, 2018.
Compositio Math., 153(1):132-174, 2017.
Proc. Lon. Math. Soc., 113(3):419-444, 2016.
J. Number Theory, 134(1):226–239, 2014.

Sometimes I have produced things that are not destined to be published. Those appear here, with a brief explanation.

Github repository of slopes code from projects with Pollack.
This manuscript split into two publications titled "Slopes of modular forms and the ghost conjecture" above. It is here for historical purposes.
Code and data from the ghost conjecture project with Pollack.
Preprint never to be published. Representation theory appeared in "Adjunction" paper. Applications known now, cf. the paper of Breuil and Herzig regarding the "finite slope" part.
Ph.D. thesis. Main arguments streamlined into "Paraboline..." above.
Video lectures
Lecture on the paper "Upper bounds for constant slope families of p-adic modular forms''
At: Princeton/IAS number theory seminar
Courtesy of the Institute for Advanced Study
Direct: link to YouTube.
Lecture on the paper "Slopes of modular forms and the ghost conjecture''
At: The p-adic Langlands Program and Related Topics
Courtesy of Matthias Strauch
Direct: link to YouTube.