John Bergdall

Assistant Professor
Bryn Mawr College

Research

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

Preprints are listed by the order they first appeared, regardless of revisions. All links provided point to the arXiv.

Publications

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

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.
Other

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

 
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
2019
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.
2016
Lecture on the paper "Slopes of modular forms and the ghost conjecture''
At: The p-adic Langlands Program and Related Topics
Courtesy of Matthis Strauch
Direct: link to YouTube.