David Hansen

David Hansen

Assistant Professor

Ph.D. Boston College, 2013
B.A. Brown University, 2010

Email: dhansen1@nd.edu
Office: 283 Hurley Bldg
Phone: (574) 631-6391
Fax: (574) 631-6579

Mailing Address:
255 Hurley Bldg
Notre Dame, IN  46556-4618

For additional information see David Hansen’s Personal Page.

Research Interests

"Broadly speaking, I’m interested in p-adic phenomena in number theory and algebraic geometry. I especially enjoy thinking about p-adic Hodge theory, the geometry and cohomology of p-adic analytic spaces, and p-adic aspects of the Langlands program.

The fields of p-adic geometry and p-adic Hodge theory were both invented by Tate in the 1960’s. Within the last decade, these fields have changed significantly, on the heels of two revolutionary developments:

1) Fargues and Fontaine’s discovery of the “fundamental curve of p-adic Hodge theory” (also known as the Fargues-Fontaine curve), and their redevelopment of much of classical p-adic Hodge theory inside the study of vector bundles on this curve.

2) Scholze’s discovery of the theory of perfectoid spaces, and their rapid application by Scholze and others to a number of outstanding problems.

Simultaneously with these developments, relative p-adic Hodge theory has reached a state of maturity, and the community has come to appreciate Huber’s theory of adic spaces as the correct framework for studying “non-Noetherian p-adic analytic spaces.” I’ve recently been working to find applications of all these new tools and ideas, and on foundational questions around adic spaces and perfectoid spaces. I’m also quite interested in Scholze’s new theory of diamonds and its applications."

Selected Publications

  • Vanishing and comparison theorems in rigid analytic geometry, submitted
  • On p-adic L-functions for Hilbert modular forms, with J. Bergdall, submitted
  • Extensions of vector bundles on the Fargues-Fontaine curve, with C. Birkbeck, T. Feng, S. Hong, Q. Li, A. Wang and L. Ye, to appear in J. Inst. Math. Jussieu
  • On the GLn-eigenvariety and a conjecture of Venkatesh, with J. Thorne, Selecta Math. Vol. 23 Issue 2
  • Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality, J. reine angew. Math. Vol. 2017 Issue 730

Please direct questions and comments to: dhansen1@nd.edu