Sean Howe. first DOT last AT utah DOT edu. JWB 323.


A randomly generated cubic surface with its real lines (mathematica notebook available below)


contact info

E-mail: first DOT last AT utah DOT edu.

Office: JWB 323

Mailing address: University of Utah Department of Mathematics, 155 S 1400 E, Salt Lake City, UT 84112


bio info

My (somewhat out-of-date) CV.

My research is currently supported by the NSF under grant DMS-2201112.

Since July 2019, I have been an Assistant Professor in the Department of Mathematics at the University of Utah.

In the academic year 2023-2024 I was a Friends of the Institute of Advanced Study Member at the special year on p-adic arithmetic geometry at the Institute for Advanced Study. From September 2017 to June 2019, I was an NSF Postdoctoral Scholar at Stanford University. In June 2017, I received my PhD from the University of Chicago, advised by Matt Emerton. In July 2012 I received a joint master's degree from Leiden University and Universite Paris-Sud 11 through the ALGANT integrated masters course.

I work in arithmetic and algebraic geometry, representation theory, and number theory (though, it seems increasingly likely that I may actually be a p-adic geometer in denial).


photo

Professional photographers took these pictures!

teaching

These days I use Canvas pretty much exclusively for course materials, but for some older courses you will find websites with interesting things on them below!


PhD students

If you are a University of Utah PhD student considering working with me then I will be happy to meet with you to discuss options; send me an email to schedule a time. If you think you are interested in the kinds of mathematics I work on, then, before picking an advisor, you should also speak with (at least!) Aaron Bertram, Srikanth Iyengar, Gordan Savin, Karl Schwede, David Schwein, and Uri Shapira, all of whom have some overlap! I also frequently co-advise students, and it can be to your benefit to have two advisors.

Current (alphabetical by last name):

Graduated (alphabetical by last name):


undergraduate research

I regularly supervise undergraduate research projects. Some highlights of past students' work:

If you are an undergraduate at the University of Utah interested in working on a research project with me, please get in touch using the contact info found above (you may also want to check out this page for information about getting paid!).

If you are an undergraduate at another institution then, due to time constraints, it is extremely unlikely that I will be able to work with you on an individual research project on an ad hoc basis. Sometimes, however, I work with external undergraduates in a more systematic way. Upcoming opportunities:


mathematical writing
preprints
  1. The completed Kirillov model and local-global compatibility for functions on Igusa varieties
    Sean Howe.
    arXiv:2506.24089
  2. Equidistribution and arithmetic Λ-distributions.
    Matthew Bertucci and Sean Howe.
    arXiv:2505.24748
  3. The negative σ-moment generating function.
    Sean Howe.
    arXiv:2505.01205
  4. Transitivity of the B^+_dR loop group action on Schubert cells.
    Sean Howe.
    arXiv:2505.01204
  5. Characterizing perfectoid covers of abelian varieties
    Rebecca Bellovin, Hanlin Cai, and Sean Howe (with an appendix by Tongmu He).
    arXiv:2501.03974
  6. Random matrix statistics and zeroes of L-functions via probability in λ-rings
    Sean Howe.
    arXiv:2412.19295
  7. Inscription and p-adic periods.  Preliminary version of November 25th, 2024.
    Use at your own risk! The notation, numbering, and some of the contents are not stable. Two sequels are announced in the body of the text; this paper should stabilize when the second of these becomes available.
  8. Admissible pairs and p-adic Hodge structures II: The bi-analytic Ax-Lindemann theorem
    Sean Howe and Christian Klevdal.
    arXiv:2308.11064

published/to appear
  1. Admissible pairs and p-adic Hodge structures I: Transcendence of the de Rham lattice
    Sean Howe and Christian Klevdal. To appear in Algebra and Number Theory.
    arXiv:2308.11065
  2. Cohomological and motivic inclusion-exclusion.
    Ronno Das and Sean Howe. Compositio Mathematica, Volume 160, Issue 9, September 2024, pp. 2228-2283
    journal (open access) · arXiv:2204.04165
  3. The conjugate uniformization via 1-motives.
    Sean Howe, Jackson Morrow, and Peter Wear. Mathematische Zeitschrift 307, 47 (2024)
    journal (view only open access) · arXiv:2208.10551
  4. Slope classicality in higher Coleman theory via highest weight vectors in completed cohomology.
    Sean Howe. Proceedings of the National Academy of Sciences. Vol. 19, No. 45, November 2022.
    journal (open access) · arXiv:2111.15576
  5. Zeta statistics and Hadamard functions.
    Margaret Bilu, Ronno Das, and Sean Howe. Advances in Mathematics. Volume 407. October 2022.
    journal (open access) · arXiv:2012.14841
  6. The spectral p-adic Jacquet-Langlands correspondence and a question of Serre.
    Sean Howe. Compositio Mathematica, 158(2), 245-286. 2022.
    journal (open access) · arXiv:1806.06807
    (Note: Some results in the earlier arXiv version have been split off to appear in another work in progress.)
  7. Motivic Euler products in motivic statistics.
    Margaret Bilu and Sean Howe. Algebra and Number Theory, Vol. 15 (2021), No. 9, 2195-2259.
    journal · arXiv:1910.05207
  8. Overconvergent modular forms are highest weight vectors in the Hodge-Tate weight zero part of completed cohomology.
    Sean Howe. Forum of Mathematics, Sigma. Vol. 9:e17 (2021) 1-24.
    journal (open access) · arXiv:2008.08029
  9. A unipotent circle action on p-adic modular forms.
    Sean Howe. Transactions of the American Mathematical Society Series B, 7 (2020), 186-226.
    journal (open access) · arXiv:2003.11129
  10. Motivic random variables and representation stability I: Configuration spaces.
    Sean Howe. Algebraic & Geometric Topology, 20-6 (2020), 3013-3045.
    journal · arXiv:1610.05723.
  11. Motivic random variables and representation stability II: Hypersurface sections.
    Sean Howe. Advances in Mathematics, Volume 350, 9 July 2019, Pages 1267-1313.
    journal · arXiv:1610.05720
  12. Transcendence of the Hodge-Tate filtration.
    Sean Howe. Journal de théorie des nombres de Bordeaux, 30 no. 2 (2018), p. 671-680.
    journal · arXiv:1610.05242.
  13. Presentations of quaternionic S-unit groups.
    Ted Chinburg, Holley Friedlander, Sean Howe, Michiel Kosters, Bhairav Singh, Matthew Stover, Ying Zhang, and Paul Ziegler. Experimental Mathematics, Volume 24, Issue 2 (2015), p. 175-182.
    journal · arXiv:1404.6091
  14. The Log-Convex Density Conjecture and vertical surface area in warped products.
    Sean Howe. Advances in Geometry, 15.4:455--468, 2015.
    journal · arXiv:1107.4402
  15. Isoperimetric problems in sectors with density.
    Alexander Diaz, Nate Harman, Sean Howe, and David Thompson. Advances in Geometry, 14.4:589--619, 2012.
    journal · arXiv:1012.0450
  16. Steiner and Schwarz symmetrization in warped products and fiber bundles with density.
    Frank Morgan, Sean Howe, and Nate Harman. Revista Matematica Iberoamericana, 27(3):909--918, 2011.
    journal · arXiv:0911.1938
  17. Isoperimetric inequalities for wave fronts and a generalization of Menzin's conjecture for bicycle monodromy on surfaces of constant curvature.
    Sean Howe, Matt Pancia and Valentin Zakharevich. Advances in Geometry, 11:273--292, 2011.
    journal · arXiv:0902.0104

theses
  1. Overconvergent modular forms and the p-adic Jacquet-Langlands correspondence.
    Sean Howe, University of Chicago PhD Thesis, 2017. Note: Some of the results of this thesis appear in "The p-adic Jacquet-Langlands correspondence and a question of Serre," above.
    knowledge.uchicago.edu · local pdf ·
  2. Higher genus counterexamples to relative Manin-Mumford.
    Sean Howe, ALGANT Master's thesis.
    algant.eu

other

Some of these are old and may be be quite rough, sorry!


mathematica notebooks

(provided as-is; feel free to use, and let me know if you do something cool!)