David Zureick-Brown's Homepage

David Zureick-Brown
Department of Mathematics and Statistics
Amherst College

Office: Seeley Mudd 502
Phone: (413) 542-2595

Office hours: Mondays 4:15-5:15 (in person) Wednesday 2:30-3:30 (zoom) Wednesday 3:30-5:30 (in person)

Slides for my colloquium talk at Colby College are available here
Spring 2024 Courses

Fall 2024 Courses

Old course webpages
  • Five College Number Theory seminar (Tu 4:00, Seeley Mudd 207)
  • Valley Geometry seminar (F 4:00, 1634 LGRT @UMASS)

Professional Information

Links for undergraduate students

Slides for talks I have given (and occasionally the tex source) are available in the directory here
Videos of some talks I have given are available here
Research (Supported by National Science Foundation award DMS-2302356)
  1. A predicted distribution for Galois groups of maximal unramified extensions
    with Yuan Liu and Melanie Matchett Wood
    accepted for publication in Inventiones mathematicae, arxiv

  2. Angle Ranks of Abelian Varieties
    with Taylor Dupuy and Kiran S. Kedlaya
    Mathematische Annalen (2023): 1-17, arxiv, published version,

  3. Heights on stacks and a generalized Batyrev--Manin--Malle conjecture
    with Jordan S. Ellenberg and Matthew Satriano
    Forum of Mathematics, Sigma, Volume 11, 2023; arxiv published version,

  4. ell-adic images of Galois for elliptic curves over Q
    with Jeremy Rouse and Andrew Sutherland and an appendix with John Voight
    Forum of Mathematics, Sigma, Volume 10, 2022; arxiv, published version, code

  5. Sporadic Cubic Torsion
    with Maarten Derickx, Anastassia Etropolski, Mark van Hoeij, and Jackson S. Morrow
    Algebra & Number Theory 15-7 (2021), 1837--1864; DOI https://doi.org/10.2140/ant.2021.15.1837; arxiv, code

  6. Deligne--Illusie Classes as Arithmetic Kodaira--Spencer Classes
    with Taylor Dupuy
    Journal de Theorie des Nombres de Bordeaux' 31 (2019), no. 2, 371--383; arxiv

  7. The canonical ring of a stacky curve
    with John Voight
    Mem. Amer. Math. Soc. 277 (2022), no. 1362; arxiv, eratta.

  8. Total p-differentials on schemes over Z/p2,
    with Taylor Dupuy, Eric Katz, Joseph Rabinoff;
    Journal of Algebra Volume 524 (2019) arxiv

  9. Chip-firing groups of iterated cones
    with Morgan Brown and Jackson S. Morrow
    Linear Algebra and its Applications, 556 (2018), 46--54; arxiv

  10. Diophantine and tropical geometry, and uniformity of rational points on curves
    with Eric Katz and Joe Rabinoff
    2015 Summer Research Insitute on Algebraic Geometry Proceedings
    Proceedings of Symposia in Pure Mathematics, Volume 97.2, 2018; arxiv

  11. Uniform bounds for the number of rational points on curves of small Mordell--Weil rank
    with Eric Katz and Joe Rabinoff
    Duke Math J. 165 (2016), no. 16, 3189--3240; arxiv, published version

  12. Elliptic curves over Q and 2-adic images of Galois
    with Jeremy Rouse
    Research in Number Theory, Volume 1, Issue 1, 2015 arxiv, code, published version

  13. A heuristic for the distribution of point counts for random curves over a finite field
    with Jeffrey D. Achter, Daniel Erman, Kiran S. Kedlaya, Melanie Matchett Wood
    Philosophical Transactions of the Royal Society A 373 (2015), arxiv,

  14. Formal GAGA for Good Moduli Spaces
    with Anton Geraschenko
    Algebraic Geometry, Volume 2, Issue 2, May 2015; arxiv, blog post (by Max Lieblich)

  15. Cohomological Descent on the Overconvergent Site
    RIMS, 2014, 1:8; arxiv, published version,

  16. Integral Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex
    with Christopher Davis
    MRL, 21 (2014), No 2.; arxiv, published version,

  17. The Chabauty-Coleman bound at a prime of bad reduction and Clifford bounds for Geometric Rank Functions
    with Eric Katz
    Compositio Mathematica 149 (2013), no. 11, arxiv, published version

  18. Random Dieudonn'e modules, random p-divisible groups, and random curves over finite fields
    with Bryden Cais and Jordan Ellenberg
    J. Math. Inst. Jussieu, 2013, arxiv, published version, code

  19. Primitive Integral Solutions to x^2 + y^3 = z^10
    IMRN 2012, no. 2, 423--436 arxiv, published version, code

  20. Rigid cohomology for algebraic stacks
    UC Berkeley thesis, 2010 pdf
  1. Cohomology with closed support on the overconvergent site; arxiv

Non-research publications
Early Career: How to balance research with everything else we have to do
Notices of the American Mathematical Society, May 2020
Videos of some of my talks

Miscellaneous advice

Other interesting math links