
Fall 2024 Courses
Old course webpages
Seminars
 Amherst College
Colloquium
(Time and location variable)
 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 DMS2430098)
Publications
 A predicted distribution for Galois groups of maximal unramified extensions
with Yuan Liu and Melanie Matchett Wood
accepted for publication in Inventiones mathematicae,
arxiv
 Angle Ranks of Abelian Varieties
with Taylor Dupuy and Kiran S. Kedlaya
Mathematische Annalen (2023): 117,
arxiv,
published version,
 Heights on stacks and a generalized BatyrevManinMalle conjecture
with Jordan S. Ellenberg and Matthew Satriano
Forum of Mathematics, Sigma, Volume 11, 2023;
arxiv
published version,
 elladic 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
 Sporadic Cubic Torsion
with Maarten Derickx, Anastassia Etropolski, Mark van Hoeij, and Jackson S. Morrow
Algebra & Number Theory 157 (2021), 18371864;
DOI https://doi.org/10.2140/ant.2021.15.1837;
arxiv,
code
 DeligneIllusie Classes as Arithmetic KodairaSpencer Classes
with Taylor Dupuy
Journal de Theorie des Nombres de Bordeaux' 31 (2019), no. 2, 371383;
arxiv
 The canonical ring of a stacky curve
with John Voight
Mem. Amer. Math. Soc. 277 (2022), no. 1362;
arxiv,
eratta.
 Total pdifferentials on schemes over Z/p2,
with Taylor Dupuy, Eric Katz, Joseph Rabinoff;
Journal of Algebra Volume 524 (2019)
arxiv
 Chipfiring groups of iterated cones
with Morgan Brown and Jackson S. Morrow
Linear Algebra and its Applications, 556 (2018), 4654;
arxiv
 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
 Uniform bounds for the number of rational points on curves of small MordellWeil rank
with Eric Katz and Joe Rabinoff
Duke Math J. 165 (2016), no. 16, 31893240;
arxiv,
published version
 Elliptic curves over Q and 2adic images of Galois
with Jeremy Rouse
Research in Number Theory, Volume 1, Issue 1, 2015
arxiv,
code,
published version
 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,
 Formal GAGA for Good Moduli Spaces
with Anton Geraschenko
Algebraic Geometry, Volume 2, Issue 2, May 2015;
arxiv,
blog post (by Max Lieblich)
 Cohomological Descent on the Overconvergent Site
RIMS, 2014, 1:8;
arxiv,
published version,
 Integral MonskyWashnitzer cohomology and the overconvergent de RhamWitt complex
with Christopher Davis
MRL, 21 (2014), No 2.;
arxiv,
published version,
 The ChabautyColeman 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
 Random Dieudonn'e modules, random pdivisible groups, and random curves over finite fields
with Bryden Cais and Jordan Ellenberg
J. Math. Inst. Jussieu, 2013,
arxiv,
published version,
code
 Primitive Integral Solutions to x^2 + y^3 = z^10
IMRN 2012, no. 2, 423436
arxiv,
published version,
code
 Rigid cohomology for algebraic stacks
UC Berkeley thesis, 2010
pdf
Unpublished
 Cohomology with closed support on the overconvergent site;
arxiv
Nonresearch 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
