dzureickbrown@amherst.edu
Department of Mathematics and Statistics
Amherst College
Office: Seeley Mudd 502
Phone: (413) 542-2595
Fall 2024 Courses
- TuTh 10-11:20am, and 1-2:20: Math 280, Graph Theory
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
- There are currently three Ph.D. students working with me.
- CV (Curriculum vitae)
- Research Interests
- Travel Schedule
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-2430098)
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): 1-17, arxiv, published version,
- 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,
- 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
- 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
- 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
- The canonical ring of a stacky curve
with John Voight
Mem. Amer. Math. Soc. 277 (2022), no. 1362; arxiv, eratta.
- Total p-differentials on schemes over Z/p2,
with Taylor Dupuy, Eric Katz, Joseph Rabinoff;
Journal of Algebra Volume 524 (2019) arxiv
- Chip-firing groups of iterated cones
with Morgan Brown and Jackson S. Morrow
Linear Algebra and its Applications, 556 (2018), 46--54; 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 Mordell--Weil rank
with Eric Katz and Joe Rabinoff
Duke Math J. 165 (2016), no. 16, 3189--3240; arxiv, published version
- 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
- 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 Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex
with Christopher Davis
MRL, 21 (2014), No 2.; arxiv, published version,
- 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
- 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
- Primitive Integral Solutions to x^2 + y^3 = z^10
IMRN 2012, no. 2, 423--436 arxiv, published version, code
- Rigid cohomology for algebraic stacks
UC Berkeley thesis, 2010 pdf
- 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
- Diophantine and Tropical Geometry,
Colloquium at The Ohio State University
- ell-adic Images of Galois for Elliptic Curves over Q,
at the 2023 Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting. (My talk is at the bottom of the page.)
- Abelian Chabauty and Tropical Geometry,
a lecture series at the 2020 Arizona Winter School
- "Moduli spaces and arithmetic statistics"
at VaNTAGe
- "Counting points, counting fields, and heights on stacks"
at BIRS Oaxaca Workshop on Arithmetic Aspects of Explicit Moduli Problems"
- Progress on Mazur's Program B
at "Rational points on irrational varieties"
- Progress on Mazur's Program B
at BIRS Workshop on "Arithmetic Aspects of Explicit Moduli Problems"
- "Rational points on curves and tropical geometry"
at BIRS Workshop on "Specialization of Linear Series for Algebraic and Tropical Curves"
Miscellaneous advice
- (OLD) Advice for prospective graduate students in Arithmetic geometry
- My experience learning
Other interesting math links