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Weighted average of class numbers for quadratic fields, with
Jennifer Park, and
Galois closures for non-commutative rings and a geometric application, with Matt Satriano, in preparation.
Odd degree number fields with odd class number (previously titled "The mean number of 2-torsion elements in class groups of odd degree number fields arising from binary n-ic forms"), with Arul Shankar and Ila Varma, to appear in Duke Math J.
Databases of elliptic curves ordered by height and distributions of Selmer groups and ranks (arXiv version), with
William Stein, and
LMS J. Comput. Math. 19 (2016), issue A, 351-370.
The raw data for this project may be accessed here for now. We hope to make the plotting functions publicly accessible in the future.
Zeta functions of a class of Artin-Schreier curves with many automorphisms, with Irene Bouw, Beth Malmskog, Renate Scheidler, Padmavathi Srinivasan, and Christelle Vincent, Directions in Number Theory: Proceedings of the 2014 WIN3 Workshop, Springer, 2016, pp. 87-124.
Orbit parametrizations for K3 surfaces, with Manjul Bhargava and Abhinav Kumar, Forum of Mathematics, Sigma 4 (2016), e18 (86 pages).
[The arxiv version has some more hyperlinks in one of the figures, which might make the paper easier to navigate.]
Coregular spaces and genus one curves, with Manjul Bhargava, Cambridge Journal of Mathematics 4 (2016), no. 1, 1-119.
On the average sizes of Selmer groups in families of elliptic curves, with Manjul Bhargava.
How many rational points does a random curve have?, Bull. Amer. Math. Soc. 51 (2014), no. 1, 27-52.
[This is an expanded version of the notes in the Current Events Bulletin of the 2013 Joint Mathematics Meetings.]
Moduli of products of stable varieties (arXiv version), with Bhargav Bhatt, Zsolt Patakfalvi, and Christian Schnell, Compositio Mathematica 149 (2013), no. 12, 2036-2070.
Genus one curves and Brauer-Severi varieties (arXiv version), with Aise Johan de Jong, Mathematical Research Letters 19 (2012), no. 06, 1357-1359.
Orbit Parametrizations of Curves (Ph.D. thesis), available on ProQuest.
The m-step, same-step, and any-step competition graphs, Discrete Appl. Math. 152 (2005), no. 1-3, 159--175.
Haiyan Fan, Wei Ho, Scott A. Reid,
A time-of-flight mass spectrometric study of laser fluence dependencies in SnO2 ablation: implications for pulsed laser deposited tin oxide thin films, Int. J. Mass Spectrometry 230 (2003), 11--17.
Scott A. Reid, Wei Ho, and F. J. Lamelas, Pulsed Laser Ablation of Sn and SnO2 target: Neutral Composition, Energetics, and Wavelength Dependence, J. Phys. Chem. B 104 (2000), no. 22, 5324--5330.