## Papers

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Weighted average of class numbers for quadratic fields, with
Kevin McGown,
Jennifer Park, and
Frank Thorne,
in preparation.

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
Jennifer Balakrishnan,
Nathan Kaplan,
Simon Spicer,
William Stein, and
James Weigandt,
*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.

Chemistry:

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.