Here is the long version of my research statement, updated November 2016.

My papers and preprints:

Slicing the stars: Counting algebraic numbers, integers, and units by degree and height (with Joseph Gunther) To appear in Algebra and Number Theory preprint (revised) arXiv

Relative Bogomolov extensions Acta Arithmetica 170 (2015), no. 1, 1-13. preprint (revised) arXiv

Small points and free abelian groups (with Philipp Habegger and Lukas Pottmeyer) International Mathematics Research Notices 2015, no. 20, 10657-10679. link to free download arXiv

On the compositum of all degree d extensions of a number field (with Itamar Gal) J. Théor. Nombres Bordeaux 26 (2014) no. 3, 655-672 link preprint arXiv

Congruences for Ramanujan's f and ω functions via generalized Borcherds products (with Jen Berg, Abel Castillo, Vítězslav Kala, Richard Moy, and Chongli Wang -- project from the 2013 Arizona Winter School) Ramanujan J. 35 (2014), no. 2, 327-338 download here preprint arXiv

Here are some tables I made which give the orders and minimal permutation degrees for all of the finite simple groups of Lie type. I could not find this information all in one place.