Publications


Average bounds for the $\ell$-torsion in class groups of cyclic extensions, (with Christopher Frei), submitted. preprint

Bounds for the $\ell$-torsion in class groups, Bull. Lond. Math. Soc. doi:10.1112/blms.12113. preprint

Weakly admissible lattices, o-minimality, and lattice point counting, Oberwolfach Reports (2017), preliminary_OWR_2017_18.pdf.

Northcott Number and Undecidability of certain Algebraic Rings, Oberwolfach Reports (2016), preliminary_OWR_2016_49.pdf. 

Weakly admissible lattices, primitive points, Diophantine approximation, and o-minimality, submitted. preprint

On a Counting Theorem of Skriganov, (with Niclas Technau), submitted. preprint

Property (N), Decidability, and Diophantine Approximation, Oberwolfach Reports (2016), preliminary_OWR_2016_21.pdf.

Weakly admissible lattices and primitive points, Oberwolfach Reports (2016), OWR_2016_03.pdf.

Asymptotic Diophantine approximation: The multiplicative case, Ramanujan J, (2017), Vol. 43, Issue 1, 83-93. preprint

Integral points of fixed degree and bounded height, Int. Math. Res. Notices, (2016), Vol. 2016, 3906-3943. preprint

Number fields without small generators, (with Jeffrey D. Vaaler)Math. Proc. Cam. Philos. Soc. 159 (2015), no. 3, 379-385. preprint

Schanuel's Theorem for heights defined via extension fields, (with Christopher Frei), Ann. Sc. Norm. Super. Pisa Cl. Sci., Vol. XV (2016), 355-398, 2016. preprint

Counting lattice points and o-minimal structures, (with Fabrizio Barroero), Int. Math. Res. Notices (2014), Vol. 2014, 4932-4957. preprint

On the Northcott property and other properties related to polynomial mappings, (with Sara Checcoli), Math. Proc. Cam. Philos. Soc. 155 (2013), no. 1, 1-12. preprint

Counting points of fixed degree and given height over function fields, (with Jeffrey Lin Thunder), Bull. Lond. Math. Soc. 45  (2013), no. 2, 283-300. preprint

A note on small generators of number fields, (with Jeffrey D. Vaaler), Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms, Contemporary Mathematics, vol. 587, Amer. Math. Soc., Providence, RI, 2013. preprint

A generalization of Schanuel's Theorem, (with Christopher Frei), Oberwolfach Reports (2012), no. 22/2012.

Lipschitz class, narrow class, and counting lattice points, Proc. Amer. Math. Soc. 140  (2012), no. 2, 677-689. preprint

On certain infinite extensions of the rationals with Northcott propertyMonatsh. Math. 162 (2011), no. 3, 341-353. preprint

Small generators of function fieldsJ. Theor. Nombres Bordeaux 22, (2010), no. 3, 544-551. preprint

On number fields with  nontrivial subfieldsInt.  J. Number Theory 7,  (2011), no. 3, 695-720. preprint

Counting points of fixed degree and bounded height on linear varietiesJ. Number Theory 130 (2010), no. 8, 1763-1784. preprint

Counting points of fixed degree and bounded height, Acta Arith. 140 (2009), no. 2, 145-168. preprint

Counting primitive points of bounded heightTrans. Amer. Math. Soc. 362 (2010), no. 9, 4793-4829. preprint



In progress