Research

I am an algebraic geometer who uses geometric techniques to study problems in number theory and algebra. I have interests in birational geometry, rational surfaces, toric varieties, Galois cohomology, and essential dimension.

Publications and Preprints

The toric Frobenius morphism and a conjecture of Orlov
(with M. Ballard and P. McFaddin) (Preprint)

On derived categories of arithmetic toric varieties
(with M. Ballard and P. McFaddin) (Preprint)

Regular pairs of quadratic forms on odd-dimensional spaces in characteristic 2
(with I. Dolgachev) (To appear in Algebra & Number Theory)

Equivariant unirationality of del Pezzo surfaces of degree 3 and 4
Eur. J. Math. 2 (2016), no. 4, 897-916.

Twisted forms of toric varieties
Transform. Groups 21 (2016), no. 3, 763-802.

Fixed points of a finite subgroup of the plane Cremona group
(with I. Dolgachev) Algebr. Geom. 3 (2016), no. 4, 441-460.

Versality of algebraic group actions and rational points on twisted varieties
(with Z. Reichstein) J. Algebraic Geom. 24 (2015), 499-530.

Pseudo-reflection groups and essential dimension
(with Z. Reichstein) J. London Math. Soc. 90 (2014), no. 3, 879-902.

Finite groups of essential dimension 2
Comment. Math. Helv. 88 (2013), no. 3, 555-585.

Essential dimensions of A7 and S7
Math. Res. Lett. 17 (2010), no. 2, 263-266.

SAGBI bases in rings of invariant Laurent polynomials
(with Z. Reichstein) Proc. Amer. Math. Soc. 137 (2009), no. 3, 835-844.

A SAGBI Basis for F[V2 ⊕ V2 ⊕ V3]Cp
(with M. LeBlanc and D. L. Wehlau) Canad. Math. Bull. 52 (2009), no. 1, 72-83.

Teaching

Spring 2018 - Math 548 - Section 001 (New course!)

Fall 2017 - Math 142 - Sections 003-006

Spring 2017 - Math 702 - Section 001

Fall 2016 - Math 701 - Section 001

Fall 2016 - Math 142 - Section H03

Spring 2016 - Math 742 - Section 001

Spring 2016 - Math 300 - Section 002

Fall 2015 - Math 141 - Sections 13/14