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

Regular pairs of quadratic forms on odd-dimensional spaces in characteristic 2
(with I. Dolgachev) Submitted.

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

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