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

Finite quasisimple groups acting on rationally connected threefolds
(with J. Blanc, I. Cheltsov, and Yu. Prokhorov) (Preprint)

Automorphisms of cubic surfaces in positive characteristic
(with I. Dolgachev) (To appear in Izvestiya: Mathematics)

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

The toric Frobenius morphism and a conjecture of Orlov
(with M. Ballard and P. McFaddin) (To appear in Eur. J. Math.)

Regular pairs of quadratic forms on odd-dimensional spaces in characteristic 2
(with I. Dolgachev)
Algebra Number Theory 12 (2018), no. 1, 99-130.

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 2018 - Math 546 - Section 001

Fall 2018 - Math 142 - Section H01

Spring 2018 - Math 548 - Section 001

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