## 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 A _{7} and S_{7}**

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[V _{2} ⊕ V_{2} ⊕
V_{3}]^{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