June 28-30:

Algebraic Groups and Algebraic Geometry:

In honor of Zinovy Reichstein's 60th Birthday


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

Consequences of the existence of exceptional collections in arithmetic and rationality
(with M. Ballard, A. Lamarche, and P. McFaddin) (Preprint)

Separable algebras and coflasque resolutions
(with M. Ballard, A. Lamarche, and P. McFaddin) (Preprint)

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

Birational self-maps of threefolds of (un)-bounded genus or gonality
(with J. Blanc, I. Cheltsov, and Yu. Prokhorov) Amer. J. Math. (To Appear).

Derived categories of centrally-symmetric smooth toric Fano varieties
(with M. Ballard and P. McFaddin) Math. Nachr. (To Appear)

On derived categories of arithmetic toric varieties
(with M. Ballard and P. McFaddin) Ann. K-Theory 4 (2019), no. 2, 211-242.

Automorphisms of cubic surfaces in positive characteristic
(with I. Dolgachev) Izv. Math. 83 (2019), no. 3, 424-500.

The toric Frobenius morphism and a conjecture of Orlov
(with M. Ballard and P. McFaddin) Eur. J. Math. 5 (2019), no. 3, 640-645.

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

Most course materials can be found on Blackboard.

Spring 2021 - Math 300 - Section H01

Spring 2021 - Math 746 - Section 001

Fall 2020 - Math 748 - Section 001

Fall 2020 - Math 142 - Sections 011/012/031/032

Spring 2020 - Math 748 - Sections 001

Spring 2020 - Math 547 - Section H01

Fall 2019 - Math 546 - Section H01

Fall 2019 - Math 141 - Sections 007/008/027/028/SL1

Spring 2019 - Math 747 - Section 001

Spring 2019 - Math 300 - Section 001

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