## 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

A. Duncan. Equivariant unirationality of del Pezzo surfaces of degree 3 and 4. (Preprint)

A. Duncan. Twisted forms of toric varieties. (Submitted)

I. Dolgachev, A. Duncan. Fixed points of a finite subgroup of the plane Cremona group. (Submitted)

A. Duncan,
Z. Reichstein.
Pseudo-reflection groups and essential dimension.
To appear in *J. Lond. Math. Soc.*

A. Duncan,
Z. Reichstein.
Versality of algebraic group actions
and rational points on twisted varieties.
To appear in *J. Algebraic Geom.*

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

A. Duncan.
Essential dimensions of A_{7} and S_{7}.
*Math. Res. Lett.* 17 (2010), no. 2, 263-266.

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

A. Duncan,
M. LeBlanc,
D. L. Wehlau.
A SAGBI Basis for F[V_{2} ⊕ V_{2} ⊕ V_{3}]^{Cp}.
*Canad. Math. Bull.* 52 (2009), no. 1, 72-83.

## Teaching

(See CTools for course materials).

Fall 2014 - Math 217/008

Fall 2014 - Math 217/001

Fall 2013 - Math 217/006

Fall 2013 - Math 217/005

Winter 2013 - Math 217/001

Fall 2012 - Math 115/016