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. (Submitted)

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. Versality of algebraic group actions and rational points on twisted varieties. J. Algebraic Geom. 24 (2015), 499--530

A. Duncan, Z. Reichstein. Pseudo-reflection groups and essential dimension. J. London Math. Soc. (2014) 90 (3): 879-902.

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

A. Duncan. Essential dimensions of A7 and S7. 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[V2 ⊕ V2 ⊕ V3]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