Research Interests

Dr. Duncan studies algebraic geometry and its connections to algebra and number theory.  In particular, he takes advantage of symmetry to study the solutions of systems of polynomial equations.  He has made important contributions to the study of toric varieties, del Pezzo surfaces, and essential dimension.  Dr. Duncan is internationally renowned and has been invited to speak on more than 40 occasions in 10 countries on 4 continents.  He has been funded by both the National Security Agency and the Simons Foundation.

Education

• Ph.D. in Mathematics, University of British Columbia (2011)
• M.Sc. in Mathematics, University of British Columbia (2007)
• H.B.Sc. in Mathematics & Physics, University of Toronto (2005)

Experience

• Associate Professor, University of South Carolina (2020 – Present)
• Assistant Professor, University of South Carolina (2015 – 2020)
• Postdoctoral Assistant Professor, University of Michigan, Ann Arbor (2012 –2015)
• Assistant Adjunct Professor, University of California, Los Angeles (2011 – 2012)

Courses Taught

• MATH 141: Calculus I
• MATH 142: Calculus II
• MATH 300: Transition to Advanced Mathematics
• MATH 546: Algebraic Structures I
• MATH 547: Algebraic Structures II
• MATH 548: Geometry, Algebra, and Algorithms
• MATH 580: Elementary Number Theory
• MATH 701: Algebra I
• MATH 701: Algebra II
• MATH 742: Representation Theory
• MATH 746: Commutative Algebra
• MATH 747: Algebraic Geometry
• MATH 748: Topics in Algebra - Galois Cohomology
• MATH 748: Topics in Algebra - Computational Algebra

Selected Publications

• I. Dolgachev and A. Duncan. Automorphisms of cubic surfaces in positive characteristic. Izv. Math. 83 (2019), no. 3, 15–92.
• I. Dolgachev and A. Duncan. Regular pairs of quadratic forms on odd-dimensional spaces in characteristic 2. Algebra Number Theory 12 (2018), no. 1, 99–130.
• A. Duncan. Twisted forms of toric varieties. Transform. Groups 21 (2016), no. 3, 763–802.
• A. Duncan and Z. Reichstein. Versality of algebraic group actions and rational points on twisted varieties. J. Algebraic Geom. 24 (2015), 499–530.
• A. Duncan. Finite groups of essential dimension 2. Comment. Math. Helv. 88 (2013), no. 3, 555–585.