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Department of Mathematics


Alexander Duncan

Title: Assistant Professor
Department: Mathematics
College of Arts and Sciences
Phone: 803-777-7508
Office: LeConte 300F
Office Hours: Monday 10:30am-11:30am
Wednesday 10:30am-12:30pm
Resources: My Website
Curriculum Vitae [pdf]

Department of Mathematics
Alexander Duncan


Ph.D. Mathematics University of British Columbia 2011
M.Sc. Mathematics University of British Columbia 2007
H.B.Sc. Mathematics & Physics University of Toronto 2005


2015 - Present Assistant Professor University of South Carolina
2012 - 2015 Postdoctoral Assistant Professor University of Michigan, Ann Arbor
2011 - 2012 Assistant Adjunct Professor University of California, Los Angeles

Courses Taught:

  • Math 141: Calculus I
  • Math 142: Calculus II
  • Math 300: Transition to Advanced Mathematics
  • Math 546: Algebraic Structures I
  • Math 548: Geometry, Algebra, and Algorithms
  • Matt 701: Algebra I
  • Matt 701: Algebra II
  • Math 742: Representation Theory
  • Math 747: Algebraic Geometry


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.

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.


Challenge the conventional. Create the exceptional. No Limits.