Doug Torrance

Research

Interests

• Algebraic geometry
• Commutative algebra
• Graph theory

Software

I am an active developer of Macaulay2 and member of the M2internals group. I am also a Debian Developer and maintain Macaulay2 and other related mathematics software for Debian.

Links

• arXiv
• Google Scholar
• MathSciNet
• Mathematics Genealogy Project (my tree, generated with geneagrapher)
• Erdős number: 4
• GitHub

Papers

• Geometry of first nonempty Terracini loci, (with Francesco Galuppi, Pierpaola Santarsiero, and Ettore Teixeira Turatti), submitted. (arXiv, code)
• Probability package for Macaulay2, to appear in J. Softw. Algebra Geom. (arXiv, code)
• Almost all subgeneric third-order Chow decompositions are identifiable, (with Nick Vannieuwenhoven), Ann. Mat. Pura Appl. (4) 201 (2022), no. 6, 2891–2905. (arXiv, certificates)
• All secant varieties of the Chow variety are nondefective for cubics and quaternary forms, (with Nick Vannieuwenhoven), Trans. Amer. Math. Soc. 374 (2021), no. 7, 4815-4838. (arXiv, certificates - cubics, quaternary forms)
• Enumeration of planar Tangles, Proc. Math. Sci. 130, 50 (2020). (arXiv, code)
• Generic forms of low Chow rank, J. Algebra Appl. 16 (2017), no. 3, 1750047, 10 pp. (arXiv)
• Castelnuovo-Mumford regularity and arithmetic Cohen-Macaulayness of complete bipartite subspace arrangements (with Zach Teitler), J. Pure Appl. Algebra 219 (2015), no. 6, 2134–2138. (arXiv)
• Nondefective secant varieties of varieties of completely decomposable forms, Ph.D. thesis, University of Idaho (2013) (arXiv)

Slides

• Semiregular Tangles
  • MAA Southeastern Section Meeting, University of Tennessee, March 15, 2024
• RInterface package
  • M2internals, December 18, 2023
• Installing and using Macaulay2
  • MAAG, Georgia Tech, April 16, 2023
• An exponential bound for nondefective secant varieties of Chow varieties
  • AMS Southeastern Section Spring Meeting, Georgia Tech, March 18, 2023
• Triangular and hexagonal Tangles
  • MAA Southeastern Section Meeting, Coastal Carolina University, March 10, 2023
• Induction and secant varieties to Chow varieties
  • AGATES: Geometry of secants workshop, IMPAN, Warsaw, Poland, October 26, 2022
• Best of Macaulay2 crashes
  • M2internals, September 2, 2021
• The Chow-Waring problem
  • University of Idaho Mathematics Colloquium, Virtual, April 15, 2021
• Enumeration of planar Tangles
  • MAA Southeastern Section Meeting, Virtual, March 6, 2021
• All secant varieties of the Chow variety are nondefective for cubics and quaternary forms
  • AMS Southeastern Section Fall Meeting, Virtual, October 10, 2020
• Macaulay2 in Debian
  • M2internals #2, June 26, 2020
• Biconal subspace arrangements
  • MAA Southeastern Section Meeting, Lee University, March 8, 2019
• Toy trains and polyplets
  • MAA Southeastern Section Meeting, Clemson University, March 23, 2018
• Generic forms of low Chow rank
  • AMS Central Section Spring Meeting, The Ohio State University, March 18, 2018 (as The Chow-Waring problem)
  • Joint Mathematics Meetings, Atlanta, GA, January 6, 2017
  • AMS Southeastern Section Spring Meeting, University of Georgia, March 5, 2016
• Properties of complete bipartite codimension two subspace arrangements
  • Joint Mathematics Meetings, Baltimore, MD, January 15, 2014
  • AMS Central Section Fall Meeting, University of Nebraska-Lincoln, October 16, 2011 (as Regularity of (n-2)-plane arrangements in Pⁿ with a complete bipartite incidence graph)
• Nondefective secant varieties of varieties of completely decomposable forms
  • Ph.D. defense, University of Idaho, April 30, 2013