John D. Wiltshire-Gordon

For the academic year 2020-2021, I was a Visiting Assistant Professor at Williams College. Previously, I was a post-doctoral fellow at the University of Wisconsin, Madison working with Jordan Ellenberg. Fall of 2016 I was a post-doc at ICERM. I have accepted a non-academic job. Here is my CV.

I study the representation theory of categories with applications in algebraic topology. I like configuration spaces, category theory, and computer algebra.

The prototypical situation: a category C acts on a collection of spaces X_c by transformations, and so the induced maps on homology form a C-module. My thesis, completed in 2016 at the University of Michigan under David Speyer, gives theory and algorithms for working with C-modules. I explain how to write a C-module using a presentation matrix and how to use that matrix to compute numbers associated to the module.


  • ExactCouples -- spectral sequences by Massey's method of exact couples; a Macaulay2 package
  • Papers

    Click a title to visit arXiv.

    In preparation

    1. Configuration spaces of axis-aligned boxes. In preparation. (with Maya Banks)


    1. On the tails of FI-modules. September 2019. (with Peter Patzt)
    2. Configuration space of a product. August 2018.
    3. Algebraic structures on cohomology of configuration spaces of manifolds with flows. August 2015. (with Jordan S. Ellenberg)
    4. Uniformly Presented Vector Spaces. June 2014.


    1. On computing the eventual behavior of an FI-module over the rational numbers. Math. Comp. 89 (2020), no. 326, 2985--3001.
    2. Models for Configuration Space in a Simplicial Complex. Colloq. Math., 155(1):127–139, 2019.
    3. Specht Polytopes and Specht Matroids. January 2017. (with Alexander Woo and Magdalena Zajaczkowska) Combinatorial algebraic geometry, 201–228, Fields Inst. Commun.
    4. Categories of Dimension Zero. Proc. Amer. Math. Soc. 147 (2019), pp. 35-50.
    5. Robust coin flipping. Advances in cryptology—EUROCRYPT 2012, 172–194, Lecture Notes in Comput. Sci., 7237, Springer, Heidelberg, 2012. (with Gene S. Kopp)

    Unpublished notes

    1. Word-Induced Measures on Compact Groups. February 2011. (with Gene S. Kopp)


    1. November 5, 2019. Boston, MA. Northeastern University Topology Seminar
    2. October 8, 2019. Ithaca, NY. Cornell U. topology seminar
    3. July 1, 2019. Berkeley, CA. Representation Stability Summer School
    4. April 28, 2019. Chicago, IL. Midwest Representation Stability Research Meeting
    5. April 11, 2019. Ann Arbor, MI. U. of Michigan Math Club
    6. April 10, 2019. Ann Arbor, MI. U. of Michigan Geometry and Topology RTG Seminar
    7. March 12, 2019. Chicago, IL. U. of Chicago Geometry and Topology Seminar
    8. November 30, 2018. Madison, WI. U. Wisconsin Algebraic Geometry Seminar
    9. September 29, 2018. Syracuse, NY. Route 81 conference
    10. August 14, 2018. Ann Arbor, MI. Michigan Representation Stability Week
    11. April 14, 2018. Madison, WI. Macaulay2 workshop
    12. March 28, 2018. West Lafayette, IN. Purdue Topology Seminar
    13. March 26, 2018. Indianapolis, IN. IUPUI Topology Seminar
    14. January 17, 2018. Oberwolfach, Germany. MFO workshop on Topology of Arrangements and Representation Stability. Slides
    15. December 11, 2017. Madison, WI. East High School
    16. April 24, 2017. Madison, WI. U. Wisconsin Combinatorics Seminar.
    17. April 2, 2017. Bloomington, IN. AMS Sectional Meeting.
    18. March 27, 2017. Madison, WI. Madison Math Circle
    19. November 14, 2016. Providence, RI. Brown U. Algebra Seminar.
    20. July 1, 2016. San Jose, CA. AIM workshop on Representation Stability.
    21. April 6, 2016. Banff, AB. BIRS workshop on Free Resolutions, Representations, and Asymptotic Algebra. Slides Video
    22. December 4, 2015. Cambridge, MA. MIT Infinite-Dimensional Algebra Seminar.
    23. November 18, 2015. West Lafayette, IN. Purdue U. Geometry and Topology Seminar.
    24. November 11, 2015. Chicago, IL. U. of Chicago Geometry and Topology Seminar.
    25. October 14, 2015. East Lansing, MI. Michigan State U. Geometry and Topology Seminar.
    26. October 4, 2015. Chicago, IL. AMS Special Session on Combinatorial and Geometric Representation Theory. Slides
    27. April 24, 2015. Minneapolis, MN. U. of Minnesota Combinatorics Seminar. Slides
    28. November 17, 2014. Houston, TX. Rice U. Topology Seminar.
    29. November 3, 2014. Berkeley, CA. UC Berkeley Combinatorics Seminar.
    30. October 28, 2014. Stanford, CA. Stanford U. Topology Seminar.
    31. October 2, 2014. Ann Arbor, MI. U. of Michigan Topology Seminar.
    32. February 3, 2014. Los Angeles, CA. U. of Southern California Algebra Seminar.
    33. January 17, 2014. Ann Arbor, MI. U. of Michigan Combinatorics Seminar.
    34. April 16, 2012. Cambridge, United Kingdom. EUROCRYPT 2012. YouTube