picture of jesse
enjoying Royal National Park
(despite the bug in my right eye)
I am a mathematician studying singularities in commutative algebra (i.e., local algebraic geometry) and modular representation theory using homological algebra. My recent work has centered on Koszul duality. See the research page for more information.
Recently I have been working at the University of Sydney to create interactive 3D web apps for undergraduate maths courses.


Google Scholar profile


  1. Gluing approximable triangulated categories
    with Amnon Neeman and Bregje Pauwels. Submitted, 18 pages.

  2. Transfer of A-infinty structures to projective resolutions
    Preprint, 20 pages.

  3. Strictly unital A-infinty algebras
    Journal of Pure and Applied Algebra, Dec. 2018, 26 pages.

  4. Golod rings and higher homotopies
    Preprint, 26 pages.

  5. The derived category of a graded Gorenstein ring
    with Greg Stevenson. Commutative Algebra and Noncommutative Algebraic Geometry, Volume II: Research Articles, MSRI Publications 68, 2015, 93-123.

  6. Building modules from the singular locus
    with Lars Winther Christensen and Ryo Takahashi.
    Math Scand., 116 (2015) no. 1, 23-33.

  7. Matrix factorizations in higher codimension
    with Mark Walker. Transaction of the AMS, 367 (2015), 3323-3370.

  8. Matrix factorizations over projective schemes
    with Mark Walker. Homology, Homotopy, and Applications, Vol. 14 (2012), No. 2, pp.37-61.

  9. The cone of Betti diagrams over a hypersurface ring of low embedding dimension
    (with Christine Berkesch, Daniel Erman, and Courtney Gibbons). Journal of Pure and Applied Algebra, 216 (2012), 2256-2268.

  10. Finite injective dimension over rings with Noetherian cohomology
    Mathematical Research Letters, Vol. 19 (2012), No. 4, 741-752.

Math apps


Resume (pdf) Academic CV (pdf)


Github account LinkedIn
Email: jesse.burke (at) sydney.edu.au
Office: 829 Carslaw