Jacob P. Matherne


You can find my works on the arXiv here.

My Google Scholar page is here.

Published papers


  1. Poincaré polynomials associated to geometric lattices.
    Oberwolfach report for workshop "Arrangements, Matroids and Logarithmic Vector Fields" 2024, Workshop 2425, Report No. 29.
    pdf | doi

  2. (with L. Ferroni, M. Stevens, and L. Vecchi) Hilbert–Poincaré series of matroid Chow rings and intersection cohomology.
    Advances in Mathematics (Adv. Math.) 2024, 449, Paper No. 109733.
    pdf | doi | arXiv

  3. (with T. Braden and N. Proudfoot) What is the Dowling–Wilson conjecture?
    Notices of the American Mathematical Society (Not. Am. Math. Soc.) October 2024, Volume 71, No. 9, 1197-1201.
    pdf | doi

  4. (with A. Morales and J. Selover) The Newton polytope and Lorentzian property of chromatic symmetric functions.
    Selecta Mathematica (Sel. Math. New Ser.) 2024, Volume 30, article number 42.
    pdf | doi | arXiv
    Update: Ricky Liu and Cynthia Vinzant found a counterexample to Conjecture 6.3 at n=8.

  5. (with P. Anderson and J. Tymoczko) Generalized splines on two-labeled graphs and polynomial splines on cycles.
    Electronic Journal of Combinatorics (EJC) 2024, Volume 31, Issue 1, P1.29.
    pdf | doi | arXiv

  6. A large class of conjecturally stable chromatic symmetric functions.
    MATRIX Annals, MATRIX Program: Theory and Applications of Stable Polynomials 2021–2022.
    doi
    Update: Ricky Liu and Cynthia Vinzant found a counterexample to Conjecture 2 (= Conjecture 6.3 in Published Paper #4 above) at n=8.

  7. (with L. Ferroni, M. Stevens, and L. Vecchi) Hilbert–Poincaré series of matroid Chow rings and intersection cohomology.
    Séminaire Lotharingien de Combinatoire (SLC) 89B.36 FPSAC'23, 12 pp.
    pdf | doi
    Note: This is the FPSAC Proceedings for Published Paper #2 above.

  8. (with T. Braden, J. Huh, N. Proudfoot, and B. Wang) A semi-small decomposition of the Chow ring of a matroid.
    Advances in Mathematics (Adv. Math.) 2022, 409A, Paper No. 108646.
    video | slides (handwritten) | pdf | doi | arXiv

  9. (with M. Kulkarni, N. Livesay, B. Nguyen, and D. Sage) The Deligne–Simpson problem for connections on G_m with a maximally ramified singularity.
    Advances in Mathematics (Adv. Math.) 2022, 408, Paper No. 108596.
    pdf | doi | arXiv

  10. (with D. Miyata, N. Proudfoot, and E. Ramos) Equivariant log concavity and representation stability.
    International Mathematics Research Notices (IMRN) 2021, rnab352.
    pdf | doi | arXiv | code

  11. (with A. Garver, S. Grosser, and A. Morales) Counting linear extensions of posets with determinants of hook lengths.
    SIAM Journal on Discrete Mathematics (SIDMA) 35 2021, no. 1, 205-233.
    pdf | doi | arXiv

  12. (with A. Garver, S. Grosser, and A. Morales) Counting linear extensions of posets with determinants of hook lengths.
    Séminaire Lotharingien de Combinatoire (SLC) 85B.60 FPSAC'21, 12 pp.
    pdf | doi
    Note: This is the FPSAC Proceedings associated to the expanded version of the article above.

  13. (with J. Huh, K. Mészáros, and A. St. Dizier) Logarithmic concavity of Schur and related polynomials.
    Transactions of the American Mathematical Society, 375, June 2022, no. 6, 4411-4427.
    slides | pdf | doi | arXiv | code

  14. (with A. Garver, K. Igusa, and J. Ostroff) Combinatorics of exceptional sequences in type A.
    Electronic Journal of Combinatorics (EJC) 2019, 1-20.
    pdf | doi | arXiv

  15. (with A. Garver) A combinatorial model for exceptional sequences in type A.
    Discrete Mathematics & Theoretical Computer Science DMTCS proc. FPSAC'15, 393-404.
    pdf | doi | arXiv
    Note: pdf and arXiv are expanded versions of the FPSAC extended abstract in doi.

  16. (with G. Muller) Computing upper cluster algebras.
    International Mathematics Research Notices (IMRN) 2015, 3121-3149.
    pdf | doi | arXiv | code (on SageMath)

Preprints


  1. (with L. Ferroni and L. Vecchi) Chow functions for partially ordered sets.
    preprint.
    pdf | arXiv

  2. (with L. Ferroni and L. Vecchi) Deletion formulas for equivariant Kazhdan–Lusztig polynomials of matroids.
    submitted.
    pdf | arXiv

  3. (with M. Kulkarni, K. Mousavand, and J. Rock) A continuous associahedron of type A.
    submitted.
    pdf | arXiv

  4. (with T. Braden, J. Huh, N. Proudfoot, and B. Wang) Singular Hodge theory for combinatorial geometries.
    submitted.
    video | slides 1 | slides 2 | poster | pdf | arXiv

  5. (with E. Bucher, C. Eppolito, and J. Jun) Matroid-minor Hopf algebra: a cancellation-free antipode formula and other applications of sign-reversing involutions.
    submitted.
    pdf | arXiv

  6. (with P. Achar and M. Kulkarni) Combinatorial Fourier transform for quiver representation varieties in type A.
    submitted.
    slides | poster | arXiv

  7. (with E. Bucher) A cancellation-free antipode formula for the restriction-contraction matroid Hopf algebra.
    preprint.
    pdf | arXiv
    Not intended for publication (subsumed by Preprint 5 above).

  8. Derived Geometric Satake equivalence, Springer correspondence, and small representations.
    This is my dissertation work.
    dissertation | slides