Research

journal articles

  1. Simplicial complexes with many facets are vertex decomposable,, with Ritika Nair, Jay Schweig, Adam Van Tuyl, and Russ Woodroofe, preprint, 10 pages.
  2. Simple homotopy for flag simplicial complexes and contractible transformations on graphs,, with Takahiro Matsushita, preprint, 6 pages, submitted (2023). Also on the ArXiv here.
  3. Chip-firing and parking functions on hypergraphs,, with Timothy Blanton, Isabelle Hong, Suho Oh, and Jenny Zhu, preprint, 15 pages.
  4. Shellability of the poset of lattice path matroid quotients,, with Carolina Benedetti, Kolja Knauer, and Yupeng Li, preprint, 15 pages.
  5. Chip-firing and critical groups of signed graphs, with Matthew Cho, Ryota Inagaki, Suho Oh, Dylan Snustad, and Bailee Zacovic, preprint, 31 pages, submitted (2023). Also on the ArXiv here.
  6. Root polytopes, tropical types, and toric edge ideals, with Ayah Almousa and Ben Smith, preprint, 45 pages, submitted (2022). Also on the ArXiv here.
  7. Homomorphism complexes, reconfiguration, and homotopy for directed graphs, with Anurag Singh, European Journal of Combinatorics 110 (2023). Also on the ArXiv here.
  8. Minimal graphs for contractible and dismantlable properties, with Jesus F. Espinoza, Martın E. Frıas-Armenta, and Hector A. Hernandez, Discrete Math. 346, Iss. 10 (2023). Also on the ArXiv here.
  9. Random subcomplexes and Betti numbers of random edge ideals, with Andrew Newman, International Mathematics Research Notices 2023, Iss. 10, pp. 8832–8871 (2023). Also on the ArXiv here.
  10. Completing and extending shellings of vertex decomposable complexes, with Michaela Coleman, Nathan Geist, and Suho Oh, SIAM Journal on Discrete Math 36, Iss. 2 (2022). Also on the ArXiv here.
  11. ntegral flow and cycle chip-firing on graphs, with Eli Meyers, Raghav Samavedam, and Alex Yi, Annals of Combinatorics 25(3), pp. 595–616 (2021). Also on the ArXiv here.
  12. Bi-coned graphs, edge-rooted forests, and h-vectors of matroid complexes, with Preston Cranford, Evan Haithcock, Joshua Marsh, Suho Oh, and Anna Truman, preprint 2020, 20 pages, Electronic Journal of Combinatorics 28(4) (2021), #P4.31. Also on the ArXiv here.
  13. Extendable shellability for d-dimensional complexes on d+3 vertices, with Jared Culbertson, Dan Guralnik, and Peter Stiller, Electronic Journal of Combinatorics 27(3) (2020). Also on the ArXiv here.
  14. Exposed circuits, linear quotients, and chordal clutters, Journal of Combinatorial Theory, Series A, 177 (2021). Also on the ArXiv here.
  15. Trees, parking functions, and standard monomials of skeleton ideals, with Weston King, Australasian Journal of Combinatorics 81(1), (2021), pp. 126–151. Also on the ArXiv here.
  16. One-skeleta of G-parking function ideals: resolutions and standard monomials, preprint 2016, 22 pages, submitted. Also on the ArXiv here.
  17. Warmth and connectivity of edge spaces of graphs, with Ragnar Freij, Advances in Applied Math, 96 (2018) pp. 176–194. Also on the ArXiv here.
  18. Face rings of cycles, associahedra, and standard tableaux, Electronic Journal of Combinatorics, Volume 23, Issue 3 (2016) . Also on the ArXiv here.
  19. Cellular resolutions from mapping cones, with Fatemeh Mohammadi, Journal of Combinatorial Theory, Series A, 128 (2014), pp. 180–206. Also on the ArXiv here.
  20. Laplacian ideals, arrangements, and resolutions, with Raman Sanyal, Journal of Algebra Combinatorics, 40, Issue 3 (2014), pp. 805–822. Also on the ArXiv here.
  21. Tropical types and associated cellular resolutions, with Michael Joswig and Raman Sanyal, Journal of Algebra, 356 (2012), pp. 304–324. Also on the ArXiv here.
  22. Cellular resolutions of cointerval ideals, with Alexander Engstrom, Mathematische Zeitschrift, Volume 270, Issue 1 (2012), pp. 145-163. Also on the ArXiv here.
  23. Algebraic properties of edge ideals via combinatorial topology, with Alexander Engstrom, Electronic Journal of Combinatorics, Volume 16, Issue 2 (2009) (The Björner Festschrift volume). Also on the ArXiv here.
  24. Topology of Hom complexes and test graphs for bounding chromatic number, with Carsten Schultz, Israel Journal of Mathematics 187, Issue 1 (2012), pp. 371–417. Also on the ArXiv here.
  25. Hom complexes and homotopy theory in the category of graphsEuropean Journal of Combinatorics 30, Number 2 (2009), pp. 490–509. Also on the ArXiv here.
  26. The universality of Hom complexes of graphsCombinatorica 29, Iss. 4 (2009), pp. 433–448. Also on the ArXiv here.
  27. Homotopy groups of Hom complexes of graphs,  Journal of Combinatorial Theory, Series A Volume 116, Issue 1 (2009), pp. 180–194. Also on the ArXiv here.
  28. Graphs with disjoint links in every spatial embedding , with Stephen Chan, Joel Foisy, Jennifer Hespen, Eman Kunz, Trent Lalonde, Quincy Loney, Katherine Sharrow, and Nathan Thomas, J. Knot Theory Ramifications 13 no. 6 (2004), pp. 737–748.
  29. Some linking properties of spatially embedded graphs (undergrad thesis), available here.
  30.  

    conference proceedings

  31. Homomorphism complexes, reconfiguration, and homotopy for directed graphs, , with Anurag Singh, Formal Power Series and Algebraic Combinatorics (FPSAC) – DMTCS Proceedings (2022).
  32. Extending and completing shellings of vertex decomposable complexes, , with Michaela Coleman, Nathan Geist, and Suho Oh, Formal Power Series and Algebraic Combinatorics (FPSAC) – DMTCS Proceedings (2021).
  33. Hom complexes and homotopy in the category of graphs, , Electron. Notes Discrete Math., 31 (2008) pp. 131–136, The International Conference on Topological and Geometric Graph Theory.

 

organizing

  • AMS Special Session at JMM 2024, San Francisco, CA, January 2024
    Chris Kapulkin, Antonio Rieser, and I will organize a special session on `Discrete homotopy theory’ at the JMM meeting to be held in San Francisco in January 2024.

  • AMS Special Session at JMM 2022 (online), April 2022

    Bennet Goeckner, Steve Klee, Gaku Liu, and I organized a special session on `Geometric and topological combinatorics’ held at the JMM meeting, originally scheduled to be held January 2022 in Seattle but postponed to April 2022 and held online due to Covid-19. More details can be found here.

  • Special Session at AMS Sectional meeting, El Paso, TX, September 12–13, 2020

    Keri Sather-Wagstaff and I organized a special session on `Free Resolutions, Combinatorics, and Geometry’ as part of the AMS sectional meeting at the University of Texas at El Paso on September 12-13. More details can be found here.

  • Special Session at AMS Sectional meeting, Denton, TX, September 9–10, 2017

    Suho Oh and I organized a special session on `Geometric combinatorics and combinatorial commutative algebra’ as part of the AMS sectional meeting held at the University of North Texas on September 9-10. More details (including schedule of speakers) can be found here.

  • Special Session at AMS Sectional Meeting/Satellite conference, San Francisco, CA, October 24-26, 2014

    Together with Alex Engstrom and Tina O’Keefe I co-organized a special session on ‘Topological combinatorics and combinatorial commutative algebra’ as part of the AMS sectional meeting held at San Francisco State University, October 25-26, 2014. In addition we organized a one day satellite conference held (also) at SFSU on Friday, October 24. Click here for the Saturday/Sunday schedule and here for the Friday conference.

  • Graduate Student Combinatorics Conference, April 21-22, 2007

    Together with Brant Jones, Matt Kahle, and Beth Kelly I helped organize the 2007 Graduate Student Combinatorics Conference, held at the U of Washington in Seattle on April 21-22, 2007. Check out the attractive conference poster here (warning: big file).

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    Other writings/songs