Jay Yang

Research

My recent research focuses on multigraded syzygies, in particular virtual resolutions. But I also have a strong interest in syzygies more broadly as well as connections between Algebraic Geometry, Commutative Algebra, and Combinatorics.

My research has blended combinatorial, computation, algebraic techniques to study syzygies. This includes a particular focus on monomial ideals as well as toric varieties.

Papers

See also: https://arxiv.org/a/yang_j_7.html
  1. Conditions for Virtually Cohen--Macaulay Simplicial Complexes (with Adam Van Tuyl) arXiv
  2. CellularResolutions M2 Package (with Aleksandra Sobieska) arXiv
  3. Hadamard Products and Binomial Ideals (with Büşra Atar, Kieran Bhaskara, Adrian Cook, Sergio Da Silva, Megumi Harada, Jenna Rajchgot, Adam Van Tuyl, and Runyue Wang) Journal of Pure and Applied Algebra arXiv
  4. Syzygies of P1×P1: data and conjectures (with Juliette Bruce, Daniel Corey, Daniel Erman, Steve Goldstein, and Robert P. Laudone) Journal of Algebra arXiv
  5. Homological and combinatorial aspects of virtually Cohen--Macaulay sheaves (with Christine Berkesch, Michael C. Loper, and Patricia Klein) Transactions of the London Mathematics Society arXiv
  6. Combinatorial aspects of virtually Cohen--Macaulay sheaves (with Christine Berkesch, Michael C. Loper, and Patricia Klein) Séminaire Lotharingien de Combinatoire
  7. Asymptotic Degree of Random Monomial Ideals (with Lily Silverstein and Dane Wilburne) Journal of Commutative Algebra arXiv
  8. Characteristic Dependence of Syzygies of Random Monomial Ideals (with Caitlyn Booms and Daniel Erman) SIAM Journal on Discrete Mathematics arXiv
  9. Virtual Resolutions of Monomial Ideals on Toric Varieties Proceedings of the AMS Series B arXiv
  10. The SchurVeronese package in Macaulay2 (with Juliette Bruce, Daniel Erman, and Steve Goldstein) JSAG arXiv
  11. Conjectures and Computations about Veronese Syzygies (with Juliette Bruce, Daniel Erman, and Steve Goldstein) Experimental Mathematics arXiv
  12. Random Flag Complexes and Asymptotics Syzygies (with Daniel Erman) Algebra & Number Theory arXiv
  13. Random Toric Surfaces and a Threshold for Smoothness Journal of Algebra arXiv