Research Interests and Publications

My research stemmed from the study of linear series on algebraic curves. To this day, it has developed into an combination of the following themes: (1) moduli of linear series and algebraic curves; (2) degeneration technique, Bruhat-Tits theory and quiver representation; (3) interdisciplinary studies involving algebraic and differential geometry, combinatorics and computer science. Here is my research statement.

Currently, I am considering the following topics:

1. Linked Flag Schemes, Quiver Grassmannians and Representations (joint with Xiang He);

2. Singularities of Brill-Noether Moduil Spaces (joint with Nero Budur, Marcel Rubió i Juncosa);

3. Weierstrass semigroups and finite covers of curves (joint with Ethan Cotterill);

4. Enriched enumeration of secant planes to algebraic curves (joint with Changho Han and Ethan Cotterill);

5. Solvability of viewing graphs. 

Publications and Preprints

1. 1. Motohico Mulase and Naizhen Zhang, Polynomial Recursion Formula for Linear Hodge Integrals, 

      Communications in Number Theory and Physics, Volume 4, No. 2, pp.267--294, 2010.

      arXiv:0908.2267

1. 2. Naizhen Zhang, Towards the Bertram-Feinberg-Mukai Conjecture, 

             Journal of Pure and Applied Algebra, Volume 220, pp.1588--1654, 2016.

     arXiv:1409.0971

1. 3. Naizhen Zhang, Expected Dimensions of Higher-Rank Brill-Noether Loci, 

      Proc. Amer. Math. Soc. 145 (2017), no. 9, 3735–3746.

            arXiv:1312.1657

1. 4.  Federico Castillo, Yairon Cid-Ruiz, Binglin Li, Jonathan Montaño, Naizhen Zhang,  When are multidegrees positive?  

       Advances in Mathematics 374 (2020), DOI 10.1016/j.aim.2020.107382

       arXiv: 2005.07808 

1. 5. Fu Liu, Brian Osserman, Montserrat Teixidor i Bigas, and Naizhen Zhang, Limit Linear Series and Ranks of Multiplication Maps,

      Transactions of the American Mathematical Society, Volume 374, Number 1, January 2021, Pages 367–405

             https://doi.org/10.1090/tran/8230

      arXiv:1701.06592

1. 6. Fu Liu, Brian Osserman, Montserrat Teixidor i Bigas, and Naizhen Zhang, The strong maximal rank conjecture and moduli spaces of curves

Algebra & Number Theory, to appear

      arXiv:1808.01290

1. 7. Ethan Cotterill, Xiang He and Naizhen Zhang, Secant Planes of a General Curve via  degenerations        

      Geometriae Dedicata (2020), DOI 10.1007/s10711-020-00545-3

             arXiv: 1901.06430

1. 8. Ethan Cotterill, Adrián Alonso Gonzalo and Naizhen Zhang, The Strong Maximal Rank Conjecture and higher rank Brill--Noether theory ,

      Journal of the London Mathematical Society (2021), DOI 10.1112/jlms.12427

      arXiv:1906.07618

1. 9. Xiang He and Naizhen Zhang, Degenerations of Grassmannians via Lattice Configurations,

     International Mathematics Research Notices, Volume 2023, Issue 1, pp. 298-349, DOI 10.1093/imrn/rnab241

1. 10. Roger Bielawski and Naizhen Zhang, Hyperkähler geometry of rational curves in twistor spaces, 

Complex Manifolds, vol. 9, no. 1, 2022, pp. 345-354.

1. 11. Ethan Cotterill, Nathan Pflueger and Naizhen Zhang, Weierstrass Semigroups from Cyclic Covers of Hyperellipitc Curves, 

Bulletin of the Brazilian Mathematical Society, Volume 54, Article number: 37 (2023),  DOI 10.1007/s00574-023-00355-7

1. 12. Xiang He and Naizhen Zhang, Degenerations of Grassmannians via lattice configurations II

    arXiv: 2305.00158