Lena Ji

Lena Ji

Institutional email: lji@illinois.edu
Non-institutional email: lenaji.math@gmail.com

Office: 304A Harker Hall

I am an Assistant Professor at the University of Illinois Urbana-Champaign. Previously, I was a postdoc at the University of Michigan. I received my PhD from Princeton University in 2021 under the supervision of Professor János Kollár.

My research is supported in part by NSF grant DMS-2501990.

Research interests: Algebraic geometry, especially Fano varieties and rationality

CV

Algebraic Geometry Seminar
Preprint Seminar

Research (arXiv page, Google Scholar, MathSciNet):

  1. Toricity in families of Fano varieties (with Joaquín Moraga) (2024). To appear in Pure Appl. Math. Q. (special issue in honor of Caucher Birkar) (arXiv)
  2. Conic bundle threefolds differing by a constant Brauer class and connections to rationality (with Sarah Frei, Soumya Sankar, Bianca Viray, and Isabel Vogt) (2024). (arXiv)
  3. The K-moduli space of a family of conic bundle threefolds (with Kristin DeVleming, Patrick Kennedy-Hunt, and Ming Hao Quek) (2024). (arXiv)
  4. Arithmetic and birational properties of linear spaces on intersections of two quadrics (with Fumiaki Suzuki) (2024). J. Éc. polytech., Math. 12 (2025), 1161–1196. (journal) (arXiv) (code with examples)
  5. Symmetries of Fano varieties (with Louis Esser and Joaquín Moraga). J. Reine Angew. Math. (2025), no. 819, 89–133. (journal) (arXiv)
  6. The fibering genus of Fano hypersurfaces (with Nathan Chen, Benjamin Church, and David Stapleton) (2023). To appear in Alg. Geom. Phys. (arXiv)
  7. A threefold violating a local-to-global principle for rationality (with Sarah Frei). Res. Number Theory 10 (2024), no. 2, Paper No. 39. (journal) (arXiv)
  8. Rationality of real conic bundles with quartic discriminant curve (with Mattie Ji). Int. Math. Res. Not. IMRN (2024), no. 1, 115–151. (journal) (arXiv)
  9. Fano hypersurfaces with no finite order birational automorphisms (with Nathan Chen and David Stapleton) (2022). To appear in Amer. J. Math. (arXiv)
  10. Curve classes on conic bundle threefolds and applications to rationality (with Sarah Frei, Soumya Sankar, Bianca Viray, and Isabel Vogt). Algebr. Geom. 11 (2024), no. 3, 421–459. (journal) (arXiv)
  11. The Noether–Lefschetz theorem in arbitrary characteristic. J. Algebraic Geom. 33 (2024), no. 3, 567–600. (journal) (arXiv)
  12. Structure of geometrically non-reduced varieties (with Joe Waldron). Trans. Am. Math. Soc. 374 (2021), no. 12, 8333–8363. (journal) (arXiv)
  13. Completely controlling the dimensions of formal fiber rings at prime ideals of small height (with Sarah Fleming, S. Loepp, Peter McDonald, Nina Pande, and David Schwein). J. Commut. Algebra 11 (2019), no. 3, 363–388. (journal) (arXiv)
  14. Controlling the dimensions of formal fibers of a unique factorization domain at the height one prime ideals (with Sarah Fleming, S. Loepp, Peter McDonald, Nina Pande, and David Schwein). J. Commut. Algebra 10 (2018), no. 4, 475–498. (journal) (arXiv)

Teaching:

Upcoming travel:

Other writing:

  1. The K-moduli of a family of conic bundles. Oberwolfach Report (2024).

REU advice: Here is my advice for undergraduates on how to apply to REUs.

Formula Morph exhibit at MoMath
Here is a picture of me, as an undergraduate, at the National Museum of Mathematics

Last updated: October 2025.