**Institutional email:** lji@illinois.edu

**Permanent email:** lenaji.math@gmail.com

**Office:** 310 Altgeld 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.

**Research interests:** Algebraic geometry, especially Fano varieties, rationality, non-closed fields, and positive characteristic.

**Research (arXiv page):**

- Toricity in families of Fano varieties (with Joaquín Moraga) (2024). (arXiv)
- 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)
- The K-moduli space of a family of conic bundle threefolds (with Kristin DeVleming, Patrick Kennedy-Hunt, and Ming Hao Quek) (2024). (arXiv)
- Arithmetic and birational properties of linear spaces on intersections of two quadrics (with Fumiaki Suzuki) (2024). (arXiv) (supplementary Magma code with examples)
- Symmetries of Fano varieties (with Louis Esser and Joaquín Moraga) (2023). To appear in
*J. Reine Angew. Math.*(arXiv) - The fibering genus of Fano hypersurfaces (with Nathan Chen, Benjamin Church, and David Stapleton) (2023). (arXiv)
- 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) - Rationality of real conic bundles with quartic discriminant curve (with Mattie Ji).
*Int. Math. Res. Not. IMRN*(2024), no. 1, 115–151. (journal) (arXiv) - Fano hypersurfaces with no finite order birational automorphisms (with Nathan Chen and David Stapleton) (2022). (arXiv)
- Curve classes on conic bundle threefolds and applications to rationality (with Sarah Frei, Soumya Sankar, Bianca Viray, and Isabel Vogt).
*Algebraic Geom.*11 (2024), no. 3, 421–459. (journal) (arXiv) - The Noether–Lefschetz theorem in arbitrary characteristic.
*J. Algebraic Geom.*33 (2024), no. 3, 567–600. (journal) (arXiv) - Structure of geometrically non-reduced varieties (with Joe Waldron).
*Trans. Am. Math. Soc.*374 (2021), no. 12, 8333–8363. (journal) (arXiv) - 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) - 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:**

- In Fall 2024, I am not teaching.

**Upcoming travel:**

- Fano varieties in Cetraro, Grand Hotel San Michele, September 9–13, 2024
- Stony Brook University, September 18, 2024
- Higher-dimensional log Calabi-Yau pairs, AIM, September 30–October 4, 2024
- Boston Algebraic Geometry Day, Harvard University, October 6, 2024
- University of Washington, October 15, 2024
- Purdue University, October 23, 2024
- Birational Geometry and Number Theory, ICMS, Edinburgh, October 28–November 1, 2024
- Cremona Groups, CIRM, May 5–9, 2025
- Real Algebraic Geometry and Birational Geometry, CIRM, June 2–6, 2025
- Structures and Symmetries in Algebraic Geometry in Krakow, University of the National Education Commission, June 9–13, 2025
- Kihei, June 30–July 4, 2025
- Summer Research Institute in Algebraic Geometry, Colorado State University, July 2025
- Mathematical Congress of the Americas 2025, University of Miami, July 21–25, 2025
- 40 Years of Higher Dimensional Geometry, Princeton University, June 8–12, 2026

**Other writing:**

- 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.

*Last updated: August 2024.*