Lena Ji

Institutional email: lenaji@umich.edu
Permanent email: lenaji.math@gmail.com

Office: 1855 East Hall

Hello! I am an NSF Postdoctoral Fellow at the University of Michigan, mentored by Professor Mircea Mustaţă. I am interested in algebraic geometry and its connections to arithmetic geometry and commutative algebra. In particular, I am interested in Fano varieties, non-algebraically-closed fields, positive characteristic, and rationality.

CV

I received my PhD from Princeton University in 2021 under the supervision of Professor János Kollár. Before that, I was an undergraduate at Columbia University, where I graduated in 2016. In Fall 2024, I will be an Assistant Professor at the University of Illinois Urbana-Champaign.

Research (arXiv page):

1. The K-moduli space of a family of conic bundle threefolds (with Kristin DeVleming, Patrick Kennedy-Hunt, and Ming Hao Quek) (2024). (arXiv)
2. Arithmetic and birational properties of linear spaces on intersections of two quadrics (with Fumiaki Suzuki) (2024). (arXiv) (supplementary Magma code with examples)
3. Symmetries of Fano varieties (with Louis Esser and Joaquín Moraga) (2023). (arXiv)
4. The fibering genus of Fano hypersurfaces (with Nathan Chen, Benjamin Church, and David Stapleton) (2023). (arXiv)
5. A threefold violating a local-to-global principle for rationality (with Sarah Frei). Res. Number Theory. 10 (2024), no. 2. (journal) (arXiv)
6. Rationality of real conic bundles with quartic discriminant curve (with Mattie Ji). Int. Math. Res. Not. IMRN 2024, Issue 1 (2024), 115–151. (journal) (arXiv)
7. Fano hypersurfaces with no finite order birational automorphisms (with Nathan Chen and David Stapleton) (2022). (arXiv)
8. Curve classes on conic bundle threefolds and applications to rationality (with Sarah Frei, Soumya Sankar, Bianca Viray, and Isabel Vogt). Accepted by Algebraic Geom. (arXiv)
9. The Noether–Lefschetz theorem in arbitrary characteristic. J. Algebraic Geom. 33 (2024), no. 3, 567–600. (journal) (arXiv)
10. Structure of geometrically non-reduced varieties (with Joe Waldron). Trans. Am. Math. Soc. 374 (2021), no. 12, 8333–8363. (journal) (arXiv)
11. 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)
12. 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 Winter 2024, I am not teaching.

Upcoming travel:

• Courant Institute NYU, April 4, 2024
• Brown University, April 12, 2024
• Higher Dimensional Geometry, Simons Center, May 6–10, 2024
• Tsinghua University, May 17–June 14, 2024
• Institut de Mathématiques de Bordeaux, June 20–22, 2024
• École Polytechnique Fédérale de Lausanne, June 24–28, 2024
• Birational Geometry and Dynamics, Les Diablerets, June 30 –July 5, 2024
• Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories, Oberwolfach, July 7–12, 2024
• Leibniz University Hannover, July 15–19, 2024
• Higher-dimensional log Calabi-Yau pairs, AIM, September 30–October 4, 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
• Bootcamp for the Algebraic Geometry Summer Research Institute, Colorado State University, July 8–12, 2025
• 40 Years of Higher Dimensional Geometry, Princeton University, June 8–12, 2026

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

Last updated: April 2024.