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.

Research (arXiv page):

1. Symmetries of Fano varieties (with Louis Esser and Joaquín Moraga) (2023). (arXiv)
2. The fibering genus of Fano hypersurfaces (with Nathan Chen, Benjamin Church, and David Stapleton) (2023). (arXiv)
3. A threefold violating a local-to-global principle for rationality (with Sarah Frei) (2023). (arXiv)
4. Rationality of real conic bundles with quartic discriminant curve (with Mattie Ji). Int. Math. Res. Not. IMRN (2023). (journal) (arXiv)
5. Fano hypersurfaces with no finite order birational automorphisms (with Nathan Chen and David Stapleton) (2022). (arXiv)
6. 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)
7. The Noether–Lefschetz theorem in arbitrary characteristic. Accepted by J. Algebraic Geom. (arXiv)
8. Structure of geometrically non-reduced varieties (with Joe Waldron). Trans. Am. Math. Soc. 374 (2021), no. 12, 8333–8363. (journal) (arXiv)
9. 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)
10. 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 2023, I am teaching two sections of Math 115 (Calculus I).

Upcoming travel:

• UT Austin, September 21, 2023
• K-stability and Birational Geometry, Clay Mathematics Institute, September 25–29, 2023
• AWM Research Symposium, Clark Atlanta University, September 30–October 1, 2023
• International Workshop on Birational Geometry, Nagoya University, October 10–13, 2023
• The University of Tokyo, October 16, 2023
• Fields Medal Symposium in Honor of Caucher Birkar, The Fields Institute, October 2023
• Tufts University, October 27, 2023
• University of Nottingham (Online), November 10, 2023
• Joint Mathematics Meetings, January 3–6, 2024
• Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories, Oberwolfach, July 7–13, 2024

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

Last updated: September 2023.