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 rationality of algebraic varieties and in positive characteristic algebraic geometry.

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):

• Rationality of real conic bundles with quartic discriminant curve (with Mattie Ji). Int. Math. Res. Not. IMRN (2023). (arXiv link)
• Fano hypersurfaces with no finite order birational automorphisms (with Nathan Chen and David Stapleton) (2022). (arXiv link)
• Curve classes on conic bundle threefolds and applications to rationality (with Sarah Frei, Soumya Sankar, Bianca Viray, and Isabel Vogt) (2022). (arXiv link)
• The Noether–Lefschetz theorem in arbitrary characteristic (2021). (arXiv link)
• Structure of geometrically non-reduced varieties (with Joe Waldron). Trans. Am. Math. Soc. 374 (2021), no. 12, 8333–8363. (arXiv link)
• 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. (arXiv link)
• 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. (arXiv link)

Upcoming travel:

• Diophantine Geometry Workshops @ MSRI/UC Berkeley, February 2–17, 2023
• Explicit Moduli Problems in Higher Dimensions, Banff, February 26–March 3, 2023
• Columbia University, March 8–10, 2023
• UCLA, April 2–8, 2023
• Johns Hopkins University, April 10–12, 2023
• UW Madison, April 13–14, 2023
• Higher Dimensional Geometry, Simons Center, May 8–12, 2023
• Conference on Rationality and Hyperbolicity, University of Notre Dame, June 26–30, 2023
• K-stability and Birational Geometry, Clay Mathematics Institute, September 25–29, 2023

Teaching:

• Fall 2021: Two sections of Math 115 (Calculus I)

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

Here is a drawing of me by Emily Ji

Here is a younger me at the National Museum of Mathematics

Last updated: March 2023.