Harold Blum

Stony Brook University - Department of Mathematics

About Me

I am currently an NSF Postdoc at Stony Brook University in the Mathematics Department. From August 2018 to June 2020, I was a postdoc at the University of Utah. In May of 2018, I completed my Ph.D. at the University of Michigan under the supervision of Mircea Mustaţă. Starting Winter 2022, I will be an assistant professor at the University of Utah.

Here is my CV.

Research interests

Algebration geometry: birational geometry, singularities, Fano varieties, K-stability, and moduli.

Contact Info

Email: harold.blum [at] stonybrook.edu
Office: Math Tower 2-121
Mail: Stony Brook University
Mathematics Department
Stony Brook, NY 11794


The existence of the Kähler-Ricci soliton degeneration, joint with Yuchen Liu, Chenyang Xu, and Ziquan Zhuang, arXiv:2103.15278.

On properness of K-moduli spaces and optimal degenerations of Fano varieties, joint with Daniel Halpern-Leistner, Yuchen Liu and Chenyang Xu, arXiv:2011.01895.

Optimal destablization of K-unstable Fano varieties via stability thresholds, joint with Yuchen Liu and Chuyu Zhou, arXiv:1907.05399.

Openness of K-semistability for Fano varieties, joint with Yuchen Liu and Chenyang Xu, arXiv:1907.02408.

Reductivity of the automorphism group of K-polystable Fano varieties, joint with Jarod Alper, Daniel Halpern-Leistner, and Chenyang Xu, Invent. Math. 222 (2020), 995-1032.

Uniqueness of K-polystable degenerations of Fano varieties, joint with Chenyang Xu, Ann. of Math. 190 (2019), 609-656.

Openness of uniform K-stability in families of Q-Fano varieties, joint with Yuchen Liu, arXiv:1808.09070. To appear in Ann. Sci. Éc. Norm. Supér.

The normalized volume of a singularity is lower semicontinuous, joint with Yuchen Liu, arXiv:1802.09658. To appear in J. Eur. Math. Soc.

Thresholds, valuations, and K-stability, joint with Mattias Jonsson, Adv. Math. 365 (2020).

Existence of valuations with smallest normalized volume, Compos. Math. 154 (2018), 820-849.

On Divisors Computing MLD's and LCT's, arXiv:1605.09662. To appear in Bull. Korean Math. Soc.

Other Writing

Singularities and K-stability, Ph.D. Thesis, University of Michigan, link.


This semester I am teaching Applied Algebra (MAT 312 / AMS 351). All course material is on blackboard.

Here is a list of my past teaching.