# 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 January 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 |

### Publications/Preprints

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. To appear in Selecta Math.

Optimal destablization of K-unstable Fano varieties via stability thresholds, joint with

**Yuchen Liu and Chuyu Zhou**, arXiv:1907.05399. To appear in Geom. Topol.

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, Bull. Korean Math. Soc.

**58**(2021), 113-132.