# Harold Blum

##### University of Utah - Department of Mathematics

### About Me

I am an Assistant Professor in the Department of Mathematics at the University of Utah University of Utah. From 2018 to 20201, I was an NSF postdoc at Stony Brook University and the University of Utah. In 2018, I completed my Ph.D. at the University of Michigan under the supervision of Mircea Mustaţă.

Here is my CV.### Research interests

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

### Contact Info

Email: | blum [at] math.utah.edu |

Office: | LCB 203 |

Mail: |
University of Utah Department of Mathematics Salt Lake City, UT 84112 |

### Publications/Preprints

Convexity of multiplicities of filtrations on local rings, joint with**Yuchen Liu and Lu Qi**, arXiv:2208.04902.

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**, Selecta Math.

**27**(2021).

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. To appear in Duke Math. J.

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**, J. Eur. Math. Soc.

**23**(2021), 1225-1256.

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 lcts's, Bull. Korean Math. Soc.

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

### Other Writing

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

This semester I am teaching Math 7800 - Topics in Algebraic Geometry. The purpose of the course is to give an introduction to the algebraic theory of K-stability. My lecture notes, which are very much a work in progress, can be found here. A more up to date version can be found on the Canvas page for the course.A list of my past teaching can be found here.