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. From 2018 to 2021, 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.
Starting Fall 2025, I will be an Assistant Professor in the School of Mathematics at Georgia Tech. My research is partially supported by NSF grant DMS-2200690.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
Good moduli spaces for boundary polarized Calabi-Yau surface pairs (joint with Yuchen Liu), arXiv:2407.00850.Moduli of boundary polarized Calabi-Yaur pairs (joint with Kenneth Ascher, Dori Bejler, Kristin DeVleming, Giovanni Inchiostro, Yuchen Liu, Xiaowei Wang), arXiv:2307.06522.
Convexity of multiplicities of filtrations on local rings (joint with Yuchen Liu and Lu Qi), Compos. Math. 160 (2024), 878-914.
The existence of the Kähler-Ricci soliton degeneration (joint with Yuchen Liu, Chenyang Xu, and Ziquan Zhuang), Forum of Math. Pi. To 11 (2023), e9.
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), Geom. Topol.. 26 (2022), 2507-2564.
Openness of K-semistability for Fano varieties (joint with Yuchen Liu and Chenyang Xu), Duke Math. J.. 171 (2022), 2753-2797.
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), Ann. Sci. Éc. Norm. Supér. 55 (2022), 1-41
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.K-stability notes. These are notes from a course I taught in the fall of 2022. I plan to make significant edits and additions to the document.
Teaching
This semester I am teaching Math 6140: Algebraic Geometry II and Math 6520: Algebraic Topology. The course websites are on Canvas.A list of my past teaching can be found here.