Starting from 2024, I am a postdoctoral research fellow at the University of Turin (UniTo). I am working with Prof. Cinzia Casagrande.
From 2020 to 2023, I was a postdoc at Humboldt-Universität zu Berlin. I worked with Prof. Gavril Farkas. Before that, in 2020, I received my PhD in mathematics from Northeastern University, supervised by Prof. Ana-Maria Castravet. Before that, I was in the graduate program of mathematics at The Ohio State University.
Email Address: given name dot family name AT unito dot IT
First name/given name: Zhuang;
Last name/family name: He.
Pronouns: he/him.
My research is in algebraic geometry. I am interested in the birational geometry on moduli spaces, with interactions with toric varieties, K3 surfaces and their (birational) automorphisms.
Recently I have been working on the question of bounding the Picard ranks of Gorenstein toric Fano varieties, from a convex geometry approach on the reflexive polytopes.
My publications and preprints:
6. The GameTheory package for Macaulay2. (Joint with Erin Connelly, Vincenzo Galgano, Giacomo Maletto, Elke Neuhaus, Irem Portakal, Hannah Tillmann-Morris, and Chenyang Zhao). Submitted. arXiv:2507.16755. (the package)
5. Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties. Submitted. arXiv:2507.15406. (codes on github)
4. Pseudo-automorphisms of rational threefolds and Kummer surfaces. Preprint. arXiv:2401.07948.
3. Birational geometry of blow-ups of projective spaces along points and lines. (Joint with Lei Yang) Int. Math. Res. Not. IMRN, 2021(9):6442–6497. (journal) arXiv:1910.11854.
2. Mori Dream Spaces and blow-ups of weighted projective spaces. J. Pure Appl. Algebra, 223(10)(2019), 4426-4445. (journal) arXiv:1803.11536.
1. Blow-ups of toric surfaces and the Mori Dream Space Property. Exp. Math, 30(3)(2021), 386–404. (journal) (.pdf) (codes)
Harmonies in Moduli Spaces, in occasion of Lucia Caporaso’s birthday, Università Roma Tre.
The Oberseminar at Otto-von-Guericke-University Magdeburg (online).
Macaulay2 in the Sciences. Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.
Group actions, combinatorial methods, and Fano varieties. Innsbruck, Austria.
Fano and uniruled varieties. Będlewo, Poland.
GAeL XXXI. Turin.
I use computer algebra systems and programs in my research. Until recently I have been using Mathematica, particularly for its symbolic computation and functional programming features.
I frequently use Macaulay2 and SageMath, for questions in toric geometry and convex geometry. I coauthored the GameTheory package for Macaulay2, as a group project in the 2024 Macaulay2 workshop, led by Irem Portakal.
I am a solver of Project Euler of level 7. I solved more than 170 questions excluding the first 100 ones, with mean difficulty of problems solved = 38%.