Zhuang He

I am a postdoctoral researcher in algebraic geometry. My research topics include: birational geometry on moduli spaces, K3 surfaces and their (birational) automorphisms, convex geometry and topological invariants of toric Fano varieties.

Until recently I worked a postdoctoral research fellow at the University of Turin. I worked with Prof. Cinzia Casagrande. Before I was a postdoc at the Humboldt University of Berlin. 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.

My email: he.zhu AT northeastern dot edu   my.name@unito.it

First name/given name: Zhuang;

Last name/family name: He.

Pronouns: he/him.

My publications and manuscripts:

7. Toric Fano Pairs with large sum of Picard ranks. In preparation.

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. To appear in Épijournal de Géométrie Algébrique. (codes on github) arXiv:2507.15406.

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)

I use computer algebra systems and programs in my research. Until recently I have been a user of 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%.

• The Geometry Seminars at University of Milan-Bicocca.

• Boundedness and Moduli Problems in Birational Geometry and Foliation Theory‏. Pisa.

• Harmonies in Moduli Spaces, in occasion of Lucia Caporaso’s birthday, Università Roma Tre.

• The Oberseminar at Otto-von-Guericke-University Magdeburg (online).