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Chenyang Zhao

I am a final year MSci student in Mathematics at Imperial College London. I am an ex-research intern of AROMATH team at Inria. My research interests lie in algebraic geometry, the keywords of my research are deformation theory, hilbert scheme (of points), moduli problems and computational algebraic geometry. I am currently working on my master thesis under Dr. Matt Booth, which focuses on deformation of algebraic schemes and applications to moduli problems (with a specific dive into the combinatoric structures of torus-fixed points of nested Hilbert scheme of points). Previously I worked on implicit representation of algebraic curves and surfaces via syzygy-based matrices with my supervisor Dr. Laurent Busé. I also contributed to the development of a Macaulay2 package on GameTheory.

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Publications

Deformation Theory and Torus-Fixed Geometry of the Nested Hilbert Scheme of Points

Deformation Theory and Torus-Fixed Geometry of the Nested Hilbert Scheme of Points

Chenyang Zhao
arXiv, 2026

We study the nested Hilbert scheme of points on the affine plane via deformation theory, torus actions, and Young diagram combinatorics. We identify tangent spaces at nested pairs, describe torus-fixed points by partitions with a removable corner, derive the tangent-weight formula using a Young-diagram shortening rule, and verify the formula computationally in Macaulay2.

PDF arXiv
The GameTheory package for Macaulay2

The GameTheory package for Macaulay2

Erin Connelly, Vincenzo Galgano, Zhuang He, Giacomo Maletto, Elke Neuhaus, Irem Portakal, Hannah Tillmann-Morris, Chenyang Zhao
arXiv, 2025

We describe the GameTheory package version 1.0 for computing equilibria in game theory available since version 1.25.05 of Macaulay2. We briefly explain the four equilibrium notions, Nash, correlated, dependency, and conditional independence, and demonstrate their implementation in the package with examples.

PDF arXiv

Interactive Playground

Young diagrams and nested fixed points

A small software companion for the thesis: removable corners, addable monomial generator directions, and the row-and-column shortening rule for tangent weights.

Open Playground

Macaulay2 Lab

Try small algebraic geometry computations

A tiny lab with Macaulay2 starter snippets for Groebner bases, monomial ideals, Young diagram boundaries, and Betti tables.

Open Lab