Overview
Topics include the Monster and Baby Monster, vertex operator algebras, and Leech-related lattices and designs. The emphasis is on explicit structures and arguments that can be checked independently.
Computation is used where it clarifies structure or supports verification.
Selected publications
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The Order of the Monster Finite Simple Group
Provides a self-contained, VOA-geometric, and computationally-assisted route to determine the order of the largest sporadic simple group and demonstates the interplay between deep theory and modern computation.
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The Conformal Packing Problem
A theoretical and computational work that bridges pure mathematics with numerical methods from 3D quantum field theory. It Applies Viazovska's sphere packing magic functions methods directly to VOAs.
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Classification of Self-Dual Vertex Operator Superalgebras of Central Charge ≤ 24
A significant step towards a complete classification in this fundamental area of VOA theory, resolving many cases and providing a systematic framework for future work.
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The 290 fixed-point sublattices of the Leech lattice
A complete computational classification that has found application in algebaic geometry for studying symmetries of hyperkähner manifolds
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On the Genus of the Moonshine Module
Provides the first systematic description of the self-dual theory at c=24 using Niemeier lattices and genera. Also yields a classification of superstring theories.
Selected talks & presentations
- The Monster and its order, Academia Sinica, Taipei (2024)
- Classification of self-dual VOAs, Harvard (2023)
- The genus of the odd Moonshine module, CIRM, Luminy (2022)
- The Conformal Packing Problem, Sichuan University (2019)
- VOAs, lattices and automorphisms, RIMS, Kyoto (2018)
- Several talks at MFO, Oberwolfach.
Research artifacts & data
- VOA/MTC database: curated tables for VOAs and modular tensor categories. Access