JungTao (Ronnie) Cheng

Published

• On the tangent bundle and the divisor theory of a general matroid

  International Mathematics Research Notices 2026, no. 17, rnag188.
  JournalarXiv

  Summary

  We construct a tangent K-class for every loopless matroid and develop a combinatorial divisor theory; in the realizable case, the class recovers the tangent bundle of the wonderful compactification.

Preprints

• Kazhdan–Lusztig polynomials of matroids need not be unimodal

  With Shurui Liu · 2026 · arXiv

  Summary

  We construct representable matroids over every finite field whose Kazhdan–Lusztig polynomials are not unimodal, disproving the log-concavity and real-rootedness conjectures.

  The initial counterexample and the projective-deletion approach were produced by the AI system Rethlas; the appendix documents the AI-assisted discovery and the subsequent mathematical development.

• Tangent classes for matroid building sets

  2026 · arXiv

  Summary

  We define tangent classes for arbitrary matroids with building sets and establish a matroidal Hirzebruch–Riemann–Roch identity and Chern-number inequalities.

• Inequalities for Chow polynomials and Chern numbers of matroids

  With Wangyang Lin · 2026 · arXiv

  Summary

  We prove moment inequalities for normalized Chow coefficients, with consequences for flags of flats, roots of Chow polynomials, and matroidal Chern numbers.

AI for mathematics

Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory

With Jihao Liu, Guoxiong Gao, Zeming Sun, Bin Wu, Shurui Liu, Jiedong Jiang, Haocheng Ju, Leheng Chen, Xiping Zhang, and Bin Dong.
Preprint, 2026 · arXiv

Summary

We introduce a mathematical reasoning system that coordinates multiple agents through a shared, verified fact graph, and evaluate it on six research-level case studies.