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Publications & Patents
Research publications, patents, and conference proceedings.
Refereed Journal Papers / Preprints
arXiv, 49 pages (2026).
Connects the GIT and Baily–Borel compactifications of the moduli space of rational elliptic surfaces through K-moduli wall crossing and automorphic forms.
arXiv, 51 pages (2026).
Develops a wall crossing theory for K-moduli of quasimaps, connecting the stable, Calabi–Yau, and log Fano regimes.
arXiv, 37 pages (2026).
Establishes criteria for canonical singularities and general type for unitary Shimura varieties, together with a sharp singularity bound in the orthogonal case.
to appear in Journal of Algebraic Geometry (2026, 65 pages).
Compares the Kirwan and toroidal compactifications of the Eisenstein Deligne–Mostow variety and proves that they are not derived equivalent.
to appear in Simons Symposia (Yuri Tschinkel's 60th birthday, 2026).
Realizes moduli spaces of five weighted points on the projective line as log canonical models and relates them to Deligne–Mostow ball quotients.
arXiv (2025, 51 pages).
Establishes general type and finiteness results for arithmetic ball quotients of even dimension using cusp forms constructed from automorphic representations.
arXiv (2025, 44 pages).
Establishes finiteness results and explicit dimension bounds for Hermitian lattices admitting free algebras of modular forms.
arXiv (2025, 23 pages).
Gives a criterion for the Kirwan and toroidal compactifications of Deligne–Mostow varieties to agree, allowing unordered and partially ordered configurations.
Advances in Mathematics 463 (2025): 110126.
Shows that two natural compactifications of the moduli space of eight unordered points on the projective line have the same cohomology but are not K-equivalent.
Journal of Algebra, Volume 647, 1 June 2024, Pages 341-399.
Quantifies the obstruction caused by branch divisors, reducing general type questions for unitary modular varieties to constructing cusp forms of small weight.
Geometriae Dedicata 218, 3 (2024).
Uses reflective modular forms to prove that certain ball quotients of dimensions three, four, and five are covered by rational curves.
Springer Proceedings in Mathematics & Statistics (PROMS, volume 409), 2023, 633-664. (Based on the original paper:arXiv:2105.08254
Gives criteria for Baily–Borel compactifications to be Fano, Calabi–Yau, or have ample canonical divisors, using reflective modular forms.
Mathematische Nachrichten (2023), 1–29.
Extends cusp form criteria for general type to ball quotients with irregular cusps by analyzing ramification along the boundary.
Acta Arithmetica 204, no. 1, 1-18 (2022).
Relates generating series of special cycles on unitary Shimura varieties to Hermitian modular forms, using the Beilinson–Bloch conjecture in the general case.
Canadian Mathematical Bulletin 64, no. 1, 39-53 (2021).
Proves, assuming the Beilinson–Bloch conjecture, that generating series of special cycles on orthogonal Shimura varieties are Hilbert–Siegel modular forms.
arXiv (2026, 13pages).
Constructs random access codes from linear codes in polynomial time, with uniform guarantees on compression and recovery as the input length grows.
arXiv (2026, 15pages).
Gives a geometric description of optimal random access codes and explicit families in which quantum encoding outperforms the best classical encoding.
Related presentation: QIT 2026.
Artificial intelligence in mathematics research. AMS special session on artificial intelligence in mathematics, American Mathematical Society (AMS). Contemporary Mathematics 835, 195-214 (2026).
Uses algebraic geometry to justify and extend the generation of training data for computing Gröbner bases with Transformers.
arXiv, 23 pages (2026).
Derives bounds on the real log canonical threshold of nonnegative matrix factorization and relates them to Bayesian generalization error.
International Conference on Learning Representations (ICLR 2025).
Develops and evaluates methods for adapting Mamba models to new tasks while updating only a small number of parameters.
Quantum Machine Intelligence 8(1) (2026).
Uses quantum kernels to infer causal relationships from limited data, with improved performance in experiments with small samples.
Related presentation: QCE 2024.
arXiv (2024, 57 pages)
Extends singular learning theory to Bayesian quantum state estimation and derives a computable criterion for selecting quantum statistical models.
Related presentation: QTML 2024.
Quantum Machine Intelligence 7, 29 (2025).
Develops a method for estimating mutual information with quantum kernels, showing numerical advantages for small samples and strongly nonlinear dependence.
Conference Proceedings (non-refereed)
4th Mathsci freshman seminar (2021)
RIMS Kokyuroku: Automorphic forms, Automorphic representations, Galois representations, and its related topics (2021).
Kinosaki Algebraic Geometry Symposium (Kyoto University Research Information Repository, 2020)
3rd Mathsci freshman seminar (2020).
RIMS Kokyuroku: Analytic, geometric and p-adic aspects of automorphic forms and L-functions (2020).
2nd Mathsci freshman seminar (2019).
Explains the Harris–Taylor approach to the local Langlands correspondence through the geometry and cohomology of Shimura varieties.
Patents
WO/2025/074851 (2025)