Yuma Mizuno

Profile

Postdoc
School of Mathematical Sciences,
University College Cork,
working with Robert Osburn

Email: mizuno.y.aj@gmail.com

Address: Western Gateway Building, University College Cork, Western Road, Cork, Ireland.

Links: GitHub  ·  researchmap · CV (PDF)

Research Interest

• cluster algebras
• and their relation to low-dimensional topology, representation theory, integrable systems, and mathematical physics

Preprints

1. Rotation fixed points of undecorated braid varieties and fusion rings of affine Lie algebras, arXiv:2610.02034.
2. The three Kanade-Russell identities modulo nine, arXiv:2609.09653.
3. Mutation Sequences along Weaves and Amalgamation of Braid Varieties, arXiv:2609.05833.
4. Adjoint Reidemeister torsion of 3-manifolds with torus boundary for semisimple algebraic groups, joint work with Tsukasa Ishibashi, arXiv:2603.00816.
5. Divisibility by p for Markoff-like Surfaces, joint work with Matthew de Courcy-Ireland and Matthew Litman, arXiv:2509.02187.

Publications

1. Lean Formalization of Generalization Error Bound by Rademacher Complexity and Dudley’s Entropy Integral, joint work with Sho Sonoda, Kazumi Kasaura, Kei Tsukamoto, and Naoto Onda, 17th International Conference on Interactive Theorem Proving (ITP 2026), vol. 382, pp. 8:1–8:17.
   doi:10.4230/LIPIcs.ITP.2026.8.
2. Periodic Y-systems and Nahm sums: the rank 2 case, SIGMA 21 (2025), 094, 17 pages. doi:10.3842/sigma.2025.094, arXiv:2301.13239.
3. Remarks on Nahm sums for symmetrizable matrices, The Ramanujan Journal, 66, 62 (2025). doi:10.1007/s11139-025-01033-6, arXiv:2305.02267. (Program: https://github.com/yuma-mizuno/modular-search-for-Nahm-sums-with-symmetrizers, Table 2 and Table 3 in CSV format).
4. q-Painlevé equations on cluster Poisson varieties via toric geometry, Selecta Mathematica. New Series, 30, 19 (2024). doi:10.1007/s00029-023-00906-2, arXiv:2008.11219.
5. Difference equations arising from cluster algebras, Journal of Algebraic Combinatorics, 54, 295-351. doi:10.1007/s10801-020-00978-9, arXiv:1912.05710.
6. Exponents associated with Y-systems and their relationship with q-series. SIGMA Symmetry Integrability Geom. Methods Appl., 16:028, 42 pages, 2020. doi:10.3842/sigma.2020.028, arXiv:1812.05863.
7. Jacobian matrices of Y-seed mutations, Advances in Applied Mathematics, 115:101987, 2020. doi:10.1016/j.aam.2019.101987, arXiv:1805.00044.
8. Quiver mutation sequences and q-binomial identities, joint work with Akishi Kato and Yuji Terashima, International Mathematics Research Notices, 2018(23):7335-7358, 2018. doi:10.1093/imrn/rnx108, arXiv:1611.05969.

Expositions

• Mutation Sequences along Weaves and Amalgamation of Braid Varieties (Sites)
• Mutations of blowups of toric surfaces and q-Painlevé systems (Sites)

Research Activities

• Braiding new ground: Vertex Algebras meet the Yang-Baxter Equation, Maynooth University, Ireland, September 17-18, 2026.

Past (since 2024)

• Workshop on Higher Teichmüller theory, knot theory and cluster algebras, University College Cork, Ireland, July 13-17, 2026.
• Paris algebra seminar, May 18, 2026.
• Research Seminar on Quantum Topology and Categorification (QTCat), University of Hamburg, Germany, April 15, 2026.
• Geometry and Mathematical Physics seminar, University of Birmingham, UK, December 9, 2025.
• Conference on "Quantum Topology", Max Planck Institute for Mathematics, Germany, May 12-16, 2025.
• Asymptotic Expansion of τ-functions and Related Topics, RIMS Kyoto University, Japan, February 17-21, 2025.
• Lean Together 2025 Virtually via Zoom, January 14-17, 2025.
• New developments in representation theory of algebras: Algebraic, combinatorial and geometric aspects, Okinawa Institute of Science and Technology, Japan, November 18-30, 2024.
• 可積分系とクラスター代数 (English translation: Integrable systems and cluster algebras), Osaka Metropolitan University, Japan, September 1-2, 2024.

Others

My thesis: Difference equations arising from cluster algebras.

The data of solutions of Q-systems computed by the fermionic formulas: json file. See Theorem 13.11 in the paper written by Kuniba, Nakanishi, and Suzuki for a mathematical explanation. These data was used for computing the exponents in the paper Exponents associated with Y-systems and their relationship with q-series.

My interest in formalising mathematics predates the recent rise of generative AI. I formalized the definition of cluster algebras in Lean. I also made some contributions to Mathlib (the Lean mathematical library). The main one is to write a library for bicategories. I also developed the coherence tactic and the the string diagram widget for bicategories (and for monoidal categories as a special case), which are available in Mathlib. I gave a demonstration of these tools at Lean Together 2025 (Youtube: Metaprogramming on monoidal categories). See also a demo in Lean 4 Web.