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.

https://researchmap.jp/yuma_mizuno

CV

CV.pdf

Research Interest

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

Preprints

1. Adjoint Reidemeister torsion of 3-manifolds with torus boundary for semisimple algebraic groups, joint work with Tsukasa Ishibashi, arXiv:2603.00816.
2. Divisibility by p for Markoff-like Surfaces, joint work with Matthew de Courcy-Ireland and Matthew Litman, arXiv:2509.02187.

Publications

1. 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.
2. 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).
3. 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.
4. Difference equations arising from cluster algebras, Journal of Algebraic Combinatorics, 54, 295-351. doi:10.1007/s10801-020-00978-9, arXiv:1912.05710.
5. 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.
6. Jacobian matrices of Y-seed mutations, Advances in Applied Mathematics, 115:101987, 2020. doi:10.1016/j.aam.2019.101987, arXiv:1805.00044.
7. 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.

Research Activities

Past (since 2024)

• Symbolic Enumeration in Algebra, The Second Seminar, University of Galway, Ireland, May 26, 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.

Slides

1. トーリック曲面のブローアップの変異とq-Painlevé系 (Mutations of blowups of toric surfaces and q-Painlevé systems), 函数方程式論サマーセミナー, August 11th 2022, slide (Japanese)

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.

I'm interested in formalising mathematics. 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.