Yuma Mizuno

Profile

Postdoc
Department of Mathematics and Informatics, Faculty of Science,
Chiba University

Email: ymizuno@math.s.chiba-u.ac.jp
It appears that the mail server sometimes becomes unstable after October 13, 2023. If you get an error when sending to the above email address, please send to the following address instead: mizuno.y.aj@gmail.com

Address: 1-33, Yayoicho, Inage-ku, Chiba-shi, Chiba, 263-8522 Japan

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. Remarks on Nahm sums for symmetrizable matrices, arXiv:2305.02267. (Table 2 and Table 3 in CSV format).
2. Periodic Y-systems and Nahm sums: the rank 2 case, arXiv:2301.13239.

Publications

1. q-Painlevé equations on cluster Poisson varieties via toric geometry, Selecta Mathematica. New Series, 30, 19 (2024).
2. Difference equations arising from cluster algebras, Journal of Algebraic Combinatorics, 54, 295-351.
3. Exponents associated with Y-systems and their relationship with q-series. SIGMA Symmetry Integrability Geom. Methods Appl., 16:028, 42 pages, 2020.
4. Jacobian matrices of Y-seed mutations, Advances in Applied Mathematics, 115:101987, 2020.
5. Quiver mutation sequences and q-binomial identities, joint work with Akishi Kato and Yuji Terashima, International Mathematics Research Notices, 2018(23):7335-7358, 2018.

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, including the coherence theorem.