Yuma Mizuno

Profile

Postdoc
School of Mathematics and Statistics,
University College Dublin

Email: mizuno.y.aj@gmail.com

Address: Belfield, Dublin 4, 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. 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.