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  2. Mr Yasushi Nagai

Mr Yasushi Nagai

Profile summary

Professional biography

1.1 Published papers

(with peer review)

  1. “Distribution of patches in tilings and spectral properties of corresponding dynamical systems”, Nonlinearity, Volume 28(2015), 2617-2638.

  2. “Distribution of patches in tilings, tiling spaces and tiling dynamical systems” RIMS Kˆokyuˆroku Bessatsu B58(2016), 33-59.

  3. joint work with Jeong-Yup Lee and Shigeki Akiyama, “Cut-and-Project Schemes for Pisot Family Substitution Tilings”, Symmetry 2018, 10(10), 511.

  4. “A general framework for tilings, Delone sets, functions and measures, and their interrelation”, Discrete and Computational Geometry 62 (2019), no.2, 241-291.

1.2 Preprints

  1. “The common structure for objects in aperiodic order and the theory of local matching topology”, arXiv:1811.04642

  2. “A new relation between geometric and dynamical properties of objects such as tilings and Delone sets”, arXiv:1811.04654

  3. joint work with Shigeki Akiyama and Jeong-Yup Lee, “On arithmetic progressions in non-periodic self-affine tilings”, arXiv: 2007.06005

  4. “Absence of absolutely continuous diffraction spectrum for certain one-dimensional S-adic tilings”, arXiv: 2011.14375

  5. joint work with Ibai Aedo, Uwe Grimm and Petra Staynova, “On long arithmetic progressions in binary Morse-like words”, arXiv:2101.02056

Research interests

I am interested in the mathematics related to quasicrystals. In particular, I study structure models of quasicrystals (tilings, Delone sets,...), especially the distribution of patterns inside them and their spectral properties.

External collaborations

I have ongoing joint works with (1) Shigeki Akiyama (University of Tsukuba, Japan) and Jeong-Yup Lee (Catholic Kwandong University, Korea), and also with (2) Uwe Grimm and Ibai Aedo in OU and Petra Staynova in University of Derby.