This is a web page of Shunsuke Kano (狩野 隼輔).
This is a web page of Shunsuke Kano (狩野 隼輔).
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I am a Lecturer (Senior Assistant Professor) of Mathematical Science Center for Co-Creative Society (MathCCS), Tohoku University.
E-mail: s.kano(at)tohoku(dot)ac.jp
Research Interests: cluster algebras, triangulated categories, Thurston Theory on surfaces, magnitude homology
Key words: categorical dynamical system, mutation loop, quiver representation, mapping class group, pseudo-Anosov mapping class, higher Teichmüller space, train track, skein algebra, Hall algebra, Donaldson--Thomas invariant, magnitude homology, causal discovery...
Sign stability is a property of mutation loops, which is a generalization of pseudo-Anosov property for mapping classes. Actually, the mapping class is generic pseudo-Anosov iff it is (uniformly) sign-stable (arXiv:2010.05214). (General pseudo-Anosov mapping classes are also sign-stable (arXiv:2303.03190).) A sign-stable mutation loop has a numerical invariant, called cluster stretch factor. For a sign-stable mutation loop, the logarithm of its cluster stretch factor coincide with the algebraic entropy of the corresponding cluster transformations (arXiv:1911.07587) and the categorical entropy of the induced autoequivalence of some 3d Calabi-Yau category (arXiv:2105.08332). In addition, an acyclic quiver is representation infinite iff its cluster Donaldson--Thomas transformation is sign-stable (arXiv:2403.01396).
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