Yusuke Nakamura

Associate Professor, Graduate School of Mathematics, Nagoya University*Profile is at the time of the award.

2025Inamori Research GrantsScience & Engineering

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Research topics: Application of algebraic geometry to enumerative combinatorics of periodic graphs

Keyword

Summary: The aim of this study is to investigate the properties of the growth sequence of periodic graphs. A periodic graph is a graph with translational symmetry, such as those appearing in tilings and crystal structures. Fixing a vertex of a periodic graph, the number b(n) of vertices reachable from it within at most n steps is called a growth sequence. In this study, we tackle open problems related to this sequence using techniques from ring theory and algebraic geometry.

Comment

This study originated from a pure mathematical interest; however, as it involves tilings and crystal structures, it is an interdisciplinary topic with potential applications in mathematical crystallography and molecular structural chemistry. I would like to actively make use of opportunities to collaborate with researchers from other fields, such as through the Seiwa Scholars Society.

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