Conventional crystals are characterized by “periodicity”, where unit structures repeat regularly in space. In contrast, quasicrystals have a new type of order known as “quasiperiodicity”. Quasicrystal structures exhibit high rotational symmetries, such as 5-, 8-, 10-, and 12-fold symmetry, which are forbidden in periodic crystals. Quasicrystals are also deeply connected to irrational numbers like the golden ratio and to fractals (self-similarity). Furthermore, quasicrystals can be understood as projections of higher-dimensional periodic crystals onto two- or three-dimensional space. In this framework, they possess a so-called “perpendicular space”, an additional dimension orthogonal to real space. My research aims to theoretically explore how such high dimensionality and high symmetry in quasicrystals manifest in electronic states and spin degrees of freedom. I am also interested in developing novel numerical and analytical methods to better describe a wide range of physical properties in electronic and spin systems, not limited to quasicrystals.