Arata KOMYO Arata KOMYO Department of Mathematics, Graduate School of Science, Kobe University Division : Algebra Associate Professor Building B, Room 326

 Research Field : Compactifications of character varieties, isomonodromic deformations Research Summary : Motivated by the conjectures on compactifications of character varieties due to Simpson and on their Mixed Hodge structures due to Hausel et al, I study compactifications of some examples of character varieties. Recently, I also study isomonodromic deformations by the moduli theory of stable parabolic connections. Primary Publications : Explicit description of jumping phenomena on moduli spaces of parabolic connections and Hilbert schemes of points on surfaces (with Masa-Hiko Saito), accepted in Kyoto Journal of Mathematics. (arXiv:math/1611.00971) Mixed Hodge structures of the moduli spaces of parabolic connections, Nagoya Math. J. 225, 185--206 (2017). An explicit description of the relative $\mathrm{SL}(4,\mathbb{C})$-character variety of the projective line, Manuscripta Math., 150, no. 3, 441--464 (2016). On compactifcations of character varieties of $n$-punctured projective line, Ann. Inst. Fourier (Grenoble), 65 no. 4, 1493--1523, (2015).