Dr. Hosomichi has made significant achievements in constructing exact solutions of 3-dimensional supersymmetric gauge theories using the localization principle and gave important contributions to the study of dynamics of M2 and M5 branes in M-theory.
One of his important achievements is the systematic construction of a class of supersymmteric gauge theories of Chern-Simons field coupled to the matter fields with a high degree of supersymmetry. Construction of these models contributed to the development of the study of dynamics of multiple M2 brane systems.
He then applied the localization method to a Chern-Simons theory defined on a squashed 3-sphere and obtained an exact expression of the partition function containing the squashing parameter. This parameter corresponds to a similar parameter in the theory of AGT correspondence which describes the decomposition of a 6-dimensional theory on M5 brane into 4-dimensional gauge theory and 2-dimensional Liouville theory. Squashed 3 sphere of Dr.Hosomichi gives an important example of M5 brane theory being decomposed into a 3-dimensional gauge theory together with a hyperbolic geometry in 3-dimensions.
Dr. Hosomichi further studied the equation characterizing the existence of supersymmetry and considered a framework of formulating rigid supersymmetric theories on general curved space time.
Dr. Hosomichi has made important contributions to string theory and M theory and is now playing a leading role in these areas in Japan. It is expected that he will continue to play a leading role and it is most appropriate for him to receive the Yukawa-Kimura prize of this year.