The $q$-Gaussians are an interpolation of independent Gaussians and free semicircles. Frisch-Bourret originally introduced them, and about 20 years later, they have been studied as operators acting on $q$-deformed Fock space by Bo\.{z}ejko-K\"{u}mmerer-Speicher. At the beginning of my talk, I would like to introduce $q$-Gaussians and refer to recent progress on related operator algebras. Subsequently, I will explain the joint work with Speicher about the existence of dual and conjugate systems for $q$-Gaussians, and the strong convergence result with respect to a parameter $q$.

Bio: Akihiro Miyagawa is a Ph.D. student in the Department of Mathematics at Kyoto University, under the supervision of Benoit Collins. His research has largely concerned free probability and analysis of operators represented on Fock spaces.