(Qiu) The operator space OUMD property was introduced by Pisier in the context of vector-valued noncommutative L_p spaces. Recently, I proved that the column Hilbert space is OUMD for all finite p > 1 . This answers positively a question asked by Zhong-Jin Ruan. It is well known that the Banach space UMD property is independent of p,  but it is still unknown whether the operator space OUMD property is independent of p

(Almus) Scattered C*-algebras form an important subclass of type I C*-algebras. We introduce a new class of operator algebras to generalize the class ofscattered C*-algebras into a nonselfadjoint setting.

(Kavruk) The tensor products and the behaviour of objects under the tensorial operations have played a substantial role in operator theory with several applications and has initiated a classification and nuclearity theory in the corresponding context (C*-algebras, operator algebras, operator spaces etc.). In this talk I will briefly explain the tensor product of operator systems and the nuclearity related properties in this setting including the exactness, local lifting property, weak expectation property etc. I will then discuss the stability of these properties under basic algebraic operations such as quotients, duality. As an application framework, two long standing open problems namely the Kirchberg Conjecture (KC) and the Smith-Ward problem (SWP) naturally fall into this context. After I recall these problems shortly I will discuss their low dimensional operator system variants. We express the Kirchberg Conjecture in terms of a problem about a four dimensional operator system and then give a three dimensional operator system version of the Smith-Ward problem. The first half of the talk is based on a joint work with V. I. Paulsen, I. G. Todorov and M. Tomforde and the second half comprises my PhD thesis and current research.