The 15th Korea Operator Algebra Seminar (KOAS)
November 2, 2018
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13:00 - 13:40 ÀÌÇÑÁÖ (µ¿±¹´ë)
Title: TBA
Abstract: TBA

13:40 - 14:20 ÀÌÈÆÈñ (¼­¿ï´ë)
Title: Temperley-Lieb channels
Abstract: We will introduce a family of quantum channels called Temperley-Lieb channels coming from the representations theory of SU(2) or free orthogonal quantum groups. We then investigate various properties of these channels, especially focusing on various channel capacities.

14:20 - 15:00 ÀÌÀÎÇù (ÀÌÈ­¿©´ë)
Title: Continuous orbit equivalence on self-similar groups
Abstract: Following Matsumoto's definition of continuous orbit equivalence for one-sided subshifts of finite type, we introduce the notion of continuous orbit equivalence to canonically associated dynamical systems, called the limit dynamical systems, of self-similar groups. We show that the limit dynamical systems of two self-similar groups are continuously orbit equivalent if and only if their associated Deaconu groupoids are isomorphic as topological groupoids. We also show that the Cuntz-Pimsner groupoids and the Cuntz-Pimsner algebras of self-similar groups are invariants for continuous orbit equivalence of limit dynamical systems.

15:00 - 15:30 Coffee Break

15:30 - 16:10 ÀÌÇöÈ£ (¿ï»ê´ë)
Title: Tracial Rokhlin property for inclusions of C*-algebras
Abstract: Since positive elements and order zero maps replace the role of projections and *-homomorphisms to deal with higher dimensional cases (or dimension greater than zero), there have been several generalizations for Phillips' (tracial) Rokhlin property. We look at on Hirshberg and Orovitz' one more carefully and extend such a notion for inclusions of C*-algebras. Then by establishing the duality between dual inclusions we suggest a dual notion of the tracial Rokhlin property for a finite abelian action.

16:10 - 16:50 °­ÀºÁö (¼­¿ï´ë)
Title: C*-ALGEBRAS OF BOOLEAN DYNAMICAL SYSTEMS
Abstract: Given a Boolean dynamical system (with no assumptions), we associate the universal Cuntz-Krieger Boolean C*-algebra by realizing as the Cuntz-Pimsner algebra of a C*-correspondence. As a corollary, we obtain an associated gauge-invariant uniqueness. We then characterize their gauge-invariant ideals. We also prove that a gauge-invariant ideal is Morita equivalent to a C*-algebra of a Boolean dynamical system. This is a joint work with Toke Meier Carlsen.

16:50 - 17:30 ÇãÀ缺 (ÇѾç´ë)
Title: Reproducing kernel Banach space and Optimazation problem in Machine learning
Abstract: We review reproducing kernel Hilbert spaces and reproducing kernel. We intorduce the notion of reproducing kernel Banach space and observe properties of semi-inner products in a reproducing kernel Banach space. As applications, we discuss a minimal norm interpolation in machine learning schemes and support vector machine and the representer theorem for a minimizer. For multi-task machine learning, we also discuss vector-valued reproducing kernel Banach spaces.

17:30 - 17:45 Concluding Remarks