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講師： Un Cig Ji 教授   （Department of Mathematics, Chungbuk National University）

Sangho Kum 教授（Department of Mathematics Education, Chungbuk National University）

Jaeseong Heo 教授（Department of Mathematics, Hanyang University）                        

日時：令和７年２月２５日（火）１３：００～１６：００

題目： 13：00～13：50　U.C. Ji

A Quantum Analogue of Ornstein-Uhlenbeck Semigroups

14：00～14：50   S. Kum

Regularized medians on symmetric cones

15：00～15：50　J. Heo

Positivity of bilinear maps and its Choi J-matrix for applications to tripartite entanglements

場所：名城大学共通講義棟東E403室

要旨：

Professor U.C.Ji

In this talk, we first discuss classical Ornstein-Uhlenbeck semigroup on infinite dimensional Gaussian space.

 Next, we explore the canonical topological isomorphisms between the spaces of two variable white noise functionals and the spaces of white noise operators. Based on the canonical topological isomorphism, we formulate a quantum analogue of the Ornstein-Uhlenbeck semigroups of which the positivity will be discussed by applying the Kolmogrov decomposition of the positive white noise operators. Additionally, we discuss the invariant measure and the invariant white noise operators under the classical quantum Ornstein-Uhlenbeck semigroup and its quantum analogue,respectively. Finally, the Gaussianity of the quantum analogue of the Ornstein-Uhlenbeck semigroup will be discussed.

Professor S.Kum

We are concerned with an extension of main results of [1] into a general symmetric cone from the convex cone of positive definite matrices. To be more specific, two regularized median optimization problems are introduced and　the existence and uniqueness of solutions are studied on symmetric cones. Moreover the Lipschitz continuity of the gradient of objective functions of the regularized median optimizations are provided for a possible design of gradient-based methods of finding the unique minimizer. Based on some results of [2], we present purely Jordan-algebraic techniques of proof in comparison with matrixanalytic ones [1].

Professor J. Heo

We consider bilinear analogues of J-positivity for linear maps on Krein spaces and introduce the Choi J-matrices of bilinear maps.  We characterize the J-positivity of bilinear maps in terms of their Choi J-matrices and discuss some applications of tripartite entanglements.