Injo Hur (Chonnam Nat’l Univ): 1D Schrodinger operators and de Branges spaces

Abstract: In this talk, we apply de Branges theory on (the spectral theory of) Schrodinger operators. More precisely, we first compare (old) de Branges spaces and Sub-Hardy spaces and then see the connection between them. After this, for 1D Schrodinger operators on $L^2(0,∞)$ defined by $H =−frac{d2}{dx2} +V(x)$, we show the one-to-one correspondence between (real-valued) potentials V and inner products on one specific de Branges space which does not depend on V as a set (and so which can be naturally expected)

Jaeseong Heo (Hanyang Univ): Free entropy and its application 

Abstract: We briefly review free probability theory and introduce the definition of free entropy. We examine applications of free entropy for some problems in von Neumann algebras. We discuss methods for estimating free entropy by calculating the volume of convex sets in Euclidean space.

Seonguk Yoo (Gyeongsang Nat’l Univ): Truncated Moment Problems with an Extension of Multiplication Operators

Abstract:  The moment problem is a fundamental mathematical problem with significant implications in probability theory, statistics, physics, and engineering. The application of this problem is vast, ranging from characterizing the distribution of a random variable to analyzing system response characteristics, image reconstruction, and solving problems in operator theory and optimization. The moment problem mathematically focuses on reconstructing the original probability distribution or measure from a given sequence of moments. To address the truncated moment problem, various techniques are employed, such as verifying the existence of a flat extension of the moment matrix, analyzing the properties of orthogonal polynomials corresponding to the moment sequence, and checking the commutativity of multiplication operators in the Hilbert space generated by the moment sequence. In this talk, we will explore an algorithm for verifying the commutativity of multiplication operators in a Hilbert space associated with a bivariate truncated moment sequence. We will also discuss the dimension stability of the Hilbert space.

Seung-Hyeok Kye (Seoul Nat’l Univ): Detecting Schmidt numbers of bi-partite quantum states

Abstract: Schmidt numbers of bi-partite states measure the degree of entanglement; the higher Schmidt number of a state is, the more entangled it is. It is very hard to determine the Schmidt numbers of bi-partite states. In fact, it is known to be NP hard, and we need Schmidt number witnesses in order to determine Schmidt numbers of bi-partite states. Such witnesses are Choi matrices of $k$-positive maps between matrix algebras and they detect Schmidt numbers through bilinear pairing between mapping spaces and tensor products. In this contexts, we begin the talk to introduce various kinds of positive maps between matrix algebras, and use Choi matrices and bi-linear pairing to explain what are Schmidt numbers and how witnesses detect Schmidt numbers. We explore recent criteria to determine if a given Hermitian matrix is Schmidt number $k$ witnesses or not, and use supporting hyperplanes for witnesses to determine Schmidt numbers. The main parts of this talk will be based on two papers with Kyung Hoon Han:

-- Global locations of Schmidt number witnesses, Phys. Rev. A 112 (2025), 032426. arXiv 2505.10288

-- Supporting hyperplanes for Schmidt numbers and Schmidt number witnesses, Open Syst. Inf. Dyn. 32 (2025), 2550008. arXiv 2506.03733

Young Joo Lee (Chonnam Nat’l Univ): Zero sums of dual Toeplitz products

Abstract:  In this talk, we consider dual Toeplitz operators acting on the orthogonal complements of the Bergman, Fock and Dirichlet spaces, and discuss recent progress on the problem of when a sum of several dual Toeplitz products equals zero.

Mingu Jung (Hanyang Univ): Group actions and the Radon-Nikodým property

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Yun-Ho Kim (Sangmyung Univ): Elliptic problems with unbalanced growth and Hardy potential

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◾Mini-Workshop on Hilbert Space Operators

Il Bong Jung (Kyungpook Nat’l Univ): TBA

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Koeun Choi (Korea Univ): TBA

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Sumin Kim (Changwon Nat’l Univ): TBA

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Yoenha Kim (Ajou Univ): TBA

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◾Tutorials on the invariant subspaces of the model operator

Lecturer: In Sung Hwang (Sungkyunkwan Univ): 

Abstracts: In this tutorial series we explore the invariant subspaces of the model operators by using the invariant subspaces of the shift operator. We try to decompose the model operator into a sum of simpler arts, connecting such a decomposition with a refinement of the spectrum of the model operator. When a further refinement of the spectrum is not any longer possible, it will be necessary to single out a chain of invariant subspaces, which leads to integral representations for the operator which are analogous to the triangular form for matrices in linear algebra. It turns however out to be most difficult to reconstruct the properties of its restrictions to the terms of the decomposition. Several of the lectures will be devoted to this reconstruction.