KWMS 한국여성수리과학회

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Lecture 1. Soon-Yi Kang (Kangwon National Univ.) q-series and integer partitions: from Euler to prime detection (13:30-14:20): Integer partition is a fundamental and natural topic in mathematics, appearing across various fields such as combinatorics, modular form theory, representation theory, and mathematical physics and so on. In this talk, we provide a comprehensive survey of the contributions by Euler, Ramanujan, and MacMahon, who are regarded as pioneers in the development of partition theory. The main emphasis is on gap partitions, partition congruences, and prime-detecting partitions.

Lecture 2. Mikyong Lim (KAIST) The Neumann-Poincaré Operator: Properties and Applications (14:30-15:20): The Neumann-Poincaré (NP) Operator is a singular integral operator that naturally arises when solving transmission problems in partial differential equations (PDEs) using boundary integral formulation. In this talk, we review essential properties of the NP operator and explore their applications to PDEs, inverse problems, and the theory of composite materials.

Lecture 3. Eunjeong Lee (Chungbuk National Univ.) Towards understanding torus orbit closures (15:30-16:20): A toric variety is a normal algebraic variety containing an algebraic torus as an open dense subset, such that the action of the torus on itself extends to the whole variety. Due to their rich symmetries, toric varieties establish a fruitful connection between geometry, topology, combinatorics, and representation theory. In this talk, we will consider a specific family of toric varieties living in a flag variety. A flag variety is a smooth projective homogeneous variety, denoted as $G/B$, where $G$ is a semisimple algebraic group and $B$ is a Borel subgroup. The maximal torus $T \subset B$ acts on $G/B$ via left multiplication. By examining the closures of torus orbits under this $T$-action, one can construct a family of toric varieties within $G/B$. For instance, a permutohedral variety can be obtained in this manner. We will explore these toric varieties in detail. This talk is based on several collaborations with Seonjeong Park and Mikiya Masuda.

Lecture 4. Hyoseon Yang (Kyung Hee Univ.) Order enhanced numerical schemes through non-polynomial approximation (16:30-17:20): We introduce an approximation method that establishes certain order enhancements by leveraging radial basis functions (RBFs) in the numerical solution of conservation laws. The use of RBFs for interpolation and approximation is a well developed area of research. Of particular interest in this work is the development of high order finite volume (FV) weighted essentially non-oscillatory (WENO) methods, which utilize RBF approximations to obtain required data at cell interfaces. The aforementioned improvement in the order of accuracy is addressed through an analysis of the truncation error, resulting in expressions for the shape parameters appearing in the basis. This paper seeks to address the practical elements of the approach, including the evaluations of shape parameters as well as a hybrid implementation.