2026년 2월 11일

강연 1. 남하얀 (건국대학교) On Irreducible Elements of Numerical Semigroup Algebras (13:30-14:30)

A numerical semigroup $S$ is a subset of the set of nonnegative integers that includes $0$, is closed under addition, and has a finite complement. The Davenport constant \(D(G)\) of a finite group \(G\) is the smallest number \(d\) such that any sequence of length \(\ge d\) contains a non-empty zero-sum subsequence. In other words, \(D(G)-1\) is the maximum length of a zero-sum-free sequence. We define a quotient ring \(\mathcal{Q}_q(S)\) of a numerical semigroup \(S\) and derive a formula for \(D(\mathcal{Q}_q(S))\). Furthermore, we compute the range of the atomic density of \(S\) in terms of \(D(\mathcal{Q}_q(S))\).

강연 2. 박은희 (강원대학교) Domain Decomposition Methods: Algorithms and Applications (14:30-15:30)

Domain decomposition methods are numerical algorithms for computing approximate solutions to partial differential equation models. This talk focuses on their structural characteristics as parallel algorithms and their key properties as efficient solvers for large-scale problems. In addition, selected PDE-based applications are presented to illustrate how domain decomposition methods are employed in practice.

강연 3. 홍재현 (IBS)  Automorphisms and deformations of regular semisimple Hessenberg varieties (15:30-16:30)

Flag varieties and their subvarieties have been studied in many areas of mathematics, including algebraic geometry, differential geometry, topology, representation theory, and combinatorics. Hessenberg varieties, introduced in 1988 by de Mari and Shayman in relation to the QR algorithm for matrix eigenvalue problems, have regained attention due to their connection to the Stanley-Stembridge conjecture in combinatorics. In this talk, we discuss their automorphisms and deformations. The GKM theory tells us that the cohomology spaces of regular semisimple Hessenberg varieties as representation spaces of the Weyl group are the same for a given Hessenberg space. One immediate question is whether two regular semisimple Hessenberg varieties associated to the same Hessenberg space are isomorphic as algebraic varieties. We show that regular semisimple Hessenberg varieties can have moduli.

Discussion (16:30-18:00)

석식 (18:10-19:30)