Tuesday, March 3, 2026

2026-03-06 / 15:30 ~ 17:30

by 양효선(경희대학교)

Quantum computing offers new possibilities for scientific computing by enabling operations on exponentially large state spaces. In this lecture, we discuss how nonlinear partial differential equations (PDEs) can be connected to quantum algorithms through mathematical linearization frameworks. After a brief introduction to the fundamentals of quantum computation and quantum numerical linear algebra, we present Koopman and Koopman–von Neumann (KvN) formulations that embed nonlinear dynamics into linear operators. We then outline how these ideas, combined with Carleman linearization and relaxation-based methods, can lead to quantum-ready formulations of nonlinear PDE solvers.

2026-03-10 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Well-quasi-ordering Eulerian directed Graphs by (strong) Immersion

by Dario Cavallaro(TU Berlin)

Directed graphs prove to be very hard to tame in contrast to undirected graphs. In particular, they are not well-quasi-ordered by any known relevant inclusion relation, and are lacking fruitful structure theorems. This motivates the search for structurally rich subclasses of directed graphs that are well behaved. Eulerian directed graphs are a particularly prominent example, sharing many similarities with undirected graphs. In fact, it is conjectured that Eulerian directed graphs are well-quasi-ordered by weak immersion, and even well-quasi-ordered by strong immersion when restricting to classes of bounded degree. We believe that we have a proof of both conjectures, and I will report on the current status, progress, and steps towards said proof and its implications. This is joint work with Ken-ichi Kawarabayashi and Stephan Kreutzer.

2026-03-09 / 16:00 ~ 17:30

편미분방정식 통합연구실 세미나 - 편미분방정식:

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Abstract: In this seminar, we study the logistic diffusion equation, a reaction–diffusion model, and its equilibria. We first establish existence and regularity of positive solutions to the parabolic problem. We then use the comparison principle to show that, as time tends to infinity, the solution converges to a steady state solving the corresponding elliptic equation. We recall why the existence of solutions to this elliptic problem is not easily obtained by standard variational methods. Finally, we discuss how stability depends on the resource term and how the solution behavior changes with the diffusion rate. References: [1] Cantrell, R.S., Cosner, C. Spatial ecology via reaction-diffusion equation. Wiley series in mathematical and computational biology, John Wiley & Sons Ltd (2003)

2026-03-03 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Problems on graph coloring

by Chính T. Hoàng(Wilfrid Laurier University)

A k-coloring of a graph is an assignment of k colors to its vertices such that no two adjacent adjacent vertices receive the same color. The Coloring Problem is the problem of determining the smallest k such that the graph admits a k-coloring. Given a set L of graphs, a graph G is L-free if G does not contain any graph in L as an induced subgraph. The complexity of the Coloring Problem for L-free graphs is known (NP-complete or polynomial-time solvable) whenever L contains a single graph. There has been keen interest in coloring graphs whose forbidden list L contains basic graphs such as induced paths, induced cycles and their complements. In this talk, I will provide a survey of recent progress on this topic.

Events for the 취소된 행사 포함