Thursday, June 8, 2023

2023-06-15 / 13:00 ~ 15:00

SAARC 세미나 - SAARC 세미나:

by ()

In astrophysical fluid dynamics, stars are considered as isolated fluid masses subject to self-gravity. A classical model of a self-gravitating Newtonian star is given by the gravitational Euler-Poisson system, while a relativistic star is modeled by the Einstein-Euler system. I will review some recent progress on the local and global dynamics of Newtonian stars, and discuss mathematical constructions of gravitational collapse that show the existence of smooth initial data leading to finite time collapse, characterized by the blow-up of the star density. For Newtonian stars, dust-like collapse and self-similar collapse will be presented, and the relativistic analogue and formation of naked singularities for the Einstein-Euler system will be discussed.

2023-06-15 / 16:00 ~ 18:00

학과 세미나/콜로퀴엄 - 대수기하학:

by 장승욱()

Tropicalizations of affine varieties give interesting ways to sketch and study affine varieties, whose tools are astonishingly elementary at the algebraic level. Not only that, studying algebraic dynamics on varieties may give interesting pictures under tropicalizations, as worked by Spalding and Veselov, or Filip. In this talk, we will introduce some basicmost ideas of tropicalizations, and play with the Markov cubic surfaces $$X^2+Y^2+Z^2+XYZ=AX+BY+CZ+D,$$ where A, B, C, D are parameters, as an example of tropical study of algebraic dynamics. It turns out that we obtain a $(\infty,\infty,\infty)$-triangle group action on the hyperbolic plane as a model of dynamics of interest. 언어: Korean (possibly English, depending on the audience)

2023-06-09 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나:

by 이동헌(고려대학교)

Sequential decision making under uncertainty is a problem class with solid real-life foundation and application. We overview the concept of Knowledge Gradient (KG) from the perspective of multi-armed bandit (MAB) problem and reinforcement learning. Then we discuss the first KG algorithm with sublinear regret bounds for Gaussian MAB problems.

2023-06-13 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Strong Erdős-Hajnal property on chordal graphs and its variants

by 조민호(IBS 극단조합및확률그룹)

A graph class $\mathcal{G}$ has the strong Erdős-Hajnal property (SEH-property) if there is a constant $c=c(\mathcal{G}) > 0$ such that for every member $G$ of $\mathcal{G}$, either $G$ or its complement has $K_{m, m}$ as a subgraph where $m \geq \left\lfloor c|V(G)| \right\rfloor$. We prove that the class of chordal graphs satisfies SEH-property with constant $c = 2/9$. On the other hand, a strengthening of SEH-property which we call the colorful Erdős-Hajnal property was discussed in geometric settings by Alon et al.(2005) and by Fox et al.(2012). Inspired by their results, we show that for every pair $F_1, F_2$ of subtree families of the same size in a tree $T$ with $k$ leaves, there exist subfamilies $F'_1 \subseteq F_1$ and $F'_2 \subseteq F_2$ of size $\theta \left( \frac{\ln k}{k} \left| F_1 \right|\right)$ such that either every pair of representatives from distinct subfamilies intersect or every such pair do not intersect. Our results are asymptotically optimal. Joint work with Andreas Holmsen, Jinha Kim and Minki Kim.

2023-06-08 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

by ()

To understand nonparametric regression, we should know first what the parametric model is. Simply speaking, the parametric regression model consists of many assumptions and the nonparametric regression model eases the assumptions. I will introduce what assumptions the parametric regression model has and how the nonparametric regression model relieves them. In addition, their pros and cons will be also presented.

2023-06-14 / 14:00 ~ 15:30

학과 세미나/콜로퀴엄 - 박사논문심사: 확률 모델 단순화를 통한 생화학네트워크 분석

by 홍혁표 (KAIST)()

2023-06-13 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 박사논문심사: 그래프 파라미터의 알고리듬 및 구조적 측면

by 안정호(KAIST)()

2023-06-09 / 10:00 ~ 11:00

SAARC 세미나 - SAARC 세미나:

by 서인석(서울대학교)

TBA

2023-06-09 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

by ()

TBD

2023-06-08 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by ()

A digital twin is a virtual representation of real-world physical objects. Through accurate and streamlined simulations, it effectively enhances our understanding of the real world, enabling us to predict complex and dynamic phenomena in a fraction of the time. In this talk, we will explore real-world applications of AI-based partial differential equation (PDE) solvers in various fields. Additionally, we will examine how such AI can be utilized to facilitate downstream tasks related to PDEs.

Events for the 취소된 행사 포함