Friday, December 3, 2021

2021-12-09 / 16:00 ~ 17:30

학과 세미나/콜로퀴엄 - 박사논문심사: 보형 표현의 산술성

by 이영민(KAIST)

심사위원장 : 배성한, 심사위원 : 김완수, 임보해, 임수봉(성균관대 수학교육학과), 최도훈(고려대 수학과)

2021-12-06 / 10:00 ~ 11:30

학과 세미나/콜로퀴엄 - 박사논문심사: 확률론의 기본적인 극한 정리들에 대한 재탐구

by 진우영(KAIST)

심사위원장 : 폴정, 심사위원 : 이지운, 남경식, 양홍석(전산학부), Greg Markowsky(Senior Lecturer, School of Mathematics, Monash University)

2021-12-03 / 10:00 ~ 11:00

SAARC 세미나 - SAARC 세미나:

by 장주희()

In astrophysical fluid dynamics, stars are considered as isolated fluid masses subject to self-gravity. A classical model to describe the dynamics of Newtonian stars is given by the gravitational Euler-Poisson system, which admits a wide range of star solutions that are in equilibrium or expand for all time or collapse in a finite time or rotate. In particular, using numerics, the Euler-Poisson system in the super-critical regime has been widely used inastrophysics literature todescribe the gravitational collapse, but its rigorous proof has been established only recently. The main challenge comes from thepressure, which actsagainstgravitational force. In this talk, I will discuss some recent progress on Newtonian dust-like collapse and self-similar collapse.

2021-12-08 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 응용수학 세미나: 금융사에서의 AI 활용 현실: 하나금융사의 신용평가모형

by 정대연(하나금융티아이)

하나금융 융합기술원은 국내 금융그룹 최초의 AI 연구소로 2018년부터 지난 4년 간 다양한 금융서비스에 현행 AI 응용기술들을 접목시키고 금융사 내 기술 전파에 큰 성과를 올려왔다. 그 중에서도 융합기술원이 연구/개발하는 신용평가 기술은 업계를 선도하고 있으며 그런 선도 기술을 만들어나가는 과정을 소개하려 한다. 또한, 응용기술 뿐만 아니라 향후 다양한 분야의 원천기술 연구를 위해 국내 유수 산업/학계 인재들이 모이는 조직으로 변형해가는 노력을 소개할 예정이다.

2021-12-03 / 13:00 ~ 14:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by ()

This series of lectures will focus on recent developments of the so-called a-contraction theory and its application to the study of discontinuous flow at high Reynolds numbers. We will first introduce the classical framework to study the stability of 1D shocks for compressible flows. Recent multi-D applications will be presented next, both in the context of compressible and incompressible flows.

2021-12-08 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 정수론:

by 김병두()

In this presentation, I will present me, Daeyeol Jeon, and Chang Heon Kim's construction of certain points on $X_1(N)$ over ring class fields (and therefore construction of points on the abelian varieties associated to newforms of level $\Gamma_1(N)$). Our work generalizes Bryan Birch's Heegner points on $X_0(N)$. Then, we show that these points form Euler systems (like the Heegner points), and we improve Kolyvagin's Euler system techniques to show that for our point $P_{\tau_K/c}$ and any ring class character $\chi$ of the extended ring class field of conductor $c$ satisfying $\chi=\overline{\chi}$, if $P_{\tau_K/c}^\chi$ is non-torsion and $G_K \to \operatorname{Aut} A_f[\pi]$ is surjective, then the corank of $\Sel(A_\chi/K)$ is 1, which implies the rank of $A_f(K)^\chi$ is 1. (Please contact Bo-Hae Im if you want to join the seminar.)

2021-12-07 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Independent domination of graphs with bounded maximum degree

by 조은경(한국외국어대)

The independent domination number of a graph $G$, denoted $i(G)$, is the minimum size of an independent dominating set of $G$. In this talk, we prove a series of results regarding independent domination of graphs with bounded maximum degree. Let $G$ be a graph with maximum degree at most $k$ where $k \ge 1$. We prove that if $k = 4$, then $i(G) \le \frac{5}{9}|V(G)|$, which is tight. Generalizing this result and a result by Akbari et al., we suggest a conjecture on the upper bound of $i(G)$ for $k \ge 1$, which is tight if true. Let $G'$ be a connected $k$-regular graph that is not $K_{k, k}$ where $k\geq 3$. We prove that $i(G')\le \frac{k-1}{2k-1}|V(G')|$, which is tight for $k \in \{3, 4\}$, generalizing a result by Lam, Shiu, and Sun. This result also answers a question by Goddard et al. in the affirmative. In addition, we show that $\frac{i(G')}{\gamma(G')} \le \frac{k^3-3k^2+2}{2k^2-6k+2}$, strengthening upon a result of Knor, \v Skrekovski, and Tepeh, where $\gamma(G')$ is the domination number of $G'$. Moreover, if we restrict $G'$ to be a cubic graph without $4$-cycles, then we prove that $i(G') \le \frac{4}{11}|V(G')|$, which improves a result by Abrishami and Henning. This talk is based on joint work with Ilkyoo Choi, Hyemin Kwon, and Boram Park.

2021-12-09 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄: Random surfaces (Liouville quantum gravity)

by 남경식(KAIST 수리과학과)

Liouville quantum gravity (LQG) surfaces are random topological surfaces which are important in statistical mechanics and have deep connections to other mathematical objects such as Schramm–Loewner evolution and random planar maps. These random surfaces are too singular and fractal in the sense that the Hausdorff dimension, viewed as a metric space equipped with its intrinsic metric, is strictly bigger than two. I will talk about the interesting geometric structure and recent progress on LQG surfaces.

Events for the 취소된 행사 포함