Wednesday, December 8, 2021

2021-12-15 / 10:00 ~ 11:00

by ()

The Yau-Zaslow formula describes the number of rational curves in a linear system on a smooth projective K3 surface in terms of a modular form. In this talk, I will review the Yau-Zaslow formula with some examples and then discuss an equivariant version of the formula for K3/abelian surfaces. When the K3/abelian surface admits a finite group G-action, we can consider a linear system with the induced action. It turns out that the equivariant version of the formula will count G-rational curves and it will also provide interesting modular forms.

2021-12-14 / 14:00 ~ 15:30

학과 세미나/콜로퀴엄 - 박사논문심사: OS 레벨의 시스템 제어 기술과 인공지능 기술을 기반으로 한 화면캡쳐 방지 시스템

by 이영(KAIST)

심사위원장 : 한상근, 심사위원 : 곽도영(명예교수), 황강욱, 강완모, 조현숙(이사장, 코드게이트 보안포럼)

2021-12-15 / 14:00 ~ 15:30

학과 세미나/콜로퀴엄 - 박사논문심사: 구조화된 비볼록-비오목 최소 최대화 문제를 위한 효율적이고 수렴하는 경사 방법들

by 이수철(KAIST)

심사위원장 : 김동환, 심사위원 : 강완모, 이창옥, 임미경, 윤세영(AI 대학원)

2021-12-14 / 10:00 ~ 11:30

학과 세미나/콜로퀴엄 - 박사논문심사: 쌍선형 밴딧 해법에 관한 연구

by 장경석(KAIST)

심사위원장 : 강완모, 심사위원 : 황강욱, 김동환, 윤세영(AI대학원), 전광성(Assistant Professor, Department of Computer Science, University of Arizona)

2021-12-13 / 14:30 ~ 16:00

학과 세미나/콜로퀴엄 - 박사논문심사: Parabolic과 Hyperbolic singular limit을 통한 reaction diffusion equation의 wave propagation

by 박현준(KAIST)

심사위원장 : 김용정, 심사위원 : 강문진, 김재경, 임미경, 안인경(고려대 세종캠퍼스 데이터계산학과)

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)

2021-12-14 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Exponential decay of intersection volume with applications on list-decodability and sphere-covering bounds

by Tuan Tran(IBS 이산수학그룹)

We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking, this happens when the metric space is (i) expanding and (ii) well-spread, and (iii) certain random variable on the boundary of a ball has a small tail. As applications, we show that the volume of intersection of balls in Hamming space and symmetric groups decays exponentially as their centers drift apart. To verify condition (iii), we prove some deviation inequalities `on the slice’ for functions with Lipschitz conditions. We then use these estimates on intersection volumes to obtain a sharp lower bound on list-decodability of random q-ary codes, confirming a conjecture of Li and Wootters [IEEE Trans. Inf. Theory 2021]; and improve sphere-covering bound from the 70s on constant weight codes by a factor linear in dimension, resolving a problem raised by Jiang and Vardy [IEEE Trans. Inf. Theory 2004]. Our probabilistic point of view also offers a unified framework to obtain improvements on other sphere-covering bounds, giving conceptually simple and calculation-free proofs for q-ary codes, permutation codes, and spherical codes. This is joint work with Jaehoon Kim and Hong Liu.

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.

2021-12-08 / 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.)

2021-12-09 / 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