Tuesday, April 11, 2023

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2023-04-14 / 16:00 ~ 17:30
학과 세미나/콜로퀴엄 - PDE 세미나: 인쇄
by 정인지(서울대학교)
We study logarithmic spiraling solutions to the 2d incompressible Euler equations which solve a nonlinear transport system on the unit circle. We show that this system is locally well-posed for L^p data as well as for atomic measures, that is logarithmic spiral vortex sheets. We prove global well-posedness for almost bounded logarithmic spirals and give a complete characterization of the long time behavior of logarithmic spirals. This is due to the observation that the local circulation of the vorticity around the origin is a strictly monotone quantity of time. We are then able to show a dichotomy in the long time behavior, solutions either blow up (in finite or infinite time) or completely homogenize. In particular, bounded logarithmic spirals converge to constant steady states. For vortex logarithmic spiral sheets the dichotomy is shown to be even more drastic where only finite time blow up or complete homogenization of the fluid can and does occur.
2023-04-14 / 11:00 ~ 12:00
학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나: 인쇄
by 황지영()
Knowledge graphs represent human knowledge as a directed graph, representing each fact as a triplet consisting of a head entity, a relation, and a tail entity. Knowledge graph embedding is a representation learning technique that aims to convert the entities and relations into a set of low-dimensional embedding vectors while preserving the inherent structure of the given knowledge graph. Once the entities and relations in a knowledge graph are represented as a set of feature vectors, those vectors can be easily integrated into diverse downstream tasks. This talk introduces a new concept of knowledge graph called a bi-level knowledge graph, where the higher-level relationships between triplets can be represented. Learning representations on a bi-level knowledge graph, machines are allowed to solve problems requiring more advanced reasoning than simple link prediction. Also, as a practical example of knowledge graph embedding, how one can utilize the knowledge representations to operate a real robot is briefly explained. This talk discusses how knowledge graph embedding models effectively deliver human knowledge to machines, which is critical in many AI applications.
2023-04-14 / 16:00 ~ 17:30
SAARC 세미나 - SAARC 세미나: 인쇄
by 정인지(서울대학교 수리과학부)
We study logarithmic spiraling solutions to the 2d incompressible Euler equations which solve a nonlinear transport system on the unit circle. We show that this system is locally well-posed for L^p data as well as for atomic measures, that is logarithmic spiral vortex sheets. We prove global well-posedness for almost bounded logarithmic spirals and give a complete characterization of the long time behavior of logarithmic spirals. This is due to the observation that the local circulation of the vorticity around the origin is a strictly monotone quantity of time. We are then able to show a dichotomy in the long time behavior, solutions either blow up (in finite or infinite time) or completely homogenize. In particular, bounded logarithmic spirals converge to constant steady states. For vortex logarithmic spiral sheets the dichotomy is shown to be even more drastic where only finite time blow up or complete homogenization of the fluid can and does occur.
2023-04-11 / 16:30 ~ 17:30
학과 세미나/콜로퀴엄 - Mathematics & Beyond Seminar: Fashion and Mathematics 인쇄
by 홍혜진((주)아티스트메이드)
다양한 소비재 중에서 유독 패션 카테고리는 그간 디지털 전환이 느린 분야였으며, 유통과 마케팅의 영역에서만 데이터를 주로 활용하는 양상을 보여왔다. 비정형적, 주관적인 의사 결정이 주를 이루는 '패션'에서 수학은 어떤 의미와 효용이 있는지 제조업을 운영하는 디자이너의 관점에서 실무 사례 위주로 이야기하려 한다.
2023-04-11 / 16:30 ~ 17:30
IBS-KAIST 세미나 - 이산수학: Two structural results for pivot-minors 인쇄
by James Davies(University of Cambridge)
Pivot-minors can be thought of as a dense analogue of graph minors. We shall discuss pivot-minors and two recent results for proper pivot-minor-closed classes of graphs. In particular, that for every graph H, the class of graphs containing no H-pivot-minor is 𝜒-bounded, and also satisfies the (strong) Erdős-Hajnal property.
2023-04-13 / 16:15 ~ 17:15
학과 세미나/콜로퀴엄 - 콜로퀴엄: 인쇄
by ()
We first survey on nodal solutions for coupled elliptic equations, using results from nonlinear scalar field equations as motivations. Then we discuss work for constructing multiple nodal solutions using various variational methods. In particular we discuss in some details the results about solutions having componentwisely-shared nodal numbers of coupled elliptic systems. These works are done by further developing minimax type critical point theory with built-in flow invariance of the associated gradient or parabolic flows, which has been a useful tool to give locations of critical points via minimum methods, also revealing complex dynamic behavior of the flow.
Events for the 취소된 행사 포함 모두인쇄
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