Thursday, November 19, 2020

2020-11-26 / 15:00 ~ 18:00

학과 세미나/콜로퀴엄 - PDE 세미나: DYNAMICAL STABILITY OF UNIFORMLY ROTATING BINARY STARS AND GALAXIES

by 석진명(경기대학교)

In this talk, we are concerned with dynamically stability of uniformly rotating binary stars and galaxies, which are represented as stationary solutions to Euler-Poisson equations and VlasovPoisson equations respectively. These solutions were constructed as minimizers of suitable variational problems by McCann in which some kind of structural stability on them is discussed. This talk focuses on the nonlinear dynamical stability of them, based on Cazenave-Lions type arguments exploiting variational characterization of stationary solutions. We will see that the uniqueness of a minimizer, which is one of the main results of our work, plays an indispensable role in analysis. This talk is based on a joint work with Prof. Juhi Jang at USC.

2020-11-26 / 15:00 ~ 18:00

학과 세미나/콜로퀴엄 - PDE 세미나: Some results on bound state and semi-classical solutions of Kirchhoff type problem

by 시에 치린(Guangdong University of Technology)

In this talk, I will give some existence results on nontrivial solutions of Kirchhoff type problem by the variational methods. In this first parts, the bound state solutions of this problem with a critical exponent have been obtained by deformation results after a local compactness result has been recovered. We found a different and interesting results when this problem is considered in a high dimension N larger than 4. In the second parts, I will give some results on semi-classical solutions

2020-11-26 / 13:00 ~ 14:00

학과 세미나/콜로퀴엄 - 대수기하학:

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For a very ample line bundle L on a projective scheme X, we say that (X,L) satisfies property QR(k) if the homogeneous ideal of the linearly normal embedding can be generated by quadrics of rank <= k. Many classical varieties such as Segre-Veronese embeddings, rational normal scrolls and curves of high degree satisfy the property QR(4). In this talk, we will briefly show that the second and higher Veronese embeddings satisfies the property QR(3). And we will discuss about the asymptotic behavior of property QR(3) for any projective scheme.

2020-11-25 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 대수기하학:

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The existence of Kaehler-Einstein metric and Kaehler-Einstein edge metric on n-dimensional complex varieties is related to the existence of Sasaki-Einstein metric on links over the varieties which is (2n+1)-dimensional real manifolds. We discuss results about existence problem of the both metrics on weighted log del Pezzo surfaces and links over the surfaces that are 5-dimensional Smale manifolds.

2020-11-19 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 산업응용수학 세미나: AI 시대의 대학수학교육 (미래사회-산업-대학수학-중등수학 교육의 연계)

by 이상구(성균관대학교)

2020년 현재 우리가 사는 사회는 인공지능(AI), 사물인터넷(IoT), 빅데이터(Big Data) 등의 첨단 정보기술이 사회와 경제 전반에 융합되어 혁신적인 변화가 일어나고 있다. 이미 스마트폰, 데이터, 정보, 인공지능, 포노사피엔스, 디지털 전환(Digital Transformation) 등의 키워드는 현 시대의 흐름을 잘 나타내주고 있으며, 헬스케어, 지능형 로봇, 가정용 인공지능 시스템, 공유자동차 등이 우리 생활에 깊이 영향을 미치고 있다. 이런 변화의 중심에 수학이 위치하고 있으며, 사회는 적절한 수학적 지식을 갖춘 인재를 필요로 하고 있다. 따라서 수학자와 수학교육자는 이런 변화를 가능케 하는 수학에 대하여 다양한 전공의 대학생들과 일반인들에게 이해시키는 것이 꼭 필요하다. 본 발표에서는 ”AI 시대의 대학수학교육 "이란 제목으로, 행렬론을 전공한 발표자가 그간의 경험을 활용하여 ‘대학생을 위한 Math for AI’ 와 '(K-MOOC) 일반인을 위한 인공지능을 의한 기초수학 입문' 과목을 개발하고 교재와 실습실을 만들어, 지난 4학기 동안 강의하면서 경험한 내용을 공유하고자 한다. (Zoom link: https://kaist.zoom.us/j/89057059601?pwd=dGI4NHRDUGNQMVQrVXg3YWxvRXA3dz09)

2020-11-26 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 콜로퀴엄: Algebraic fibre space via convex bodies

by 최성락(연세대학교)

Algebraic fibre spaces are relative versions of algebraic varieties. For an algebraic fibre space f:X->Y, the varieties X,Y and the general fibre F are deeply related by various formulas and conjectures on the invariants of varieties. For example, the Iitaka conjecture is still an open problem which predicts that the Kodaira dimension of X is at least the sum of kodaira dimensions of F and Y. We explain how the geometry of algebraic fibre spaces can be studied by convex bodies called Okounkov bodies.

Events for the 취소된 행사 포함