On the Schauder theory for elliptic PDEs

In this talk, we will discuss two interesting problems on hypersurfaces in the projective space. The first one is the absolute Galois theory on the function field of a very general hypersurface in the projective space. The other one is the c...

거울대칭은 수학의 다른 두 분야의 이론 간 연관관계를 제시하며, 물리학의 초끈이론에서 비롯되어 수학의 여러 분야에 지난 2~30년간 많은 영향을 주었다. 이번 강연에서는 곡면 (구, 토러스 등)에서 곡선들과 이에 둘러싸인 다각형이 만드는 기하학과 이와 ...

We discuss how the closed connected 1-dimensional manifold, namely the circle, can help understanding 3-manifolds. We describe so-called the universal circle proposed by a lengendary mathematician, William Thurston, and discuss certain gene...

헤지펀드에서 사용하고 있는 전략들을 간단히 소개하고 수학적 아이디어가 사용되는 예를 들어 퀀트의 필요한 능력을 소개한다. 수학과 헤지펀드의 관점에서 머신러닝(인공지능)의 사용 예를 설명한다.

Since Belavin, Polyakov, and Zamolodchikov introduced conformal field theory as an operator algebra formalism which relates some conformally invariant critical clusters in two-dimensional lattice models to the representation theory of Viraso...

최근, 노트북, 비디오 카메라, 휴대용 전화기 등과 같은 휴대용 전자 제품의 수요가 급격하게 증대되고, 전기 자동차, 에너지 저장용 축전지, 로봇, 위성 등의 개발이 본격화됨에 따라, 반복적인 충방전이 가능한 고성능 배터리에 대한 관심이 늘어나고 있다. ...

Anomalous diffusion phenomenon has been observed in many natural systems, from the signalling of biological cells, to the foraging behaviour of animals, to the travel times of contaminants in groundwater. In this talk, I will first discuss t...

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초록: SNU-abstract.pdf

기술적 관점에서 AI Technology를 가볍게 살펴보고, 소개하는 서비스 별로 AI를 접목했을 때 어떤 진보 혹은 혁신이 가능한지, 그로 인해 어떤 사업적 가능성이 있는지를 살펴보겠습니다. AI 는 모두가 생각하는 장미빛 청사진 만을 가진것이 아니라 과거의 많...

There are three Bieberbach theorems on flat Riemannian manifolds; characterization, rigidity and finiteness. These extend to almost flat manifolds. We discuss characterization, rigidity and finiteness of infra-nilmanifolds (almost flat manif...

The general theory implies that the distribution of an irreducible Markov chain converges to its stationary distribution as time diverges to infinity. The speed of corresponding convergence is a significant issue in the study of mathematical...

Symplectic geometry has one of its origins in Hamiltonian dynamics. In the late 60s Arnold made a fundamental conjecture about the minimal number of periodic orbits of Hamiltonian vector fields. This is a far-reaching generalization of Poinc...

In late 1970's John McKay discovered the astonishing identity 196884=196883+1, which lead Conway and Norton to formulate the famous Monstrous Moonshine conjectures about the Monster group, the largest sporadic finite simple group. The simple...

Emerging infectious diseases have long been recognized as a continuous, inevitable, unpredictable threat to the global public health. Hence, understanding the underlying dynamics why they spread and what causes epidemics gives key ideas of i...

In this talk, we discuss some results of convex and non-convex optimization methods in image processing. Examples including image colorization, blind decovolution and impulse noise removal are presented to demonstrate these methods. Their a...

Modern mathematics with axiomatic systems has been developed to create a complete reasoning system. This was one of the most exciting mathematical experiments. However, even after the failure of the experiment, mathematical research is still...