The mean curvature flow is an evolution of hypersurfaces satisfying a geometric heat equation. The flow naturally develops singularities and changes the topology of the hypersurfaces at singularities, Therefore, one can study topological pr...

완전동형암호는 암호화된 상태에서 모든 계산을 지원하는 이상적인 암호로서 암호학계의 성배(holy grail)로 불리며 1978년 이후 오랫동안 미해결 문제로 알려져 있었다. 2009년 Gentry에 의해 처음 만들어진 후 많은 연구를 거쳐 실용화를 앞두고 있으며 2011...

동형암호(Homomorphic Encryption)는 암호화된 상태에서 복호화없이 계산을 수행하는 암호로서 1978년 제안된 이후 오랜 연구를 거쳐 최근 실용화를 앞두고 있다. 본 강연에서는 우선 동형암호의 개념과 최근 연구결과 그리고 이의 기계학습에의 응용을 소개한...

The disk embedding problem is of fundamental importance in the study of 4-dimensional topology. I will discuss its significance and difficulty, including how disk embedding makes dimension four intrinsically different from other dimensions. ...

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We start with the famous Heisenberg uncertainty principle to give the idea of the probability in quantum mechanics. The Heisenberg uncertainty principle states by precise inequalities that the product of uncertainties of two physical quantit...

정년퇴임 기념강연회: 숙제

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 ...

Among many different ways to introduce derived algebraic geometry is an interplay between ordinary algebraic geometry and homotopy theory. The infinity-category theory, as a manifestation of homotopy theory, supplies better descent results ...

It is a fascinating and challenging problem to count number fields with bounded discriminant. It has so many applications in number theory. We give two examples. First, we compute the average of the smallest primes belonging to a conjugacy ...

For a given compact Lie group G, classifying all manifolds equipped with G-actions is one of the most fundamental and important problems in differential geometry. In this talk, We will discuss the problem in the symplectic category and expl...

Fitch is a formal proof system recently gaining momentum in logic education due to its structural similarity to human reasoning. We introduce Fitch via its web-implementation at http://www.proofmood.com. Then we compare Fitch with more well-...

Since Fourier introduced the Fourier series to solve the heat equation, the Fourier or polynomial approximation has served as a useful tool in solving various problems arising in industrial applications. If the function to approximate with t...

The 21st century is the age of life science. Two issues in the life sciences are that humans live long, healthy lives and maintain a steady state of the earth's ecosystems despite disturbances. In this talk, we will look at how mathematics i...

We obtain a quantitative and robust proof that incompressible fluid models are strongly ill-posed in critical Sobolev spaces, in the sense that norm inflation and even nonexistence occur for critical initial data. We then show how to use th...

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...

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...

Diffusion of information, rumors or epidemics via various social networks has been extensively studied for decades. In particular, Kempe, Kleinberg, and Tardos (KDD '03) proposed the general threshold model, a generalization of many mathemat...

이 강연에서는 최근 음악, 영화 추천 등 다양한 Recommendation System의 기본 아이디어인 Matrix Completion 문제와, 이를 해결하기 위해 Singular Value Decomposition을 통한 차원 축소 및 내재 공간 학습이 어떤 원리로 이루어 지는지 설명합니다. 그리고 ...