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 ...

Many problems in financial mathematics are closely related to the stochastic optimization problem because the optimal decision must be made under the uncertainty. In particular, optimal stopping, singular control, and optimal switching prob...

In this colloquium talk, we study the Vlasov-Maxwell equations, a collisionless model in the field of kinetic theory. The model is a fundamental model for the dynamics of plasmas and was introduced in 1938 by Vlasov. Due to the hyperbolic n...

인공지능은 지난 60년 동안 큰 변화를 거쳤다. 초기의 논리기호기반 연역적 지능 시스템 패러다임에서 현재의 데이터기반 귀납적 지능 시스템 패러다임으로 전환되었다. 이제는 인공지능을 개발하기 위해서 사람이 더 이상 직접 프로그래밍하지 않는다. 사람은...

A circle action on a manifold can be thought of as a periodic flow on a manifold (periodic dynamical system), or roughly a rotation of a manifold. During this talk, we consider symplectic/Hamiltonian circle actions on compact symplectic mani...

In this talk, I will introduce the audience to the original beauty that leads to exploring the mathematical elements in music. I will cover the following topics on the connection between music and mathematics. - Harmonics & equations - ...

Volume entropy of a compact manifold is the exponential growth rate of balls in the universal cover. This seemingly coarse invariant contains a lot of geometric information of the manifold. We will discuss some relations to other invariants,...

Ergodic theory of horocycle flow and nilflow has been proved to be useful for analyzing the randomness of Mobius function, a function which reveals the mystery of prime numbers. In this survey talk, we will introduce Mobius function and seve...