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...

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...

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...

Non-vanishing modulo a prime of special values of various $L$-functions are of great importance in studying structures of relevant arithmetic objects such as class groups of number fields and Selmer groups of elliptic curves. While there hav...

The talk will review a new approach to the limits of the quantum N-body dynamics leading to the Hartree equation (in the large N limit) and to the Liouville equation (in the small Planck constant limit). This new strategy for studying both l...

현대 연속시간 포트폴리오 선택이론에 대하여 설명한다. 마코위츠 의 정적 선택이론으로 시작하여 머튼의 연속시간 선택이론을 설명한다. 1950년대 우주 개발을 위하여 개발된 최적 제어이론이 연속시간 포트폴리오 선택이론에 어떻게 사용되었는가를 설명하고...

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...

Symplectic geometry arose from the study of classical mechanics, and later many interesting symplectic invariants has been found since Gromov introduced techniques of J-holomorphic curves. Miraculously, such invariants are closely related wi...

We rely on intuition every day, and we use mathematics every day. Intuition is fast, powerful and omniapplicable, but sometimes wrong. Mathematics is efficient, powerful and correct, when applicable. Whenever there is an uncertainty, a proof...

학부생을 위한 이 강연에서는 고전적 튜링 기계의 기본적 정의로부터 시작하여 • 튜링기계를 비롯한 다양한 컴퓨터 모델의 복잡도 개념; • 계산(불)가능성 – 특히 디오판틴 방정식의 알고리즘적 해결법 (힐버트의 10번째 문제); • Non-deterministic 튜링 기계...

Unconditional results without an unproved hypothesis such as the generalized Riemann hypothesis (GRH) are very weak for an individual number field. But if we consider a family of number fields, one can prove just as strong results as we woul...

In this presentation, we introduce how matrices appeared in the history of mathematics and how they are used in today's fields. Also, we consider the necessary mathematics concepts to define the matrix functions. and the existence and conver...

The spherical average has been a source of many problems in harmonic analysis. Since late 90's, the study of the maximal spherical means on the Heisenberg group $mathbb{H}^n$ has been started to show the pointwise ergodic theorems on the gro...

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...

We derive a general solution of the heat equation through two modied separation methods. The obtained solution is expressed as linearly combined kernel solutions in terms of Hermite polynomials, which appears to provide an explanation of non...

Elliptic curves defined over the rationals satisfy two finiteness properties; its group of rational points is a finitely generated abelian group and it has only finitely many points with integral coordinates. Bhargava and his collaborators e...

Convergence of Fourier series and integrals is the most fundamental question in classical harmonic analysis from its beginning. In one dimension convergence in Lebesgue spaces is fairly well understood. However in higher dimensions the probl...

Dynamics of many particle system can be described by PDE of probability density function. The Boltzmann equation in kinetic theory is one of the most famous equation which describes rarefied gas dynamics. One of main property of the Boltzman...

The Lagrange spectrum is the set of approximation constants in the Diophantine approximation for badly approximated numbers. It is closely related with the Markov spectrum which corresponds the minimum values of indefinite quadratic forms ov...

Lagrangian Floer theory in symplectic manifold associate a category (A infinity category) to a symplectic manifold. More than 20 years ago a relation of a relation between Lagrangian Floer theory and Gauge theory was studied by Floer himself...