Sullivan sketched a proof of his structural stability theorem for differentiabl group actions satisfying certain expansion-hyperbolicity axioms. We relax Sullivan’s axioms and introduce a notion of meandering hyperbolicity for group a...

We present a mathematical justification of cloaking due to anomalous localized resonance (CALR). We consider the dielectric problem with a source term in a structure with a layer of plasmonic material. Using layer potentials and symmetrizati...

It has been more than thirty years since white noise analysis was launched systematically. It is now a good time to have an overview of the theory and to reflect on its advantages in order to anticipate further developments of this theory. O...

In this talk, numerical methods to solve second-order elliptic partial dierential equations will be presented. First, some of the existing methods, such as the standard Galerkin method, mixed nite element methods etc., will be briey discusse...

Sheaf quantization of Hamiltonian isotopies and non-displacability problems

국제수학자대회(ICM, International Congress of Mathematicians)는 1897년 쮜리히에서 처음 개최되었고, 매 4년마다 개최된다. 100여국 4천여 명 정도의 규모로 9일 동안 계속된다. 우리시대 최고의 수학자들이 참여하며, 필즈상(Fields Medal)을 개막식에서 ...

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...

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Concordance is a relation which classifies knots in 3-space via surfaces in 4-space, and it is closely related with low dimensional topology. Satellite operators are one of the main tools in the study of knot concordance, and it has been wi...

In this talk, we will consider the hyperbolic Kac-Moody algebra associated to a certain rank 3 Cartan matrix and generalized Kac-Moody algebras that contain the hyperbolic Kac-Moody algebra. The denominator funtions of the generalized Kac-Mo...

Magnetic Resonance Electrical Impedance Tomography (MREIT) is a late medical imaging modality visualizing static conductivity images of electrically conducting subjects. When we inject current into the object, it produces internal distributi...

The original Riemann-Hilbert problem is to construct a liner ordinary differential equation with regular singularities whose solutions have a given monodromy. Nowadays, it is formulated as a categorical equivalence of the category of regular...

We will talk about the Fourier restriction theorems for non-degenerate and degenerate curves in Euclidean space Rd. This problem was first studied by E. M. Stein and C. Fefferman for the circle and sphere, and it still remains an unsolved pr...

In this talk, we investigate some regularity results for non-uniformly elliptic problems. We first present uniformly elliptic problems and the definition of non-uniform ellipticity. We then introduce a double phase problem which is characte...

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 ...

In his survey paper in the Bulletin of the AMS from 2002, R. J. Gardner discussed the Brunn-Minkowski inequality, stating that it deserves to be better known and painted a beautiful picture of its relationship with other inequalities in anal...

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...

Given a group of isometries of a metric space, one can draw a random sequence of group elements, and look at its action on the space.  What are the asymptotic properties of such a random walk?  The answer depends on the geometry of the space...

Free probability is a young mathematical theory that started in the theory of operator algebras. One of the main features of free probability theory is its connection with random matrices. Indeed, free probability provides operator algebrai...