Zeros of linear combinations of zeta functions

Fermat´s last theorem

We survey work on a class of nonlinear elliptic PDEs that was initiated by Moser. Methods from PDE, dynamical systems, and geometry set in the framework of the calculus of variations are used to construct a rich collection of solutions.

On some nonlinear elliptic problems

We will review a number of topological themes in number theory, starting with homology and ending with a discussion arithmetic homotopy.

A fundamental problem in differential geometry is to characterize intrinsic metrics on a two-dimensional Riemannian manifold M2 which can be realized as isometric immersions into R3. This problem can be formulated as initial and/or boundary ...

우리의 직관에 의하면 우주는 4차원으로 이루어져있다. 달리 말하면 우리가 어떤 사건을 기술 할 때 네 개의 숫자(공간3 + 시간1) 이면 충분하다는 것 이다. 세상에 다른 여분의 차원이 더 있다고 가정 여러 물리 법칙을 통일적으로 기술할 수 있음이 알려졌다...

Counting circles in Apollonian circle packings and beyond

Sheaf quantization of Hamiltonian isotopies and non-displacability problems

Given a one-parameter family of algebraic varieties, its point-wise limit is usually too small whereas its algebraic limit is usually too big. I will introduce a notion of meaningful geometric limit and explain how it can be effectively comp...

We discuss on why we study partial differential equations.

Symmetry Breaking in Quasi-1D Coulomb Systems

Partial differential equations with applications to biology

A COMBINATORIAL FORMULA FOR INFORMATION FLOW IN A NETWORK

Ward's identities and the related concept of the stress-energy tensor are standard tools in conformal field theory. I will present a mathematical overview of these concepts and outline relations between conformal field theory and Schramm-Loe...

In this lecture, I will convey subtle interplay between dynamics of Hamiltonian flows and La-grangian intersection theory via the analytic theory of Floer homology in symplectic geometry. I will explain how Floer homology theory (`closed str...

Global result for multiple positive radial solutions of p-Laplacian system on exterior domain In this talk, we consider p-Laplacian systems with singular indefinite weights. Exploiting Amann type three solutions theorem for the singular syst...

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 ...

We will show that the averaging formula for Nielsen numbers holds for continuous maps on infra-nilmanifolds: Let M be an infra-nilmanifold with a holonomy group Phi and f : M -> M be a continuous map. Then N(f ) = 1/| Phi | Sum_{A in Phi} | ...

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-...