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...

In this talk, I will explain a relationship of the Chern-Simons invariant and the eta invariant for Schottky hyperbolic manifolds. The relating formula involves a defect term given by the Bergman tau function over the conformal boundary Riem...

둘레가 같은 평면의 영역중에서 넓이가 최대인 것은 원이라는 것이 등주부등식이다. 이와 똑 같은 등주부등식이 극소곡면에 대해서도 성립할 것이라는 예상이 90년 전에 제기되었다. 이 예상의 역사와 현주소에 대해서 알아보기로 하자.

오랜 세월동안 기득권을 누려오던 통신 업계는 이제 성장의 한계에 직면해 있다. 통신의 고유 영역이던 음성통화와 데이터 통신은 스마트폰의 활성화, 사업구조의 변화 등으로 인해 여타 산업군들에게 그 자리를 내어주며 더이상 캐시카우의 역할을 하지 못하...

A function from a group G to integers Z is called a quasi-morphism if there is a constant C such that for all g and h in G, |f(gh)-f(g)-f(h)| < C. Surprisingly, this idea has been useful. I will overview the theory of quasi-morphisms includi...

Sheaf quantization of Hamiltonian isotopies and non-displacability problems

The significance of dimensions in mathematics

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In the early 90's, physicists Bershadsky-Cecotti-Ooguri-Vafa conjectured that the analytic torsion was the counterpart in complex geometry of the counting problem of elliptic curves in Calabi-Yau threefolds. It seems that this conjecture is ...

Representation theory is to study the actions of groups or algebras on vector spaces. Recently, its categorical version, categorical representation theory, attracts researchers in representation theory. In this theory we replace "vector spac...