An equivalent condition to Bohr's for Dirichlet series

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-...

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...

It is a fascinating and challenging problem to count number fields with bounded discriminant. It has so many applications in number theory. We give two examples. First, we compute the average of the smallest primes belonging to a conjugacy ...

Among many different ways to introduce derived algebraic geometry is an interplay between ordinary algebraic geometry and homotopy theory. The infinity-category theory, as a manifestation of homotopy theory, supplies better descent results ...

거울대칭은 수학의 다른 두 분야의 이론 간 연관관계를 제시하며, 물리학의 초끈이론에서 비롯되어 수학의 여러 분야에 지난 2~30년간 많은 영향을 주었다. 이번 강연에서는 곡면 (구, 토러스 등)에서 곡선들과 이에 둘러싸인 다각형이 만드는 기하학과 이와 ...

정년퇴임 기념강연회: 숙제

We start with the famous Heisenberg uncertainty principle to give the idea of the probability in quantum mechanics. The Heisenberg uncertainty principle states by precise inequalities that the product of uncertainties of two physical quantit...

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The disk embedding problem is of fundamental importance in the study of 4-dimensional topology. I will discuss its significance and difficulty, including how disk embedding makes dimension four intrinsically different from other dimensions. ...

Let be a cyclic group with generator . The discrete logarithm problem with auxiliary inputs (DLPwAI) is asked to find with auxiliary inputs , ,…, . In Eurocrypt 2006, an algorithm is proposed to solve DLPwAI in when . In this paper, we reduc...

완전동형암호는 암호화된 상태에서 모든 계산을 지원하는 이상적인 암호로서 암호학계의 성배(holy grail)로 불리며 1978년 이후 오랫동안 미해결 문제로 알려져 있었다. 2009년 Gentry에 의해 처음 만들어진 후 많은 연구를 거쳐 실용화를 앞두고 있으며 2011...

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...

The mean curvature flow is an evolution of hypersurfaces satisfying a geometric heat equation. The flow naturally develops singularities and changes the topology of the hypersurfaces at singularities, Therefore, one can study topological pr...

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...

Fermat´s last theorem

Fano varieties are fundamental objects in algebraic geometry. These can be considered as the unique output of the -K -minimal model program on the varieties with effective anticanonical divisors. Thus the initial models should encode the in...