A naive definition of mathematics may be “the science of quantity and space”. And in the simpler explanation, they correspond to arithmetic and geometry. One of modern dictionaries, Encyclopedia Britannica, defines it as “the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects” But it is more difficult to understand. Probably it may not be easy to define unanimously the mathematics. But we all know that the mathematics is an indispensable tool for the science and the engineering in modern times.
  The word engineering originated from the ingenium, may be defined as “the application of scientific, economic, social, and practical knowledge in order to invent, design, build, maintain, research, and improve structures, machines, devices, systems, materials and processes”. The engineering discipline is also extremely broad as the mathematics is. Therefore, the engineering area based on the classical mechanics will be dealt in this lecture. Since the early stage of mechanics was not much different from the physics and mathematics, the classical mechanics based areas like civil engineering, mechanical engineering, aerospace engineering, and etc., are now utilizing the mathematics most.
  In this lecture, the intersection and the differences of three disciplines, mathematics, science and engineering, will be explained after defining the three disciplines. And then some famous and important contributors to the classical mechanics, who were then mathematician and/or physicist, will be introduced and their connection with mathematics will be illustrated along with some equations. And then, the cooperation and the convergence of mathematics and engineering will be emphasized by introducing some representative examples.

We study Legendrian singular links up to contact isotopy. Using a special property of the singular points, we can define the singular connected sum of Legendrian singular links. This concept is a generalization of the connected sum and can be interpreted as a kind of tangle replacement. This method provides a way to classify Legendrian singular links.

2015 년 3 월 13 일(금) 오후 2시 00분 - 6시 00분

제목 : 이자율 파생 상품의 이해

강연자 : 전인태 (카톨릭대학)

장 소 : E6-1 #1409

초록 :

보통 금융기관은 천문학적인 금액을 이자율 관련 상품에 투자하고 있기 때문에 이자율 변동위험에 크게 노출되어 있다. 따라서 채권의 거래로부터 얻어지는 이자율의 구조 및 헤징 방법론은 금융기관의 최대의 관심사 중의 하나이고 금융공학에서 가장 중요하게 다루어지고 있다. 본 강의에서는 이자율 결정의 메커니즘, 이자율위험을 헤지하기 위한 이자율파생상품의 종류 및 구조, 가격결정 방법론 등에 대하여 소개한다.

This is a talk on T. Saito’s recent work.

For a sheaf on a surface, Deligne and Laumon defined the characteristic cycle implicitly using the total dimension of the nearby cycles under the “non-fierce” assumption. In general, T. Saito defined the characteristic cycle of a sheaf on a surface by combining the approach using the Radon transform and the non-logarithmic version of ramification theory developed by Abbes and Saito. In this talk, under the stability of nearby cycles and the existence of singular supports on a surface, we show how to construct characteristic cycle using Radon transform

Abstact: In this talk, we mainly introduce our recent work on the weight distributions of a class of cyclic codes from two distinct finite fields. We will show that these codes have three or four nonzero weights. Moreover, some optimal or nearly optimal cyclic codes are found.

An Abelian differential defines a flat structure on the underlying Riemann surface, such that it can be realized as a plane polygon with edges suitably identified. Varying the shape of the polygon induces a GL(2,R)-action on the moduli space of Abelian differentials, which is called Teichmueller dynamics. In this lecture series, I will give an elementary introduction to Teichmueller dynamics, with a focus on a beautiful interplay between algebraic geometry, combinatorics, dynamics, and number theory. 

  In this talk, we consider the so called sharp Hardy inequalities in a limiting case for   where  is an -dimensional ball.  We introduce a new transformation which relates the above inequality to the usual Hardy inequality in the whole space.
  As a result, we improve the sharp Hardy inequality in a limiting case on a ball by adding some remainder terms.

An Abelian differential defines a flat structure on the underlying Riemann surface, such that it can be realized as a plane polygon with edges suitably identified. Varying the shape of the polygon induces a GL(2,R)-action on the moduli space of Abelian differentials, which is called Teichmueller dynamics. In this lecture series, I will give an elementary introduction to Teichmueller dynamics, with a focus on a beautiful interplay between algebraic geometry, combinatorics, dynamics, and number theory. 

신호(음성 또는 영상)의 분석, 처리, 축약, 복원, 잡음제거, 특이신호의 감지 등에는 고전적으로 푸리에급수 또는 푸리에변환 등이 주로 많이 이용되어 왔다. 보다 국소적인 신호분석을 위한 노력으로 short-time Fourier 변환의 형태를 거처. 최근에는 웨이브릿 또는 가보 함수계를 이용한 신호(또는 함수)의 이산적인 표현 및 복원의 새로운 이론이 도입되어 널리 사용되고 있다. 1980년대 후반 I. Daubechies 에 의한 웨이브렛 직교계의 발견으로 웨이브렛의 이론과 응용의 연구가 폭발적으로 이루어 지고 있으며, Gabor 힘수계의 이론은 1946년의 D. Gabor 가 통신이론을 위하여 처음 제기되었으나, 웨이브렛 이론과 더불어 재조명되면서 활발히 연구가 수행되고 있다. 두 이론은 평행으로 전개되면서 최근 들어 근본적인 문제가 해결되고 재기되면서 응용조화해석(applied harmonic analysis)분야의 중심축을 이루고 있다. 이번 강연에서는 수학적인 면에서 기초적인 이론을 소개하여 수학과 학생들의 새로운 수학에 대한 이해를 돕고자 한다.

참석하고자 하시는 분은 아래 링크를 통해 사전등록 해주시면 감사하겠습니다^^
http://goo.gl/qMbQu2

일  시 : 3월 13일(금)  14:00 – 18:00

장  소 : 세미나실 E6-1 #1409

연  사 : 지 동 표 교수 (서울대학교)

강의내용 

1. Several cases where physics constrians computation,

      Several cases where computation constrains physics.

     Abstract: Computation can be thought as abstract process. But it is closely related to physics as our personal computer are fundamentally a physical device. Hence fundamental physics law might  constrain computation. Conversely complexity of computations gives constraints to  law  of physics.

We will discuss several cases of each without any technicality.

2. Information, entropy and all that

  Abstract: We will discuss about information theory from scratch and even will explain exotic  phenomena in quantum world

3. Quantum helps classical

    Abstract: We will several several mathematical facts which have nothing to do with quantum mechanics,

   but using quantum information theory  we can prove them much more  easily, or find better refined form of the statements.

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정확한 날씨예보 생산을 위한 예보관과 관측자료의 기여도가 각각 28%와 32%이나 수치예보모델이 미치는 영향은 40%라는 조사 결과가 있다. 기상청은 날씨예보 정확도 향상을 위하여 천리안 기상위성과 같은 관측 인프라 구축 뿐 아니라 수치예보모델 발전에 많은 투자를 하고 있다. 기상청 수치예보모델의 역사는 1989년 수치예보반을 설립하면서 처음 시작하였으며, 1995년 일본기상청의 전지구예보모델을 거쳐 영국의 통합모델을 도입 운영하고 있다. 기상청에서 운영하는 수치예보모델의 정확도는 세계 6위 또는 그 이상인 것으로 여러 비교 검증 결과가 보여주고 있으나 기상청은 이에 만족하지 않고 자체 선진 수치예보모델 기술 확보를 위하여 9년 동안 총 1000억원의 연구비를 투자하여 한국형수치예보모델 개발 사업을 추진 중에 있다. 수치예보모델의 문제 해결 및 발전을 위하여 응용수학과 같은 분야의 지식과 경험이 매우 필요하다. 이번 세미나에선 수치예보모델에 대한 응용수학 분야의 공동연구 과제 발굴에 필요한 기반 정보를 제공하기 위하여 기상청 수치예보모델의 현황과 문제점에 대해 발표할 예정이다.

An Abelian differential defines a flat structure on the underlying Riemann surface, such that it can be realized as a plane polygon with edges suitably identified. Varying the shape of the polygon induces a GL(2,R)-action on the moduli space of Abelian differentials, which is called Teichmueller dynamics. In this lecture series, I will give an elementary introduction to Teichmueller dynamics, with a focus on a beautiful interplay between algebraic geometry, combinatorics, dynamics, and number theory. 

An Abelian differential defines a flat structure on the underlying Riemann surface, such that it can be realized as a plane polygon with edges suitably identified. Varying the shape of the polygon induces a GL(2,R)-action on the moduli space of Abelian differentials, which is called Teichmueller dynamics. In this lecture series, I will give an elementary introduction to Teichmueller dynamics, with a focus on a beautiful interplay between algebraic geometry, combinatorics, dynamics, and number theory. 

대한민국 전자 산업은 수십년간 국가 경제 성장의 동력이 되며 성장해 왔다. 초기 일본업체로 부터 기술을 배우며, 때로는 copy도 하고, 가격경쟁력을 통해 성장을 하다, 세계최고 수준에 올라섰다. 그러나 지금은 apple, Google 등 SW기반의 Platform을 강점으로 하는 기업들과, 급속하게 성장하는 중국업체들 사이에서 어려운 경쟁을 해 나가고 있다. 세계 경제가 어려워지는 최근의 상황에서 돌파구는 무엇일까? 어떻게 해결해 나갈 수 있을까?

Cluster algebras were discovered by Fomin and Zelevinsky in 2001. Since then, they have been shown to be related to diverse areas of mathematics and physics such as Total positivity, Quiver representations, String theory, Statistical physics, Non-commutative geometry, Teichmüller theory, Hyperbolic geometry, Tropical geometry, KP solitons, Integrable systems, Quantum mechanics, Lie theory, Algebraic combinatorics, Number theory and Poisson geometry.
We explain these connections between various fields in elementary languages.

정수론 mini-workshop

일시: 2015. 2. 27일(금)

           14:00-14:50 최소영(동국대)

           15:00-15:50 전병흡 (연세대)     

         16:00-16:50 이정연 (이화여대)

Title and Abstract

Rational period funcions and cycle integrals in hinger level cases (최 소영 교수, 동국대)

abstract : Generalizing the results of Duke, Imamoglu and Toth we give an effective basis for the space of period polynomials in higer level case.

From Euler-Maclaurin formula to the rationality and integrality of zeta values (전 병흠 박사, 연세대)

abstract : By using the Euler-Maclaurin summation formula and asymptotic expansion of Shintani generating function, we express the zeta values. From this expression, we derive the result of Klingen-Siegel concerning the zeta values of totally real number fields. We also discuss the method which can derive the integrality by using the related homological properties.

Indivisibility of class numbers of real quadratic function fields (이 정연 박사, 이화여대)

abstract : In this paper we work on indivisibility of the class numbers of real quadratic

function fields. We find an explicit expression for a lower bound of the density of real quadratic function fields (with constant field whose class numbers are not divisible by a given prime . We point out that the explicit lower bound of such a density we found only depends on the prime , the degrees of the discriminants of real quadratic function fields, and the condition: either or not.

 In this talk we discuss characterizations of Burniat surfaces constructed by bidouble covers. Mendes Lopes and Pardini dealt with a characterization of a Burniat surface with K^2=6. They showed that a minimal surface S of general type with p_g=0, K^2=6 and the degree 4 of the bicanonical map of S is a Burniat surface with K^2=6. Zhang considered the surface S with K^2=5. He proved that the surface S with K^2=5 is a Burniat surface with K^2=5 when the image of the bicanonical map of S is smooth. We consider that a minimal surface S of general type with p_g=0, K^2=4 and the degree 4 of the bicanonical morphism of S is a Burniat surface with K^2=4 and of non nodal type when the image of the bicanonical morphism of S is smooth.

Let S be a complete intersection surface defined by a net N of quadrics in P^5. In this talk we analyze GIT stability of nets of quadrics in P^5 up to projective equivalence, and discuss some connections between a net of quadrics and the associated discriminant sextic curve. In particular, we prove that if S is normal and the discriminant of S is stable then N is stable. And we prove that if S has the reduced discriminant and the discriminant is stable then the N is stable. Moreover, we prove that if S has simple singularities then the associated discriminant has simple singularities.

 In 2007, Y. Lee and J. Park provided a new method to construct surfaces of general type via Q-Gorenstein smoothing. Using the same technique, we were able to attain an algebraic construction of some Dolgachev's surfaces, for which there was an analytic construction (using logarithmic transform), but nothing have been known on its algebraic construction. In this talk, we shortly introduce the technique of Y. Lee and J. Park, and discuss how we construct Dolgachev's surfaces using this technique. On the other hand, P. Hacking provided a way to construct an exceptional vector bundle associated to a degeneration of surfaces with p_g = q = 0. We explicitly provides how to yield such vector bundles on Dolgachev's surfaces, and discuss what can be studied with these bundles. 

 

Finding a criterion of when a q-hypergeometric series can have modularity is an interesting open problem in number theory. Nahm's conjecture relates this question to the Bloch group in algebraic K-theory. I will give an introduction to the conjecture and explain its close relationship with various objects such as the dilogarithm function, Y-systems and Q-systems.

In this lecture series I will explore several problems of analytic number theory in the context of function fields over a finite field. Some of the problems can be approached by methods different that those of traditional analytic number theory and the resulting theorems can be used to check existing conjectures over the integers, and to generate new ones. Among the problems discussed are: counting primes in short intervals and in arithmetic progressions; Chowla's conjecture on the autocorrelation of the Möbius function, the additive divisor problem, moments of L-functions, and statistics of zeros of L-functions and connections with random matrix theory.