과거 보험계리(Actuarial science)는 대수의 법칙(the law of large numbers)에 기반한 확률론적 방법론을 사용하였으나  최근에는 금융공학 및 통계학과 결합하여  다양한 적용 사례를 보여주고 있습니다. 

    보험부채를 시가평가하는 IFRS4 2단계의 할인율 산출, 

    변액보험 보증옵션 평가 및 헤지제도 도입,
    클러스터링을 이용한 대표계약 모델링, 

    확률론적 사망률 모형을 이용한 장수지수 산출 등  국내 보험계리 분야의 최근 동향을  소개합니다.

    또한, 현재 사회문제화 되고 있는 보험사기 방지와 관련한 보험개발원의 보험사기 예측 시스템도 소개합니다

A k-colouring of a graph G is a partition of V(G) into k independent sets. The chromatic number χ(G) is defined as the smallest k so that G has a k-colouring. Alternatively, we can view colourings as homomorphisms to complete graphs, and define χ(G) to be the smallest k so that there is a homomorphism from G to K_k. The variants of χ(G) (for example, fractional chromatic number) are defined by replacing the complete graph K_kwith a representative of a different class of graphs (for example, Kneser graphs).

In this talk, we will consider the vector chromatic number of a graph. A vector colouring of a G is a map from V(G) to vectors in R^m (for some m). The goal is to map adjacent vertices to vectors that are far apart. We will look at representations of a graph on its least eigenspace as examples of vector colourings. For distance-regular graphs, these colourings are optimal. Furthermore, we give a method for determining if these colourings are unique. This leads to proofs that certain classes of distance-regular graphs are all cores.

Prandtl (1936) first employed the shock polar analysis to show that, when a steady supersonic flow impinges a solid wedge whose angle is less than a critical angle (i.e., the detachment angle), there are two possible configurations: the weak shock solution and the strong shock solution, and conjectured that the weak shock solution is physically admissible. The fundamental issue of whether one or both of the strong and the weak shocks are physically admissible has been vigorously debated over several decades and has not yet been settled in a definite manner. In this talk, I address this longstanding open issue and present recent analysis to establish the stability theorem for steady weak shock solutions as the long-time asymptotics of unsteady flows for all the physical parameters up to the detachment angle for potential flow.

This talk is based on collaboration with Gui-Qiang G. Chen (Univ. of Oxford) and Mikhail Feldman(UW-Madison ).

The first lecture is about how elliptic partial differential equations
(PDEs) may be reformulated as Fredholm second kind integral equations
for the purpose of obtaining fast and accurate numerical solutions. A
discretization scheme for integral equations, called the Nyström
scheme, is presented. Advantages with this integral equation approach
to solving elliptic PDEs are reviewed, as are current trends and
challenges. In particular, I will discuss the difficulties that arise
on domains whose boundaries contain singularities such as corners, and
how to the Recursively Compressed Inverse Preconditioning (RCIP)
method is used to combat these difficulties. Numerical examples cover
applications to electromagnetic scattering and to solid mechanics.y

The first lecture is about how elliptic partial differential equations
(PDEs) may be reformulated as Fredholm second kind integral equations
for the purpose of obtaining fast and accurate numerical solutions. A
discretization scheme for integral equations, called the Nyström
scheme, is presented. Advantages with this integral equation approach
to solving elliptic PDEs are reviewed, as are current trends and
challenges. In particular, I will discuss the difficulties that arise
on domains whose boundaries contain singularities such as corners, and
how to the Recursively Compressed Inverse Preconditioning (RCIP)
method is used to combat these difficulties. Numerical examples cover
applications to electromagnetic scattering and to solid mechanics.

금융시장에서 거래되는 상품 또는 계약의 적정가치에 대한 논의는 금융시장의 태동과 더불어 시작되어 아직도 수 많은 방법론이 나타났다가 동시에 사라져가는 소위 정답이 없는 문제라고 할 수 있다. 이러한 금융시장에서 1970년 대 이후 확률론, 편미분방정식과 같은 수리적 방법론으로 무장된 사람들이 어떠한 관점에서 금융시장을 바라보았고, 이들의 노력이 금융상품의 적정가치 발견에 있어서 어떠한 프레임을 제공하였는가에 대해서 함께 생각해 보고자 한다.

참석하고자 하시는 분은 아래 링크를 통해 사전등록을 해주시면 감사하겠습니다^^

https://goo.gl/XlDVBt

Let $M_{lambda}$ be the $lambda$-component Milnor link. For $lambda ge 3$, we determine completely when a finite slope surgery along $M_{lambda}$ yields a lens space including $S^3$ and $S^1times S^2$, where {it finite slope surgery} implies that a surgery coefficient of every component is not $infty$. For $lambda =3$ (i.e. the Borromean rings), there are three infinite sequences of finite slope surgeries yielding lens spaces. For $lambda ge 4$, any finite slope surgery does not yield a lens space. We also discuss generalizations of our present results. Our main tools are Alexander polynomials and Reidemeister torsions.

    실토릭공간은 (Z_2)^n 작용이 있는 n차원 위상공간입니다. 이들은 토릭다양체 등의 고전적인 대상과 밀접한 관련이 있어서 다양한 분야에서 오랫동안 연구되어 왔습니다. 하지만 토릭 다양체들과는 다르게 이들의 위상적 성질에 대해서는 많이 알려진 바가 없습니다. 이들 중 대부분은 simply connected 가 되지 않는 등 위상적 구조가 복잡해서 위상적 불변값을 계산하기도 쉽지 않기 때문입니다.

수학은 수천 년간 그 지식을 축척하며 발전해 온 유일한 학문이다. 수학은 완벽한 해를 추구한다는 점에서도 다른 학문과 구별된다. 수학은 오랜 세월 동안을 차곡 차곡 탑을 쌓듯이 발전해 왔고, 따라서 발전 과정에 대한 역사적 고찰이 현대수학을 이해하는데 큰 도움이 된다. 과학이라는 말이 만들어진 지, 그리고 과학이 사람들의 삶을 바꾸기 시작한 지 불과 200여년 밖에 되지 않았다. 앞으로 과학은 수만 년, 수백만 년 발전을 지속할 가능성이 크다. 지금의 수학은 미래에 우주의 언어로서 필수적으로 과학의 발전에 이바지할 것이다.

실토릭공간은 (Z_2)^n 작용이 있는 n차원 위상공간입니다. 이들은 토릭다양체 등의 고전적인 대상과 밀접한 관련이 있어서 다양한 분야에서 오랫동안 연구되어 왔습니다. 하지만 토릭 다양체들과는 다르게 이들의 위상적 성질에 대해서는 많이 알려진 바가 없습니다. 이들 중 대부분은 simply connected 가 되지 않는 등 위상적 구조가 복잡해서 위상적 불변값을 계산하기도 쉽지 않기 때문입니다.

 차별이나 사회적 배제와 같은 부정적 경험이 어떻게 인간의 건강을 해치는지를 규명하는 것은 보건산업, 보건정책의 측면에서 매우 중요한 문제이다. 그러한 연구는 공동체의 건강을 증진시키기 위해, 어떠한 제도적 변화가 필요한지에 대해 말해주기 때문이다. 차별경험과 건강의 관계를 고찰하는 연구에서는 주로 설문조사를 통해 차별의 경험을 측정하고 그 경험이 건강과 어떠한 연관성을 보이는지에 대해 통계적으로 규명한다. 그런데, 차별경험을 보고하는 과정은 연구 대상자의 내적 검열을 포함해 다양한 사회적 요인들에 의해 영향을 받고, 그로 인한 차별경험 측정의 불확실성을 통계적으로 어떻게 다룰 것인가는 논의가 계속되는 이슈이다. 본 발표에서는 차별경험과 건강에 대한 기존 연구를 소개하고, 차별경험을 정확히 측정하는 문제와 관련하여 역학(Epidemiologist)자로서의 고민을 공유하고자 한다.

초록:  계산수학이란 수학적 문제에 대하여 효율적이며 믿을 수 있는 컴퓨터 해를 구하고자 하는 연구분야이다. 계산수학은 엄밀한 수학적 이론을 이용하여 오차를 분석하고 대용량 계산과 병렬계산 알고리즘을 만들오 내며 계산 모델링과 이 모델에 대한 모의실험을 한다. 이러한 계산수학은 컴퓨터가 생겨나기 이전 16세기 경부터 계산을 보다 편하게 하기 위하여 발달하였다. 네이피어의 로그의 발견, 뉴턴의 비선형방정식 해법과 보간법 등이 그 예이다. 20세기 들어서 컴퓨터가 생겨나고 선형방정식계와 상미분방정식, 편미분방정식 등을 푸는 방법들이 폭발적으로 개발되었다. 몬테 카를로 방법, 대형 선형방정식계를 푸는 반복해법, fast Fourier Transform, 유한요소법 등이 개발되었다. 또한 병렬계산기가 만들어 지면서 이를 활용하는 수치방법들이 개발되고 있다. 본 강연에서는 계산수학의 태동과 발전을 살펴보고 앞으로 어떻게 발전해 나아가게 될 지를 살펴본다.

참석하고자 하시는 분은 아래 링크를 통해 사전등록을 해주시면 감사하겠습니다^^

https://goo.gl/rQeiXt

  The dynamical degree is the exponential rate of the volume growth. The dynamical degree is one of the essential quantity to study of rational surface mappings. For example, a birational mapping on $mathhbb{P}^2$ is birationally equivalent to a rational surface automorphism if and only if the dynamical degree is a Salem number. For any given birational mapping $f$ on $mathhbb{P}^2$, it is known that we can always construct a modification whose action on $H^{2,2}$ gives the dynamical degree of $f$.

  We will discuss how to construct such modifications and how to compute the dynamical degree of a given rational map.

 Let X be a manifold obtained by blowing up points of k-dimensioanl projective space. We say f: X ----> X is a pseudo-automorphism if for every codimension 1 variety H, both the codimensions of f(H) and f^{-1}(H) are equal to 1. In this talk , we will discuss an explicit method for constructing pseudo-automorphisms on X. The centers of blowups are chosen to lie on an algebraic curve of degree (k+1) with one singular point and are determined using the arthmetic on the curve. These pseudo-automoprhisms have dynyamical degree greater than 1. This is a joint work with Eric Bedford and Jeffery Diller.

I will introduce examples of non-normal very ample toric 3-folds.
Next I will give classes of toric 3-folds whose any ample line bundles are
normally generated. Main subject is how to prove normality of
toric 3-folds admitting surjective morphism onto the projectie line.

Let f be a rational surface automorphism with positive entropy. It is known that the entropy of f is determined by its ``orbit data'', thee positive integers and a permutation sigma in S_3. Under the assumption that there is a curve C such that the closure of f(C - I(f)) = C, one can construct an automorphism with given entropy. We will discuss possible configuration of invariant curves and the construction of an automorphism with given invariant curve. This construction can be done in any dimension (ge 2).

A Fatou set is where the dynamics of a mapping is regular. On interesting kind is a rotation domain, a Fatou component on which the automorphism induces a torus action. In this second part we will discuss a rational surface automorphism with a ``huge'' rotation domain. It is huge in the sense that it contains both a curve of fixed points and isolated fixed points and there is a global linear model for it.

외환 파생상품 시장에서 거래되고 있는 옵션들과 활용 예시를 소개하고 가격결정의 주요 요소인 volatility surface의 구축과 관련된 이슈들을 소개한다. 마지막으로 유동성이 상대적으로 낮은 cross FX rate의 volatility surface를 multi-factor stochastic volatility 모형으로 추정하는 방법을 제시한다.

 The revolution of molecular biology in the early 1980s has revealed complex network of non-linear and stochastic biochemical interactions underlying biological systems. To understand this complex system, mathematical modeling has been widely used.
 In this talk, I will introduce the typical process of applying mathematical models to biological systems including mathematical representation of biological systems, model fitting to data, analysis and simulations, and experimental validation. I will also describe our efforts to develop and integrate mathematical tools across the different steps of the modeling process.
 Finally, I will discuss the shortcomings of our present approach and how they point to the parts of current toolbox of mathematical biology that need further mathematical development.

  I will give an estimate of degree of ideals defining toric
varieties
by using the dimension of the varieties, and give a characterization
of toric varieties whose dfining ideals need elements of the highest degree.
And I also talk about higher syzigies of toric varieties.

무선통신 망 성능분석에 널리 사용되는 라이시안 분포(S. O. Rice)를 소개하고

We give a closed formula for the expression of sums of period polynomials multiplied its associated Hecke eigenform on level N with N square-free. We also show that for N=2, 3, 5 this formula completely determines the Fourier expansions all Hecke eigenforms of all weights on level N. This is joint work with Youngju Choie and Don Zagier.

The revolution of molecular biology in the early 1980s has revealed complex network of non-linear and stochastic biochemical interactions underlying biological systems. To understand this complex system, mathematical modeling has been widely used.

 In this talk, I will introduce the typical process of applying mathematical models to biological systems including mathematical representation of biological systems, model fitting to data, analysis and simulations, and experimental validation. I will also describe our efforts to develop and integrate mathematical tools across the different steps of the modeling process. Finally, I will discuss the shortcomings of our present approach and how they point to the parts of current toolbox of mathematical biology that need further mathematical development.

The theory of algebraic cycles with modulus, such as the additive higher Chow group introduced by Bloch and Esnault and the Chow group with modulus by Binda, Kerz and Saito, is an emerging branch of algebraic cycle theory. The concept "modulus" concerns how cycles behave at the boundary, expressed by a Cartier divisor. In this talk we exhibit how the contravariance (in affine smooth varieties) of these theories can be deduced from a new moving lemma with modulus. We explain what kind of difficulties are caused by the modulus condition when establishing it.

초록:  1920년대 말기에 폴란드 태생의 수학자 Stefan Bergman 박사는 지금은 Bergman kernel function이라는 이름으로 알려진 개념을발견하였다. 복소함수론의 전통 깊은 코시 적분공식처럼 복소해석함수를 재생해낼 수 있는 적분 공식을 구성하는 함수 (이런 것들을 통틀어 kernel function이라 부른다)를 발견하고, 연구를 거듭하며 이로부터 파생되는 Kaehler(캘러) 거리 텐서를 포함한 여러 개념을 구성하고 이를 통해 복소함수론을 “재구성”할 수 있을 것으로 예상하였다. 그의 착상은 여러 위대한 수학자들에 의해 발전되고 연구되어 지난90여년 간 활발히 연구되어 왔다. 이 강연에서는 이 분야의 발생에서부터 현재의 연구까지 역사와 주요 연구 결과를 살펴 보고, 최근 연구의 발전 방향 등을 소개하며 앞으로 나아갈 길을 조망해 보려 한다.

참석하고자 하시는 분은 아래 링크를 통해 사전등록을 해주시면 감사하겠습니다^^
https://goo.gl/7qB5uV

 In this talk, we consider the problem of determining which modular curves can have infinitely many K-rational points when K varies over all the number fields of fixed degree.

The Ramsey number of a graph G is the minimum integer n for which every edge coloring of the complete graph on n vertices with two colors admits a monochromatic copy of G. It was first introduced in 1930 by Ramsey, who proved that the Ramsey number of complete graphs are finite, and applied it to a problem of formal logic. This fundamental result gave birth to the subfield of Combinatorics referred to as Ramsey theory which informally can be described as the study of problems that can be grouped under the common theme that “Every large system contains a large well-organized subsystem.”

In this talk, I will review the history of Ramsey numbers of graphs and discuss recent developments.

The hydrodynamic limit theory of Guo, Papanicolaou and Varadhan suggests a concrete way of analyzing the large-scale behavior of a non-equilibrium interacting particle system. Although the hydrodynamic limit theory has been successfully applied for numerous models, the particle system can be better understood by studying the so-called empirical process. Accordingly, Quastel, Rezakhanlou and Varadhan suggested a way to achieve this by using the symmetric simple exclusion process (SSEP) as a sample model. Despite their methodology being very robust, such an analysis is difficult because of several technical obstacles. Consequently, results were only achieved for two systems: the SSEP and zero-range process (ZRP). Recently, we obtained a third result of this type in the system of locally interacting Brownian motion. This model is a kind of continuum system, whereas the two previous models are lattice systems. Our work verifies that the results of SSEP and ZRP are valid for our model as well.
  We start by introducing the standard methods and classic results of the hydrodynamic limit theory and present our results thereafter.

We will recall how the regularity of powers of ideals behave

in general. Then we will present results concerning powers of ideals of maximal minors of matrices of linear forms. Joint with WinfiredBruns and Matteo Varbaro.

Let R be a commutative Noetherian ring. It is a classical result that R is regular if and only if it has finite global dimension. In recent years, certain non-commutative rings which are modules-finite over R and has finite global dimension have become objects of intense interests. They can serve as "non-commutative desingularizations" of Spec(R) and have come up in the three-dimensional solution of the Bondal-Orlov conjecture, higher Auslander-Reiten theory and non-commutative minimal model program. Despite all that attention, these objects remain rather mysterious, for examle we do not know fully  when they exist, or what global dimensions can occur. In this talk I will describe some very recent work on these questions. Some of the work are joined with E. Faber, C. Ingalls, O. Iyama, R. Takahashi, I. Shipman and C. Vial. 

We study multigraded ideals with a radical generic initial ideal.
Our main new result is that if a multigraded ideal has a radical multigraded generic initial ideal then the same is true for every multigraded hyperplane section and for every multigradedprojection.
Connection to universal Gr"obner bases for determinantal ideals, Koszul algebras associated to subspaces configurations and to ideals associated to the multiview varieties of Aholt, Sturmfels and Thomas will be discussed. Joint work with Emanuela De Negri and Elisa Gorla.