In this talk we discuss a utility-deviation risk portfolio selection problem. By considering the first order condition for the objective function, we derive a primitive static problem, called Nonlinear Moment Problem, subject to a set of constraints involving nonlinear functions of “mean-field terms”, to completely characterize the optimal terminal wealth. Under a mild assumption on utility, we establish the existence of the optimal solutions for both utility-downside-risk and utility-strictly-convex-risk problems, their positive answers have long been missing in the literature. In particular, the existence result in utility-downside-risk problem is in contrast with that of mean-downside-risk problem considered in Jin-Yan-Zhou (2005) in which they prove the non-existence of optimal solution instead and we can show the same non-existence result via the corresponding Nonlinear Moment Problem. (Joint work with K.C. Wong and S.C.P. Yam)

In this talk, we consider the optimal dividend payment strategy for an insurance company, having two collaborating business lines. The surpluses of the business lines are modelled by diffusion processes. The collaboration between the two business lines permits that money can be transferred from one line to another with or without transaction costs while money must be transferred from one line to another to help both business lines keep running before simultaneous ruin of the two lines eventually occur. (Joint work with J.W. Gu and M. Steffensen)

Brain can be divided into several regions based on its functions or structures. And these regions are functionally connected with each other. Fibre tracking on the white-matter from diffusion-tensor image is one of approaches to study brain connectivity. This presentation will introduce static brain connectivity and discuss its clinical applications.

폐에는 매우 복잡하고 고도로 조직화된 형상이 들어있다. 이러한 형상이 다양한 이유로 변형되면서 만성폐쇄성폐질환(COPD)과 같은 질환이 나타나게 된다. 하지만 폐의 형상 변화에 있어서 기체교환면이 줄어들거나 기관지 벽이 두꺼워지는 것 이상의 어떤 '질서'또는 '필수 정보'가 손상되는 것이 궁극적으로 폐기능 저하로 이어지게 되는지는 여전히 잘 설명하지 못하고 있으며, 그것을 어떻게 측정하거나 평가해야 할 지 힌트가 부족한 상황이다. 이와 같은 질문에 답하기 위해서는 다학제간 연구가 통합적으로 필요하다. 이번에는 특히 폐 형상에서 질서를 계량화하고 비교하는 데 쓸 수 있는 수학적 도구를 찾아보고, 질문을 구체적인 수학적 문제로서 정의하는 데 초점을 맞추려 한다.

Heart and Lung have intrinsic motions to fulfill their own functionalities. Physically, these organ's motions are generated from physical potentials and mass distribution composing them. Thus in reverse, physically and mathematically relevant modeling for their genuine motions may lead us to better understanding about key clinical features in need. 3 case studies will be presented to discuss possible improvements on physical modelings under current clinical circumstances.

We define and study grid diagrams for singular links.

A face of an oriented knot diagram on the two sphere is called a coherent (resp. incoherent) region if the orientation of its boundary is coherent (resp. incoherent). In this talk, we investigate the number of the coherent faces and incoherent faces of an oriented knot diagram, and give some relations between the number of the incoherent regions and the canonical genus of a knot. This is a joint work with Kokoro Tanaka (Tokyo Gakugei University)

There exists an interesting family of finite-dimensional representations called the Kirillov-Reshetikhin modules over the quantum affine algebra $U_q(widehat{mathfrak{g}})$. The isotypic decomposition of theses modules or their tensor products as $U_q(mathfrak{g})$-modules is given by the fermionic formula which can be regarded as a representation theoretic version of completeness of the Bethe ansatz.

In spite of its elegance, it quickly becomes impractical as the rank of $mathfrak{g}$ increases due to its complicated combinatorial nature. Thus it is advantageous to have a more explicit description of this decomposition for practical purposes. Such a formula is well-known in classical types, but remains largely conjectural in exceptional types.

In this talk, I will talk about linear recurrence relations satisfied by the sequence ${Q_m^{(a)}}_{m=0}^{infty}$ of the characters of the Kirillov-Reshetikhin modules and how they shed light on the above problem. The key idea is to regard this decomposition as a summation over the lattices points in a suitable polyhedron.

The canonicai genus of a Whitehead double of a knot is less than or equal to its crossing number. Tripp observed that the equality holds for 2-braid knots and conjectured that the equality holds for all knots. However, Jang and Lee found counterexamples for this conjecture. In this talk, we discuss this conjecture for non-prime alternating knots.

In this talk, I attempt to provide a comprehensive introduction to the matroid properties that hold for almost all matroids.

One of the most prominent subjects which is widely adopted in fintech area is machine learning. One can analyze big data to classify and predict various objects using machine learning techniques. Especially, machine learning shows strong applicability in credit valuation. In this talk, we introduce some methods of machine learning and illustrate how to value credits.

LIBOR is one of the most important floating interest rates, since it is widely used as the underlying of the swap contract. Recently, however, there are some attempts to replace LIBOR with another benchmark rate due to some drawbacks of LIBOR. In this talk, we investigate the flaws of LIBOR and introduce overnight index swap(OIS) as an alternative.

Kollar—Shepherd-Barron—Alexeev (KSBA) have given a general construction that provides a geometric compactification for the moduli space of varieties of general type. Unfortunately, even in relatively simple cases (e.g. surfaces of general type with small invariants) it is difficult to understand the boundary points and the structure of this KSBA compactification. Thus, it is natural to try to compare the KSBA construction with other constructions, in particular with Hodge theoretic constructions of the moduli space. The Hodge theoretic construction has the advantage of having a lot of structure (of arithmetic and representation theoretic nature), but except a few cases (essentially abelian varieties and K3s) it is highly transcendental. In this talk, I will report on joint work with P. Griffiths, M. Green and C. Robles on the study of the moduli and periods of H-surfaces (Horikawa surfaces). The H-surfaces are surfaces of general type with p_g=2, q=0, K^2=2. They are essentially the simplest case where both the KSBA and Hodge theoretic construction are non-trivial. Considering and comparing the two approaches gives a rich picture which suggests an important role for the period map in the study of moduli spaces beyond the classical cases of abelian varieties and K3s.

We will discuss a toy model of heavy tails and show how this does not follow central limit behavior. We will then see how this relates to models in physics including random matrices. In the random matrix setting, we equate limiting spectral distributions (LSD) to spectral measures of rooted graphs. The LSD result also includes matrices with i.i.d. entries (up to self-adjointness) having infinite second moments, but following central limit behavior. In this case, the rooted graph is the natural numbers rooted at one, so the LSD is well-known to be the semi-circle law.