# 세미나 및 콜로퀴엄

구글 Calendar나 iPhone 등에서 구독하면 세미나 시작 전에 알림을 받을 수 있습니다.

Credit derivatives such as CDS and CDOs are financial instruments to hedge against the default risk. CDS is a kind of insurance that compensates for the loss of bonds issued by an individual company. CDOs issue a new security called tranche, which has various types of profit and risk structures. This lecture covers the structure and pricing of CDS and CDOs.

Let M be a closed manifold that admits a nontrivial cover diffeomorphic to itself. Which manifolds have such a self-similar structure? Examples are provided by tori, in which case the covering is homotopic to a linear endomorphism. Under the assumption that all iterates of the covering of M are regular, we show that any self-cover is induced by a linear endomorphism of a torus on a quotient of the fundamental group. Under further hypotheses we show that a finite cover of M is a principal torus bundle. We use this to give an application to holomorphic self-covers of Kaehler manifolds.

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자연과학동 1409호
기타
박진서 (한국과학기술정보연구원 미래정보연구센터 과학계량연구실)
VOSviewer와 KnowledgeMatrix Plus를 활용한 과학기술 지식맵 작성방법

논문 및 특허분석을 포함한 연결망 분석에서 시간이 가장 많이 소요되는 단계가 데이터 전처리와 행렬생성, 그리고 Pajek과 Gephi 등과 같은 네트워크 분석 전문 S/W에 적합한 입력데이터를 만드는 과정입니다. KnowledgeMatrix Plus는 1) 한글 및 영문 명사 추출, stemming, 시소러스 등을 통해 데이터 전처리를 지원하고, 2) 다양한 형태의 1-mode matrix와 2-mode matrix를 생성하여, 3) 네트워크 분석 및 가시화 S/W인 VOSviewer, Pajek, Gephi에서 즉시 분석을 할 수 있도록 지원하는 소프트웨어입니다. 이번 세미나를 통해 데이터 전처리에서 행렬생성, 네트워크 분석 및 가시화까지의 전과정을 다양한 공개 S/W를 활용하여 분석하는 방법을 함께 공유하고자 합니다.

○ 당일 세미나 자료 이외의 조금 긴 자료와 샘플데이터는,

http://mirian.kisti.re.kr/km/km.jsp 의 \'Notice - 과학기술 계량분석 공개 튜토리얼 자료집\'(압축파일)을 참조하시기 바랍니다.

○ Gephi의 경우 기존 자바와 충돌이 일어나 설치가 되어도 실행이 안 될 경우가 있습니다.

이 경우에 첨부한 gephi_jre7_지정하는 방법.pdf를 참조하시기 바랍니다.

In this talk, I will describe a project (work in progress) with Sang-Bum Yoo, on birational geometry of moduli spaces of parabolic bundles on the projective line in the framework of Mori’s program. It exhibits an interesting connection between representation theory and birational algebraic geometry via invariant theory.

The Langlands program consists of a huge web of tantalizing conjectures in many different directions, e.g., relating number theory, representation theory, algebraic geometry, and harmonic analysis in an unexpected way. After a leisurely introduction to the program through a brief historical review, we introduce yet another point of view on the program, inspired by work of physicists Kapustin and Witten, by investigating a certain 4-dimensional quantum field theory. Incidentally, this turns out to provide surprising new structures on the program. This talk, based on my thesis work, is mostly aimed at non-specialists.

The KdV equation is a nonlinear partial differential equation describing waves on shallow water surfaces. In spite of its nonlinearity, this is exactly solvable as it admits a surprisingly rich structure like infinite-dimensional symmetries, called the KdV hierarchy. From a completely different direction, for a Calabi-Yau manifold X, one can consider a generating function of certain enumerative invariants of X. Witten conjectured and Kontsevich proved the mysterious claim that when X is a point, the generating function is governed by the KdV hierarchy. I will explain a program toward understanding what happens when X is a general Calabi-Yau manifold. This talk is based on a joint project in progress with Weiqiang He and Si Li.

In a financially globalized world emerging market countries have different attributes from developed ones. Emerging countries may not be able to enjoy such benefits as consumption smoothing, efficient investment and risk diversification as developed countries do. One example is the sovereign wealth fund, a precautionary savings fund run by government. Instead, they may suffer so-called capital inflow problem caused by massive capital inflows followed by a sudden stop and reversal. The global financial crisis which hit Korea in 2008 is a classic example. The root source of the problem is that these countries, located in the periphery of the global financial world, cannot produce safe assets. The direct implication is that emerging market countries must import safe assets often financed by current account surplus. Furthermore, the central banks in emerging market countries should ultimately bear the risk of currency and maturity mismatches of domestic residents. That is, they should serve not only a lender of last resort but as an insurer of last resort, which makes central banking in emerging market countries complicated. Considering that capital flows are procylical and emerging countries are unable to produce safe assets capital flows to/from emerging market countries even strengthen the case for procylicality. Consequently, it is inevitable that emerging economies in the periphery are heavily influenced by the monetary policy of the center countries, and have essentially no room for independent monetary policy. In fact, the trilemma (inability to choose flexible exchange rates, capital mobility and independent monetary policy) in theory turns out a dilemma in reality. This seminar has two parts, central banking in emerging market and central banking in Korea. After reviewing central banking in emerging market in general I will discuss specific issues related to the monetary policy of the Bank of Korea.

In a financially globalized world emerging market countries have different attributes from developed ones. Emerging countries may not be able to enjoy such benefits as consumption smoothing, efficient investment and risk diversification as developed countries do. One example is the sovereign wealth fund, a precautionary savings fund run by government. Instead, they may suffer so-called capital inflow problem caused by massive capital inflows followed by a sudden stop and reversal. The global financial crisis which hit Korea in 2008 is a classic example. The root source of the problem is that these countries, located in the periphery of the global financial world, cannot produce safe assets. The direct implication is that emerging market countries must import safe assets often financed by current account surplus. Furthermore, the central banks in emerging market countries should ultimately bear the risk of currency and maturity mismatches of domestic residents. That is, they should serve not only a lender of last resort but as an insurer of last resort, which makes central banking in emerging market countries complicated. Considering that capital flows are procylical and emerging countries are unable to produce safe assets capital flows to/from emerging market countries even strengthen the case for procylicality. Consequently, it is inevitable that emerging economies in the periphery are heavily influenced by the monetary policy of the center countries, and have essentially no room for independent monetary policy. In fact, the trilemma (inability to choose flexible exchange rates, capital mobility and independent monetary policy) in theory turns out a dilemma in reality. This seminar has two parts, central banking in emerging market and central banking in Korea. After reviewing central banking in emerging market in general I will discuss specific issues related to the monetary policy of the Bank of Korea.

In order to measure the return or risk of an investment, it is necessary to reflect the correlation between the return of investment assets and the default random variables. Traditionally, correlation coefficients explain the dependency structure between elliptic distributions such as normal distribution well, but new dependency measures are needed because the actual data show a much different pattern from the elliptical distributions. Copulas are widely used as an alternative to these correlation coefficients and are often used in risk management and the valuation of credit derivatives such as CDOs. This lecture will cover the basic concepts of copula and its applications.

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Fusion Hall(1F), KI Bldg.(#E4), KAIST, Daejeon
해외 석학 특별 강연 시리즈
Terence Tao (UCLA)
Finite time blowup constructions for supercritical equations

Many basic PDE of physical interest, such as the three-dimensional Navier-Stokes equations, are "supercritical" in that the known conserved or bounded quantities for these equations allow the nonlinear components of the PDE to dominate the linear ones at fine scales. Because of this, almost none of the known methods for establishing global regularity for such equations can work, and global regularity for Navier-Stokes in particular is a notorious open problem. We present here some ways to show that if one allows some modifications to these supercritical PDE, one can in fact construct solutions that blow up in finite time (while still obeying conservation laws such as conservation of energy). This does not directly impact the global regularity question for the unmodified equations, but it does rule out some potential approaches to establish such regularity.

2017 CMC Distinguished Lecture Series by Terence Tao

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E6-1, ROOM 1409
Discrete Math
Henry Liu (Central South University, Changsha, China)
Highly connected subgraphs in sparse graphs

Let G be a graph on n vertices with independence number α. How large must a k-connected subgraph G contain? We shall present the best possible answers when α=2 and α=3. Some open questions will also be presented.

The discrepancy of a sequence f(1), f(2), ... of numbers is defined to be the largest value of |f(d) + f(2d) + ... + f(nd)| as n,d range over the natural numbers. In the 1930s, Erdos posed the question of whether any sequence consisting only of +1 and -1 could have bounded discrepancy. In 2010, the collaborative Polymath5 project showed (among other things) that the problem could be effectively reduced to a problem involving completely multiplicative sequences. Finally, using recent breakthroughs in the asymptotics of completely multiplicative sequences by Matomaki and Radziwill, as well as a surprising application of the Shannon entropy inequalities, the Erdos discrepancy problem was solved in 2015. In this talk I will discuss this solution and its connection to the Chowla and Elliott conjectures in number theory.

2017 CMC Distinguished Lecture Series by Terence Tao

Hyperrings and hyperfields are algebraic structures which generalize commutative rings and fields. In this talk, we aim to introduce these exotic structures and also provide examples which illustrate how hyperrings and hyperfields show up in algebraic geometry and combinatorics following the idea of Baker and Bowler on `matroids over hyperfields'.

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자연과학동 E6-1, ROOM 1409
Discrete Math
권오정 (Technische Universitat Berlin, Berin, Germany)
On low rank-width colorings

We introduce the concept of low rank-width colorings, generalizing the notion of low tree-depth colorings introduced by Nešetřil and Ossona de Mendez in [Grad and classes with bounded expansion I. Decompositions. EJC 2008]. We say that a class C of graphs admits low rank-width colorings if there exist functions N:ℕ→ℕ and Q:ℕ→ℕ such that for all p∈ℕ, every graph G∈C can be vertex colored with at most N(p) colors such that the union of any i≤p color classes induces a subgraph of rank-width at most Q(i).

Graph classes admitting low rank-width colorings strictly generalize graph classes admitting low tree-depth colorings and graph classes of bounded rank-width. We prove that for every graph class C of bounded expansion and every positive integer r, the class {Gr: G∈C} of r-th powers of graphs from C, as well as the classes of unit interval graphs and bipartite permutation graphs admit low rank-width colorings. All of these classes have unbounded rank-width and do not admit low tree-depth colorings. We also show that the classes of interval graphs and permutation graphs do not admit low rank-width colorings. In this talk, we provide the color refinement technique necessary to show the first result. This is joint work with Sebastian Sierbertz and Michał Pilipczuk.

In this talk, we consider stochastic partial differential equations, especially, a parabolic Anderson model. This model shows intermittent phenomena, i.e., the solution becomes very big on small regions of different scales (we say tall peaks occur on small islands). We provide a way to quantify tall peaks and small islands by using the macroscopic fractal dimension theory by Barlow and Taylor. This is based on joint work with Davar Khoshnevisan and Yimin Xiao.

The interactions between particles and uid have received a bulk of attention due to a number of their applications in the eld of, for example, biotechnology, medicine, and in the study of sedimentation phenomenon, compressibility of droplets of the spray, cooling tower plumes, and diesel engines, etc. In this talk, we present coupled kinetic- uid equations. The proposed equations consist of Vlasov-Fokker-Planck equation with local alignment forces and the incompressible Navier-Stokes equations. For the equations, we establish the global existence of weak solutions, hydrodynamic limit, and large-time behavior of solutions. We also remark on blow-up of classical solutions in the whole space.

High-frequency financial data allow us to estimate large volatility matrices with relatively short time horizon. Many novel statistical methods have been introduced to address large volatility matrix estimation problems from a high-dimensional Ito process with micro-structure noise contamination. Their asymptotic theories require sub-Gaussian or some finite high-order moments assumptions. These assumptions are at odd with the heavy tail phenomenon that is pandemic in financial stock returns and new procedures are needed to mitigate the influence of heavy tails. In this paper, we introduce the Huber loss function with a diverging threshold to develop a robust realized volatility estimation. We show that it has the sub-Gaussian concentration around the conditional expected volatility with only finite fourth moments. With the proposed robust estimator as input, we further regularize it by using the principal orthogonal component thresholding (POET) procedure to estimate the large volatility matrix that admits an approximate factor structure. We establish the asymptotic theories for such low-rank plus sparse matrices. The simulation study is conducted to check the finite sample performance of the proposed estimation methods.

2017 제4회 정오의 수학산책

강연자: 양성덕 (고려대)

일시: 2017년 6월 2일(금) 12:00 ~ 13:15

장소: 카이스트 자연과학동 E6-1 3435호

제목: 고차원 공간의 계량과 곡률

내용: TBA

등록: 2017년 5월 31일(수) 오후 3시까지

https://goo.gl/forms/ol819KdGNA5SdGSr2

문의: hskim@kias.re.kr / 내선:8545

The circle is the only connected closed 1-dimensional manifold, and maybe that's why it has so many interesting features. In this talk, we would like to emphasize that there are many things we still do not know about this one of the simplest manifolds. We will survey many interesting recent results around the circle in the context of low-dimensional topology.