# Department Seminars & Colloquia

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This seminar has two purposes. One is to understand the nature of finance and the current international monetary order that contributed to the root cause of the global financial crisis. They are the financial system risk caused by maturity transformation, which is the core of the financial activity, the procyclicality of finance in which credit expands in an asset market boom and shrinks in a recession, and safe assets, etc. Another is to understand the ripple effect of the 21st century digital technology revolution. Just as cryptocurrencies cause conflicts with states monopolizing creating money, currencies based on digital platforms are causing conflicts with existing finance by shifting the core function of finance from intermediation to payment and settlement. Moreover, the democratization of finance thanks to the development of digital technology is another conflicting factor against the existing elite-centered finance, where the financial elite evaluates risks and receives rewards. Along with asset inflation, the pandemic has significantly increased debt on the one hand and accelerated the digitalization of finance on the other. The challenge in the post-pandemic era is to normalize increased debt and liquidity to a sustainable level while minimizing economic costs, and to come up with an alternative solution to the dilemma of the dollar-centered international monetary order. The first day of the seminar will focus on the attributes of finance, and the second day will discuss the challenges facing finance in the post-pandemic era and the digitalization of finance.

2개 세션으로 나누어 진행

2개 세션으로 나누어 진행

2개 세션으로 나누어 진행

The ions in a fully ionized electrostatic plasma are described by the Euler-Poisson system with the Boltzmann relation. We numerically observe the behavior of solutions to the 1D Euler-Poisson system for various initial data and how solitary waves and singularities are developed. We also introduce some results on the linear stability of solitary waves and the formation of singularities. These are joint works with Junho Choi and Bongsuk Kwon.

In this talk, we prove a generalization of the del Pezzo-Bertini classification of varieties of minimal degree to higher secant varieties of minimal degree. It states that higher secant varieties of minimal degree are mostly divided into two classes: scroll type and Veronese type. Its proof is based on methods of gluing some 1-generic matrices. We also present some simple examples to explain our result. This is a joint work with Prof. Sijong Kwak.

Free-by -cyclic groups have been studied as algebraic counterparts of cusped hyperbolic mapping torus groups. Free-by-cyclic groups and cusped hyperbolic mapping torus groups share many algebraic properties. Nonetheless, free-by-cyclic groups are more complicated because not every free-by-cyclic group is realized as a cusped hyperbolic mapping torus group. In this talk, I explain some basic concepts and summarize some previous results related to free-by-cyclic groups. Also, I discuss some problems about free-by-cyclic groups.

The Yau-Zaslow formula describes the number of rational curves in a linear system on a smooth projective K3 surface in terms of a modular form. In this talk, I will review the Yau-Zaslow formula with some examples and then discuss an equivariant version of the formula for K3/abelian surfaces. When the K3/abelian surface admits a finite group G-action, we can consider a linear system with the induced action. It turns out that the equivariant version of the formula will count G-rational curves and it will also provide interesting modular forms.

Liouville quantum gravity (LQG) surfaces are random topological surfaces which are important in statistical mechanics and have deep connections to other mathematical objects such as Schramm–Loewner evolution and random planar maps. These random surfaces are too singular and fractal in the sense that the Hausdorff dimension, viewed as a metric space equipped with its intrinsic metric, is strictly bigger than two. I will talk about the interesting geometric structure and recent progress on LQG surfaces.

(KAIST 입시일정과 겹쳐 1주 연기합니다)

(KAIST 입시일정과 겹쳐 1주 연기합니다)

하나금융 융합기술원은 국내 금융그룹 최초의 AI 연구소로 2018년부터 지난 4년 간 다양한 금융서비스에 현행 AI 응용기술들을 접목시키고 금융사 내 기술 전파에 큰 성과를 올려왔다. 그 중에서도 융합기술원이 연구/개발하는 신용평가 기술은 업계를 선도하고 있으며 그런 선도 기술을 만들어나가는 과정을 소개하려 한다. 또한, 응용기술 뿐만 아니라 향후 다양한 분야의 원천기술 연구를 위해 국내 유수 산업/학계 인재들이 모이는 조직으로 변형해가는 노력을 소개할 예정이다.

온라인, 오프라인 동시진행

온라인, 오프라인 동시진행

In this presentation, I will present me, Daeyeol Jeon, and Chang Heon Kim's construction of certain points on $X_1(N)$ over ring class fields (and therefore construction of points on the abelian varieties associated to newforms of level $\Gamma_1(N)$). Our work generalizes Bryan Birch's Heegner points on $X_0(N)$. Then, we show that these points form Euler systems (like the Heegner points), and we improve Kolyvagin's Euler system techniques to show that for our point $P_{\tau_K/c}$ and any ring class character $\chi$ of the extended ring class field of conductor $c$ satisfying $\chi=\overline{\chi}$, if $P_{\tau_K/c}^\chi$ is non-torsion and $G_K \to \operatorname{Aut} A_f[\pi]$ is surjective, then the corank of $\Sel(A_\chi/K)$ is 1, which implies the rank of $A_f(K)^\chi$ is 1. (Please contact Bo-Hae Im if you want to join the seminar.)

This series of lectures will focus on recent developments of the so-called a-contraction theory and its application to the study of discontinuous flow at high Reynolds numbers. We will first introduce the classical framework to study the stability of 1D shocks for compressible flows. Recent multi-D applications will be presented next, both in the context of compressible and incompressible flows.