# Department Seminars & Colloquia

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Morihiko Saito's theory of mixed Hodge modules is a far generalisation of classical Hodge theory, which is based on the theory of perverse sheaves, D-modules, variations of Hodge structures. One can think of mixed Hodge modules as a certain class of D-modules with Hodge structures. Naturally they are accompanied by perverse sheaves via the Riemann–Hilbert correspondence. This guide consists of about 8 talks, which may cover: review of classical Hodge theory, D-modules and filtered D-modules, nearby and vanishing cycles, etc. The main goal is to understand the notion of mixed Hodge modules and to explain two important theorems: the structure theorem and the direct image theorem. If time permits, we discuss recent applications of the theory in algebraic geometry.

줌 아이디: 352 730 6970 암호 : 1541 대기실에서 개별 승인하오니 실명으로 접속하세요.

줌 아이디: 352 730 6970 암호 : 1541 대기실에서 개별 승인하오니 실명으로 접속하세요.

Morihiko Saito's theory of mixed Hodge modules is a far generalisation of classical Hodge theory, which is based on the theory of perverse sheaves, D-modules, variations of Hodge structures. One can think of mixed Hodge modules as a certain class of D-modules with Hodge structures. Naturally they are accompanied by perverse sheaves via the Riemann–Hilbert correspondence. This guide consists of about 8 talks, which may cover: review of classical Hodge theory, D-modules and filtered D-modules, nearby and vanishing cycles, etc. The main goal is to understand the notion of mixed Hodge modules and to explain two important theorems: the structure theorem and the direct image theorem. If time permits, we discuss recent applications of the theory in algebraic geometry.

줌 정보: 회의 ID: 352 730 6970 암호: 4401 대기실에서 개별 승인을 기다리십시오. 실명으로 들어오시기 바랍니다.

줌 정보: 회의 ID: 352 730 6970 암호: 4401 대기실에서 개별 승인을 기다리십시오. 실명으로 들어오시기 바랍니다.

We talk about a convergence of kinetic vorticity of Boltzmann toward the vorticity of incompressible Euler in 2D. The talk would be self-contained (1) covering necessary background in basic Boltzmann theory, asymptotic expansion (Hilbert expansion). (2) When the Euler vorticity is below Yudovich, we prove a weak convergence toward Lagrangian solutions, (3) while for the Yudovich class we have a strong convergence toward a unique solution with a rate.

Morihiko Saito's theory of mixed Hodge modules is a far generalisation of classical Hodge theory, which is based on the theory of perverse sheaves, D-modules, variations of Hodge structures. One can think of mixed Hodge modules as a certain class of D-modules with Hodge structures. Naturally they are accompanied by perverse sheaves via the Riemann–Hilbert correspondence. This guide consists of about 8 talks, which may cover: review of classical Hodge theory, D-modules and filtered D-modules, nearby and vanishing cycles, etc. The main goal is to understand the notion of mixed Hodge modules and to explain two important theorems: the structure theorem and the direct image theorem. If time permits, we discuss recent applications of the theory in algebraic geometry.

zoom 방 번호 : 352 730 6970 암호: 일삼삼일 (대기실에서 승인을 기다려 주십시오.) 총 8회의 강연을 계획중이고 매주 금요일 1회씩 진행하여 3월 말- 4월 초까지 진행할 계획입니다.

zoom 방 번호 : 352 730 6970 암호: 일삼삼일 (대기실에서 승인을 기다려 주십시오.) 총 8회의 강연을 계획중이고 매주 금요일 1회씩 진행하여 3월 말- 4월 초까지 진행할 계획입니다.

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.