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.

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Zoom 회의 ID: 352 730 6970, 암호: 7178 대기실에서 개별 승인하오니, 실명으로 접속하시기 바랍니다.

Random simple and multigraph models based on exchangeable random measures, sometimes named graphexprocesses or generalisedgraphonmodels, have recently been proposed as a flexible class of sparse random graph models. This class of models can be seen as a generalisationof the popular graphonmodels. I will present this class of models, discuss some of their asymptotic properties, in particular the asymptotic behaviourof the degree distribution and of the clustering coefficients. I will also present some particular parametric models within this class and their use for discovering latent communities in sparse real-world networks.

In this talk, we present a short history of L^p-theories for partial differential equations. In particular, we introduce recent developments handling fractional derivatives and degenerate estimates in weighted spaces.

When a biological system is modeled using a mathematical procedure, the following step is normally to estimate the system parameters. Despite the numerous computational and statistical techniques, estimating parameters for complex systems can be a difficult task. As a result, one can think of revealing parameter-independent dynamical properties of a system. More precisely, rather than estimating parameters, one can focus on the underlying structure of a biochemical system to derive the qualitative behavior of the associated mathematical process. In this talk, we will discuss introduce reaction network theory. A reaction network is a graphical configuration of a biochemical system. One of the most important problems in this field is to relate dynamical properties and the underlying reaction network structure. When abundances of biochemical species (variables) in the system are small, then the randomness inherent in the molecular interactions is crucial to the system dynamics, and the abundances are modeled stochastically as a jump by jump fashion continuous-time Markov chain. The goal of this talk is to 1. walk you through the basic modeling aspect of the stochastically modeled reaction networks, and 2. to show how to derive stability (ergodicity) of the associated Markov process solely based on the underlying network structure.

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ZOOM Meeting ID: 868 7549 9085 Direct link: https://kaist.zoom.us/j/86875499085

In this talk we will discuss a Hirzebruch-Riemann-Roch (HRR) type theorem for matrix factorization categories of Deligne-Mumford stacks. We will first discuss a proof of a Hochschild-Kostant-Rosenberg type isomorphism and show how it can be used to define a Chern character formula which allows us to prove the HRR type theorem. This talk is based on a joint work with Dongwook Choa and Bumsig Kim.

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Zoom details: ID: 352 730 6970 Password: 1098. Please come with your real names.

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.

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Zoom 회의 ID: 352 730 6970 암호: 4114 대기실에서 개별 승인하니, 실명으로 접속하시기 바랍니다.

We prove global Holder gradient estimates for bounded positive weak solutions of fast diffusion equations in smooth bounded domains with homogeneous Dirichlet boundary condition, which then leads us to establish their optimal global regularity. It solves a problem raised by Berryman and Holland in 1980. This is joint work with Jingang Xiong.

The Gordon-Bender-Knuth identities are determinant formulas for the sum of Schur functions of partitions with bounded length. There are interesting combinatorial consequences of the Gordon-Bender-Knuth identities, for instance, connections between standard Young tableaux of bounded height, lattice walks in a Weyl chamber, and noncrossing matchings. In this talk we prove an affine analog of the Gordon-Bender-Knuth identities and study their combinatorial properties. As a consequence we obtain an unexpected connection between cylindric standard Young tableaux and r-noncrossing and s-nonnesting matchings. This is joint work with JiSun Huh, Christian Krattenthaler, and Soichi Okada.

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ZOOM Meeting ID: 868 7549 9085 Direct link: https://kaist.zoom.us/j/86875499085

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.

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Zoom 회의 ID: 352 730 6970 암호: 0971 대기실에서 개별승인을 하오니 실명으로 접속하시기 바랍니다.

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.

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Zoom info: 352 730 6970 암호: 2032 대기실에서 개별 승인을 하니 실명으로 접속하시기 바랍니다.

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.

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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.

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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.

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.

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.

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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.