Monday, July 15, 2024

2024-07-22 / 16:00 ~ 18:00

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In this lecture, we will discuss the formal/mathematical connection between the Boltzmann equation and the compressible Euler equation. For the mathematical justification we study the convergence of real analytic solutions of Boltzmann equations toward smooth solutions of the compressible Euler equation (before shock). This lecture will be accessible to graduate students.

2024-07-18 / 16:00 ~ 17:00

편미분방정식 통합연구실 세미나 - 편미분방정식:

by Sung-Jin Oh()

In general relativity, spacetime is described by a (1+3)-dimensional Lorentzian manifold satisfying the Einstein equations, and initial data sets (i.e., fixed-time configurations) correspond to embedded spacelike hypersurfaces. The initial data sets are required to satisfy underdetermined PDEs called constraint equations -- in the language of differential geometry, these are exactly the Gauss and Codazzi equations. The goal of my talk will be to elucidate the flexibility of these objects -- specific results to be presented include extension, gluing, asymptotics-prescription, and parametrization of asymptotically flat initial data sets, often with sharp assumptions. Basic to our approach is a novel way to construct solution operators for divergence-type equations with prescribed support properties, which should be of independent interest. This part is based on joint work with Phil Isett (Caltech), Yuchen Mao (UC Berkeley), and Zhongkai Tao (UC Berkeley).

2024-07-22 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 계산수학 세미나:

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In this work, we investigate optimal control problems in heterogeneous porous media. Based on the partial differential equation constraint connecting the state and the control, we produce the associated control as a dependent quantity of the state. Then, we introduce the reduced optimal control problem which contains only the state variable. Here we employ $C^0$ interior penalty finite element methods for the spatial discretization to solve the reduced optimal control problem resulting in a fourth-order variational inequality. We provide a priori error estimates and stability analyses. Several numerical examples validate and illustrate the capabilities of the proposed algorithm.

2024-07-18 / 17:00 ~ 18:00

편미분방정식 통합연구실 세미나 - 편미분방정식: Cylindrical and hypoelliptic functional inequalities

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In this talk, we will discuss cylindrical and hypoelliptic extensions of Hardy, Sobolev, Rellich, Caffarelli-Kohn-Nirenberg, and other related functional inequalities. We will then concentrate on discussing their best constants, ground states for higher-order hypoelliptic Schrödinger-type equations, and solutions to the corresponding variational problems.

2024-07-19 / 14:00 ~ 16:00

IBS-KAIST 세미나 - 수리생물학:

by 임동주()

Phenotypic selection occurs when genetically identical cells are subject to different reproductive abilities due to cellular noise. Such noise arises from fluctuations in reactions synthesizing proteins and plays a crucial role in how cells make decisions and respond to stress or drugs. We propose a general stochastic agent-based model for growing populations capturing the feedback between gene expression and cell division dynamics. We devise a finite state projection approach to analyze gene expression and division distributions and infer selection from single-cell data in mother machines and lineage trees. We use the theory to quantify selection in multi-stable gene expression networks and elucidate that the trade-off between phenotypic switching and selection enables robust decision-making essential for synthetic circuits and developmental lineage decisions. Using live-cell data, we demonstrate that combining theory and inference provides quantitative insights into bet-hedging–like response to DNA damage and adaptation during antibiotic exposure in Escherichia coli.

2024-07-19 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 기타: Introduction to Milnor K-theory 3: the Milnor exact sequence

by 사킵 무쉬타크 샤(Indian Statistical Institute - Bangalore)

Mr. Saqib Mushtaq Shah, a KAIX visiting graduate student from ISI Bangalore who will stay at KAIST for 8 weeks, is going to give a series of weekly talks on the Milnor K-theory from the beginning. It is part of his KAIX summer internship works.

2024-07-17 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 기타: Introduction to complex algebraic geometry and Hodge theory #9

by 김재홍(KAIST)

This is part of an informal seminar series to be given by Mr. Jaehong Kim, who has been studying the book "Hodge theory and Complex Algebraic Geometry Vol 1 by Claire Voisin" for a few months. It will summarize about 70-80% of the book.

2024-07-22 / 16:00 ~ 18:00

학과 세미나/콜로퀴엄 - 위상수학 세미나:

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Knot homology theories revolutionized the study of knots and links, much like (simplicial or singular) homology theory revolutionized the study of topological spaces. One of the major knot homology theories, Khovanov homology, was introduced by M. Khovanov in 2000 as a "categorification of the Jones polynomial." One notable feature of Khovanov homology is its ability to detect the unknot, a feature not known to be possessed by the Jones polynomial. Recently, it has found notable applications in low-dimensional topology, including the detection of exotic surfaces in the 4-ball. Day 1: Jones polynomial and its categorification.

Events for the 취소된 행사 포함