Saturday, July 20, 2024

2024-07-26 / 14:00 ~ 15:30

학과 세미나/콜로퀴엄 - 기타: Introduction to Milnor K-theory 4: the norm maps for Milnor K-theory

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.

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

편미분방정식 통합연구실 세미나 - 편미분방정식:

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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.

2024-07-22 / 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.

2024-07-23 / 14:30 ~ 16:00

학과 세미나/콜로퀴엄 - 위상수학 세미나:

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We introduce a version of Heegaard diagrams for 5-dimensional cobordisms with 2- and 3-handles, 5-dimensional 3-handlebodies, and closed 5-manifolds. We show that every such 5-manifold can be represented by a Heegaard diagram, and two Heegaard diagrams represent diffeomorphic 5-manifolds if and only if they are related by certain moves. As an application, we construct Heegaard diagrams for 5-dimensional cobordisms from the standard 4-sphere to the Gluck twists along knotted 2-spheres. This provides some equivalent statements regarding the Gluck twists being diffeomorphic to the standard 4-sphere.

2024-07-24 / 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 3: Recent developments of Khovanov homology and its applications to low-dimensional topology.

2024-07-23 / 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 2: Numerical invariants from Khovanov homology and their applications.

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

학과 세미나/콜로퀴엄 - 위상수학 세미나:

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Events for the 취소된 행사 포함