학과 세미나 및 콜로퀴엄




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This is an introductory reading seminar presented by a senior undergraduate student, Jaehak Lee, who is studying the subject.
Host: 박진현     Contact: 박진현 (2734)     한국어     2024-04-05 00:08:09
I tell a personal story of how a mathematician working in complex algebraic geometry had come to discover the relevance of Cartan geometry, a subject in differential geometry, in an old problem in algebraic geometry, the problem of deformations of Grassmannians as projective manifolds, which originated from the work of Kodaira and Spencer. In my joint work with Ngaiming Mok, we used the theory of minimal rational curves to study such deformations and it reduced the question to a problem in Cartan geometry.
Host: 박진형     Contact: 박진형 (042-350-2747)     한국어     2024-03-28 14:49:38
We introduce a general equivalence problems for geometric structures arising from minimal rational curves on uniruled complex projective manifolds. To study these problems, we need approaches fusing differential geometry and algebraic geometry. Among such geometric structures, those associated to homogeneous manifolds are particularly accessible to differential-geometric methods of Cartan geometry. But even in these cases, only a few cases have been worked out so far. We review some recent developments.
Host: 박진형     Contact: 박진형 (042-350-2747)     한국어     2024-03-28 14:50:43
This lecture explores the topics and areas that have guided my research in computational mathematics and machine learning in recent years. Numerical methods in computational science are essential for comprehending real-world phenomena, and deep neural networks have achieved state-of-the-art results in a range of fields. The rapid expansion and outstanding success of deep learning and scientific computing have led to their applications across multiple disciplines, ranging from fluid dynamics to material sciences. In this lecture, I will focus on bridging machine learning with applied mathematics, specifically discussing topics such as scientific machine learning, numerical PDEs, and mathematical approaches of machine learning, including generative models and adversarial examples.
Host: 백형렬     영어     2024-02-22 11:29:34
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. There will be 6-8 seminars during Spring 2024, and it will summarize about 70-80% of the book.
Host: 박진현     Contact: 박진현 (2734)     한국어     2024-04-05 00:02:49
This is an introductory reading seminar presented by a senior undergraduate student, Jaehak Lee, who is studying the subject.
Host: 박진현     Contact: 박진현 (2734)     한국어     2024-04-05 00:09:55
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. There will be 6-8 seminars during Spring 2024, and it will summarize about 70-80% of the book.
Host: 박진현     Contact: 박진현 (2734)     한국어     2024-04-05 00:04:14
The finite quotient groups of étale fundamental groups of algebraic curves in positive characteristic are precisely determined, but without explicit construction of quotient maps, by well-known results of Raynaud, Harbater and Pop, previously known as Abhyankar's conjecture. Katz, Rojas León and Tiep have been studying the constructive side of this problem using certain "easy to remember" local systems. In this talk, I will discuss the main results and methods of this project in the case of a specific type of local systems called hypergeometric sheaves.
Host: Bo-Hae Im     미정     2024-03-29 09:15:57
In this talk, we consider the Boltzmann equation in general 3D toroidal domains with a specular reflection boundary condition. So far, it is a well-known open problem to obtain the low-regularity solution for the Boltzmann equation in general non-convex domains because there are grazing cases, such as inflection grazing. Thus, it is important to analyze trajectories which cause grazing. We will provide new analysis to handle these trajectories in general 3D toroidal domains.
Contact: 강문진 (0423502743)     미정     2024-03-25 10:13:23