학과 세미나 및 콜로퀴엄




2023-09
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2023-10
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In this talk, I will explain the setting of online convex optimization and the definition of regret and constraint violation. I then will introduce various algorithms and their theoretical guarantees under various assumptions. The connection with some topics in machine learning such as stochastic gradient descent, multi-armed bandit, and reinforcement learning will also be briefly discussed.
Host: 김범호, 김석범, 이현우     Contact: 김석범 (+821048049534)     한국어     2023-09-14 13:00:41
In this talk, we consider the blow-up dynamics of co-rotational solutions for energy-critical wave maps with the 2-sphere target. We briefly introduce the (2+1)-dimensional wave maps problem and its co-rotational symmetry, which reduces the full wave map to the (1+1)-dimensional semilinear wave equation. Under such symmetry, we see that this problem has a unique explicit stationary solution, so-called "harmonic map". Then we point out some of the works of analyzing the long-term dynamics of the flow near the harmonic map. Among them, we focus on the smooth blow-up result that corresponds to the stable regime. In particular, the case where the homotopy index is one has a distinctive nature from the other cases, which allows us to exhibit the smooth blow-up with the quantized blow-up rates corresponding to the excited regime.
Host: 김범호, 김석범, 김영종, 이현우     Contact: 김석범 (+821048049534)     한국어     2023-09-14 12:58:06
This talk aims to explore the application of calculus of variations in materials sciences. We will discuss the physics behind solid-solid phase transitions and elastic energy. Then the Allen-Cahn model in studying interfaces and their energy will be introduced. Finally, we will examine the Ohta-Kawasaki model and its role in understanding self-assembly in block copolymers. Recent research advancements in the Ohta-Kawasaki problem will also be presented.
Host: 김범호, 김석범, 김영종, 이현우     Contact: 김영종 (+821094985488)     한국어 (필요한 경우 영어 가능) ( )     2023-09-01 11:34:08