05/31 15:00 Youngjoon Hong (KAIST)

Title : Theory guided machine learning for partial differential equationsSpeaker : Youngjoon Hong (KAIST)

05/24 15:00 Hyeontae Jo (Korea University Sejong Campus)

Title : Can we infer the distribution function included in the differential equationSpeaker : Hyeontae Jo (Korea University Sejong Campus)

05/03 15:00 Dohyun Kwon (University of Seoul)

Title : De Giorgi's Minimizing MovementsSpeaker : Dohyun Kwon (University of Seoul)Abstract : The study of gradient flows holds significant importance across various fields, including partial differential equations, optimization, and machine learning. In this talk, we aim to explore the relationship between gradient flows and their time-discretized formulations, known as De Giorgi's minimizing movements scheme. We focus on how De Giorgi's minimizing movements coincide with gradient flows in two different spaces: the space of sets and the space of probability measures called Wasserstein space. Then, we discuss their implications for the well-posedness and long-time behavior of some PDEs, including mean curvature flow and the nonlinear Fokker-Planck equation.

04/26 15:00 Ki-Ahm Lee (Seoul National University)

Title : Degenerate/Singular Partial Differential EquationsSpeaker : Ki-Ahm Lee (Seoul National University)Abstract : In this talk, we are going to consider various degenerate or singular operatorin partial differential equations related to free boundary problems and mathematical finance.We will discuss its underlined geometry and how the generalized polynomials appears in the regularity theory.

04/05 15:00 Kyeong Hun Kim (Korea university)

Title : Parabolic PDEs and SPDEs with space-time non-local operatorsSpeaker : Kyeong Hun Kim (Korea University)Abstract : Parabolic equations are related to time dependent natural phenomena. For instance, the classical heat equation with local operators describes the normal diffusion. On the other hand, the description of abnormal diffusion and randomly moving particles with jumps requires the use of non-local operators.In this talk, I will give a short introduction to the parabolic PDEs and stochastic PDEs having non-local operators with respect to time and space variables.

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