Sunday, September 18, 2022

2022-09-22 / 16:30 ~ 17:30

by ()

Polarization is a technique in algebra which provides combinatorial tools to study algebraic invariants of monomial ideals. Depolarization of a square free monomial ideal is a monomial ideal whose polarization is the original ideal. In this talk, we briefly introduce the depolarization and related problems and introduce the new method using hyper graph coloring.

2022-09-23 / 10:00 ~ 11:00

SAARC 세미나 - SAARC 세미나:

by Kim, Ildoo()

In this talk, we present a short history of Lp theories for (stochastic) partial differential equations. In particular, we introduce recent developments handling degenerate equations in weighted Sobolev spaces. It is well known that there exist probabilistic representations of solutions to second order (stochastic) partial equations, which enables us to use many interesting probabilistic theories to investigate solutions. Recently, by applying probabilistic tools, we obtain interesting new type weighted estimates to second order degenerate (stochastic) partial differential equations.

2022-09-23 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by ()

A family of surfaces is called mean curvature flow (MCF) if the velocity of surface is equal to the mean curvature of the surface at that point. Even starting from smooth surface, the MCF typically encounters some singularities and various generalized notions of MCF have been proposed to extend the existence past singularities. They are level set flow, Brakke flow and BV flow, just to name a few. In my talk I explain a recent global-in-time existence result of a particular generalized solution which has some desirable properties. I describe a basic outline of how to construct the solution.

2022-09-21 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

by 라준현()

It is challenging to perform a multiscale analysis of mesoscopic systems exhibiting singularities at the macroscopic scale. In this paper, we study the hydrodynamic limit of the Boltzmann equations \begin{equation} \mathrm{St} \partial_t F + v \cdot \nabla_x F = \frac{1}{\mathrm{Kn} } Q(F, F) \end{equation} toward the singular solutions of 2D incompressible Euler equations whose vorticity is unbounded \begin{equation} \partial_t u + u \cdot \nabla_x u + \nabla_x p = 0, \quad \mathrm{div} u = 0. \end{equation} We obtain a microscopic description of the singularity through the so-called kinetic vorticity and understand its behavior in the vicinity of the macroscopic singularity. As a consequence of our new analysis, we settle affirmatively an open problem of convergence toward Lagrangian solutions of the 2D incompressible Euler equation whose vorticity is unbounded ($\omega \in L^{\mathfrak{p} }$ for any fixed $1 \le \mathfrak{p} < \infty$). Moreover, we prove the convergence of kinetic vorticities toward the vorticity of the Lagrangian solution of the Euler equation. In particular, we obtain the rate of convergence when the vorticity blows up moderately in $L^{\mathfrak{p} }$ as $\mathfrak{p} \rightarrow \infty$ (localized Yudovich class).

2022-09-23 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by ()

2022-09-22 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by ()

Over recent years, data science and machine learning have been the center of attention in both the scientific community and the general public. Closely tied to the ‘AI-hype’, these fields are enjoying expanding scientific influence as well as a booming job market. In this talk, I will first discuss why mathematical knowledge is important for becoming a good machine learner and/or data scientist, by covering various topics in modern deep learning research. I will then introduce my recent efforts in utilizing various deep learning methods for statistical analysis of mathematical simulations and observational data, including surrogate modeling, parameter estimation, and long-term trend reconstruction. Various scientific application examples will be discussed, including ocean diffusivity estimation, WRF-hydro calibration, AMOC reconstruction, and SIR calibration.

Events for the 취소된 행사 포함