Venue

• Webinar by Zoom 　

Program

　January 20, 2021 (Wednesday)

• 14:00 ～ 15:00   Tadahisa FUNAKI (Waseda University)
      Ginzburg-Landau equation and stochastic Allen-Cahn equation
• 15:10 ～ 16:10   Tadahisa FUNAKI (Waseda University)
      Stochastic motion by mean curvature

　January 27, 2021 (Wednesday)

• 14:00 ～ 15:00   Tadahisa FUNAKI (Waseda University)
      Sharp interface limit without conservation
• 15:10 ～ 16:10   Tadahisa FUNAKI (Waseda University)
      Stochastic mass-conserving Allen-Cahn equation

　February 3, 2021 (Wednesday)

• 15：30～16：30   Shang-Yuan SHIU (National Central University, Taiwan)
      Phase Analysis for a family of Stochastic Reaction-Diffusion Equations

  Abstract: We consider a reaction-diffusion equation of the following type: \[ \frac{\partial}{\partial t} u(t,x;\lambda) =\triangle u(t,x;\lambda) +V(u(t,x;\lambda)) +\lambda\sigma\left(u(t,x;\lambda)\right)\frac{\partial^2}{\partial t\partial x}W(t,x),\,t\in (0,\infty),\,x\in \mathbb{R}, \] where $W(t,x)$ is a Gaussian noise and $\lambda>0$. We assume that the initial data $u_0(x)$ is nonrandom and $\sigma$ is a Lipschitz countinuous function. The above equation is Fisher-KPP type if $V(x)=x(1-x)$; and Allen-Cahn type if $V(x)=x(1-x)(1+x)$. We will show that in both cases [could be more general], when $\lambda$ is sufficiently large [noise is strong], there is a unique invariant measure; when $\lambda$ is sufficiently small [noise is weak], there are infinitely many invariant measures. This is joint work with Davar Khoshnevisan (University of Utah), Kunwoo Kim (POSTECH) and Carl Mueller (University of Rochester).

• 17：00～18：00   Henri Elad ALTMAN (Imperial College London, UK)
      Bessel SPDEs and renormalized local times

  Abstract: Bessel processes are a classical family of stochastic diffusions obeying singular dynamics which, in a certain regime, involve a remarkable renormalization procedure.　More recently a family of stochastic PDEs related to Bessel processes has been introduced, the dynamics of which involve similar but more acute renormalizations. In my talk I shall introduce these processes and explain the remarkable underlying structure. Applications to scaling limits of dynamical critical wetting models will be mentioned. This is based on joint work with Lorenzo Zambotti.

　February 10, 2021 (Wednesday)

• 14：00～15：00   Dejun LUO (Chinese Academy of Sciences, China）
      Suppression of explosion by transport noises for some nonlinear PDEs

  Abstract: There are many examples of nonlinear PDEs which exhibit the dichotomy of global existence for small initial data and finite-time explosion for large ones. Motivated by the theory of stabilization by noise in finite dimensional setting, we will show that, when such equations are perturbed by multiplicative noise of transport, the possible explosion will be suppressed under a suitable scaling limit of the noise, yielding long time existence with large probability. We will also mention some recent attempts in obtaining quantitative convergence rate. This talk is based on joint works with Franco Flandoli and Lucio Galeati.

　February 19, 2021（Friday）

• 13：30～15：00   Jun MISUMI (Kochi University)
      TBA
• 15：10～16：10   Jun MISUMI (Kochi University)
      TBA

　February 24, 2021 (Wednesday)

• 14：00～15：00   Nobuo YOSHIDA (Nagoya University)
      TBA
• 15：10～16：10   Nobuo YOSHIDA (Nagoya University)
      TBA