2021 Probability Webinar will be held via Zoom.

If you wish to attend the webinar, please register to the organizer Bin XIE by e-mail: bxie AT shinshu-u.ac.jp. After registration，the information about joining the webinar will be sent to you. We are looking forward to meeting you online.

## 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