We consider nonlinear Schrödinger equation on 1D torus, with localized damping and Haar noise acting on only 2 Fourier modes. The interplay between damping and noise motivates us to study the exponential convergence of solution to the unique invariant measure. When using coupling arguments, two fundamental obstacles are the lack of smoothing effect and the degeneracy of noise. The first difficulty is overcome by introducing asymptotic compactness of linearized system. And the second difficulty is tackled by geometric control approach. This talk is based on joint work with Shengquan Xiang and Zhifei Zhang.

The talk will be streamed through "Tencent": https://meeting.tencent.com/dm/hZoLIDG0e8Sl. Meeting code: 266-360-299. To join via a web browser: go to https://voovmeeting.com/; click "Log in" in the upper-right corner and login either by a Google/Apple account, or by a verification code received on phone or email; click "Join now" in the upper-right corner and type the number of the meeting 148-207-215 in the "Enter meeting ID" field; when prompted, select "Join from browser".

Sub-Riemannian and sub-Finsler geometry is a natural generalization of Riemannian geometry to the case where a Riemannian metric is defined, generally speaking, not on the entire tangent space at each point, but on some subspace. The talk will give the definition of sub-Riemannian and sub-Finsler distance between points on a smooth manifold. Known methods for finding shortest paths to compute this distance will be discussed, and examples will be considered.

The talk will be streamed through “Kontur Talk”: https://mian.ktalk.ru/hf3of8n6pemt?pinCode=9235