Web page of Shengquan XIANG

About me

I am a tenure track assistant professor at School of Mathematical Sciences, Peking University.

Former student at École Normale Supérieure de Paris and Peking University. In 2019 I obtained my PhD degree on PDE's control problems at Sorbonne Université under the supervision of Prof. Jean-Michel Coron. Before joining Peking University I worked at EPFL, in the group of Prof. Joachim Krieger.

You can contact me by shengquan.xiang[AT]manwacomic.net

Research

Controlled flow of geometric maps

In [16, 18, 19, 26] we initiated the research on the controlled flow of geometric maps. Unlike the case with Euclidean space target, the geometric maps' control problems rely heavily on topological and geometric properties of the Riemannian manifold target and nonlinear effects and controls.

Randomly forced dispersive equations

In [20, 21, 24] we introduced a criterion for exponential mixing and large deviations of random dynamical systems, which can be applied to dispersive equations, and obtained the statistical properties of the randomly forced NLW and NLS equations. We emphasise the use of control ideas and nonlinear smoothing to these problems.

Dispersive equations and quantitative control

The interest is based on the quantitative and constructive control approaches for dispersive equations. This research line includes the damped focusing NLW [7], the semiclassical Schrödinger equations [12], and in particular KdV equations [1, 2, 3, 6, 22, 25].

Quantitative rapid stabilization

By constructing explicit control force we enhance the dissipation of the system, to make it decay as fast as we want. My contributions include the Fredholm backstepping for general operators [10, 11, 17], the frequency Lyapunov method for parabolic equations [8, 9], and the first global type result [4].

Smoothing traffic flows with autonomous vehicles (application)

We designed algorithm on autonomous vehicles to stabilize stop-and-go waves [14, 15], which has been used in MegaVanderTest. This test deployed 100 vehicles in November of 2022, and was the largest coordinated open-road test to smooth traffic flow.