**Zu Chongzhi Mathematics Research Seminar**

**Date and Time (China standard time): **Tuesday, November 28, 8:30-9:30 pm

**Zoom: **914 7831 9396;** Passcode: **dkumath

**Title**: Enhanced dissipation for alternating shear flows

**Speaker**: Kyle Liss

**Bio**: I received my Ph.D. from the University of Maryland in the summer of 2021 under the supervision of Jacob Bedrossian. In the fall of 2021, I was an ICERM postdoc at Brown University and have been a postdoc at Duke University since the beginning of 2022. My current research focuses on mixing and enhanced dissipation in the advection-diffusion equation, and the analysis of stochastic models motivated by hydrodynamic turbulence.

**Abstract**: The dynamics of a passive scalar, such as temperature or concentration, transported by an incompressible flow can be modeled by the advection-diffusion equation. Advection often results in the formation of complicated, small-scale structures and can result in solutions dissipating energy at a rate much faster than the corresponding heat equation in regimes of weak diffusion. This phenomenon is typically referred to as *enhanced dissipation*. In this talk, I will discuss a recent joint work with Tarek Elgindi and Jonathan Mattingly in which we construct an example of a divergence-free velocity field on the two-dimensional torus that results in optimal enhanced dissipation. The flow consists of time-periodic, alternating piece-wise linear shear flows. The proof is based on the probabilistic representation formula for the advection-diffusion equation and ideas from hyperbolic dynamics.